Ps at the Interfaces
On the Syntax, Semantics, and Morphology
of Spatial Prepositions in German
Von der Fakultät “Informatik, Elektrotechnik und Informationstechnik” der
Universität Stuttgart zur Erlangung der Würde eines Doktors der
Philosophie (Dr. phil.) genehmigte Abhandlung
Vorgelegt von
Boris P. Haselbach
aus Stuttgart
Hauptberichterin: PD Dr. Antje Roßdeutscher
1. Mitberichterin: Prof. Dr. Dr. h.c. Artemis Alexiadou
2. Mitberichter: Prof. Dr. h.c. Hans Kamp, PhD
Tag der mündlichen Prüfung: 25. September 2017
Institut für Maschinelle Sprachverarbeitung der Universität Stuttgart
2017
ii
Contents
Abstracts in English and German vii
Acknowledgments xiii
List of Abbreviations xv
List of Figures xix
List of Tables xxi
1 Introduction 1
2 Syntax 11
2.1 Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.1 Types of features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.2 Category features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.3 Syntacticosemantic features . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.1.4 Content features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2 Building structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.2.1 Tree-structural relations and projection . . . . . . . . . . . . . . . . . . . . 36
2.2.2 Syntactic operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.2.3 Complements, specifiers, and adjuncts . . . . . . . . . . . . . . . . . . . . 47
2.3 Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3 Morphology 59
3.1 Vocabulary Insertion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.2 Linearization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.3 Ornamental morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.4 Operations on nodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.4.1 Impoverishment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.4.2 Fusion and Fission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.5 Morphological Merger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
iii
iv Contents
3.6 Readjustment Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4 Semantics 93
4.1 Semantic construction algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.1.1 Context-sensitive interpretation . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.1.2 Discourse Representation Theory . . . . . . . . . . . . . . . . . . . . . . . . 99
4.1.3 Reproducing a textbook example . . . . . . . . . . . . . . . . . . . . . . . . 106
4.2 Figure and Ground . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.3 Space as seen through the eyes of natural language . . . . . . . . . . . . . . . . . 117
4.3.1 Material objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.3.2 Spatial ontology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
4.3.3 Primary Perceptual Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
4.3.4 Boundaries of material objects and regions . . . . . . . . . . . . . . . . . . 138
4.3.5 Spatial contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
4.3.6 Conditions on line segments . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
4.4 Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
4.4.1 Mereological structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
4.4.2 Incremental relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
4.5 Spatial paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
4.6 Prepositional aspect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
4.7 Force-effective prepositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
4.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
5 Spatial prepositions at the interfaces 181
5.1 Classifying spatial prepositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
5.1.1 Place and path prepositions . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
5.1.2 Prepositions and geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
5.1.3 Prepositions and aspect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
5.1.4 Categories and syntacticosemantic features in prepositions . . . . . . . 194
5.2 On the cartographic decomposition of prepositions . . . . . . . . . . . . . . . . . 196
5.3 Abstract Content features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
5.3.1 Interiority . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
5.3.2 Contiguity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
5.3.3 Verticality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
5.4 Lexical prepositional structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
5.4.1 Place prepositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
5.4.1.1 Geometric prepositions . . . . . . . . . . . . . . . . . . . . . . . . 209
5.4.1.2 Pseudo-geometric prepositions . . . . . . . . . . . . . . . . . . . 212
5.4.1.3 Non-geometric prepositions . . . . . . . . . . . . . . . . . . . . . 221
Contents v
5.4.2 Goal and source prepositions . . . . . . . . . . . . . . . . . . . . . . . . . . 225
5.4.2.1 Geometric prepositions . . . . . . . . . . . . . . . . . . . . . . . . 233
5.4.2.2 Pseudo-geometric prepositions . . . . . . . . . . . . . . . . . . . 238
5.4.2.3 Non-geometric prepositions . . . . . . . . . . . . . . . . . . . . . 244
5.4.3 Route prepositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
5.5 Functional prepositional structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
5.5.1 C-features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
5.5.2 Deictic features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
5.5.3 Aspectual features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
5.6 Spatial prepositions in verbal contexts . . . . . . . . . . . . . . . . . . . . . . . . . 278
5.6.1 Place preposition and stative posture verb . . . . . . . . . . . . . . . . . . 279
5.6.2 Goal preposition and unaccusative motion verb . . . . . . . . . . . . . . . 281
5.6.3 Route preposition and transitive motion verb . . . . . . . . . . . . . . . . 284
5.6.4 Goal preposition and unergative verb . . . . . . . . . . . . . . . . . . . . . 288
5.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
6 Prepositional case 293
6.1 Prepositional case in German . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
6.2 Previous approaches to prepositional case . . . . . . . . . . . . . . . . . . . . . . . 299
6.2.1 Den Dikken (2010): Structural case . . . . . . . . . . . . . . . . . . . . . . . 299
6.2.2 Caha (2010): Peeling off case . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
6.2.3 Arsenijevic´ and Gehrke (2009): External accusative . . . . . . . . . . . . . 302
6.2.4 Bierwisch (1988): Case from the lexicon . . . . . . . . . . . . . . . . . . . . 303
6.3 Morphological case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
6.3.1 Abstract Case vs. morphological case . . . . . . . . . . . . . . . . . . . . . 304
6.3.2 Feature decomposition of case . . . . . . . . . . . . . . . . . . . . . . . . . . 313
6.3.3 Morphological case assignment . . . . . . . . . . . . . . . . . . . . . . . . . 317
6.4 Morphological case assignment of prepositions . . . . . . . . . . . . . . . . . . . . 327
6.4.1 Prepositions assign inherent dative . . . . . . . . . . . . . . . . . . . . . . . 327
6.4.2 Impoverishment to accusative . . . . . . . . . . . . . . . . . . . . . . . . . . 333
6.4.3 Outlook for other cases and other languages . . . . . . . . . . . . . . . . . 336
6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
7 Conclusions and prospect for future work 341
A Synopses 353
A.1 Synopsis of spatial prepositions at the interfaces . . . . . . . . . . . . . . . . . . . 353
A.2 Synopsis of morphological case assignment . . . . . . . . . . . . . . . . . . . . . . 358
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B Proofs 359
B.1 Negative NINF-paths give rise to bounded route PPs . . . . . . . . . . . . . . . . 359
B.2 Positive NINF-paths give rise to unbounded route PPs . . . . . . . . . . . . . . . 362
C Grapheme/phoneme mapping 367
D Picture credits 369
Bibliography 371
Abstracts in English and German
Abstract in English
In this thesis, I spell out the syntax, semantics, and morphology of spatial prepositions in
German. I do this by using a parsimonious model of grammar with only one combinatorial
engine that generates both phrases and words: syntax (Marantz 1997, Bruening 2016). I follow
the tenets of the Minimalist Program (MP) (Chomsky 1995) with Bare Phrase Structure (BPS)
as its phrase structural module. I show that combining Distributed Morphology (DM)
(Halle and Marantz 1993, Embick 2015) to model Phonological Form (PF) and Discourse
Representation Theory (DRT) (Kamp and Reyle 1993, Kamp et al. 2011) to model Logical
Form (LF) makes it possible to gain deeper and new insights into the system of German
spatial prepositions.
I classify spatial prepositions along a widely accepted typology (Jackendoff 1983, Piñón
1993, Zwarts 2005b, 2008, Gehrke 2008, Svenonius 2010). Place prepositions denote static
locations (regions), while path prepositions denote dynamic locations (spatial paths). I
model spatial paths denoted by path prepositions as rectilinear line segments; they can
be directed, as in the case of goal and source prepositions, or undirected, as in the case
of route prepositions – a distinction that can be accounted for in terms of Krifka’s (1998)
directed and undirected path structures. As for directed goal and source prepositions, which
I consider to be derived from place prepositions, I follow Krifka (1998) and Beavers (2012) in
assuming that directed spatial paths receive their direction from a mapping between motion
events and their spatial projections. I identify two types of goal and source prepositions:
(i) (pseudo)-geometric goal and source prepositions and (ii) non-geometric goal and source
prepositions. When combined with manner of motion verbs, (pseudo)-geometric goal and
source prepositions give rise to achievement predicates, while non-geometric goal and source
prepositions give rise to accomplishment predicates. That is, the former denote spatial paths
conceptualized as punctual, while the latter denote spatial paths conceptualized as extended.
Route prepositions – the morphologically simplex ones in German are durch (‘through’),
um (‘around’), and über (‘over, across’) – are importantly different from source and goal
prepositions. They are not directed and they turn out to be semelfactive-like. I propose that
they denote spatial paths with a tripartite structure, consisting of a non-initial, non-final path
(the NINF-path) that is flanked by two tail paths, one at each end. It can be shown that route
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viii Abstracts in English and German
prepositions do not commit to direction, which is why I advocate that spatial paths denoted
by route prepositions should be modeled in terms of Krifka’s (1998: 203) plain path structure
H, which is undirected – an algebraic structure that has not received much attention yet.
In addition, I propose to classify spatial prepositions according to a classification that is
orthogonal to the one described in the previous paragraph. This classification involves three
classes: (i) geometric prepositions, (ii) pseudo-geometric prepositions, and (iii) non-geometric
prepositions. Geometric prepositions refer to geometric relations that can be spelled out in a
parsimonious, perception-driven model of space (Kamp and Roßdeutscher 2005). Typical
examples of prepositional phrases headed by geometric prepositions are: in der Kiste (‘in
the.DAT box’), in die Kiste (‘into the.ACC box’), aus dem Haus (‘out of the house’), an der
Wand (‘on the wall’), and auf dem Tisch (‘upon the table’). The geometric prepositions are
further subdivided into (i) the topological prepositions in (‘in’), aus (‘out of’), an (‘on’), and auf
(‘upon’); and (ii) the projective prepositions hinter (‘behind’), vor (‘in front of’), über (‘above’),
unter (‘under’), and neben (‘beside’). While route prepositions are different from both goal and
source prepositions, each route preposition shares a geometric concept with a topological goal
preposition (derived from a topological place preposition) and, in one case, with a topological
source preposition: (i) interiority is shared by in, aus, and durch; (ii) contiguity is shared by
an and um; and (iii) verticality is shared by auf and über. The projective prepositions are not
treated in this thesis, but the topological prepositions and the route prepositions are central
targets. Pseudo-geometric prepositions look like geometric prepositions, but do not refer
to geometric relations. Instead, they express functional locative relations. Typical examples
of prepositional phrases headed by pseudo-geometric prepositions are: in der Schweiz (‘in
[the.DAT] Switzerland’), in die Schweiz (‘to [the.ACC] Switzerland’), and auf Sylt (‘on Sylt’).
It can be shown that pseudo-geometric prepositions behave differently from geometric
prepositions in several ways. For example, they do not license a postpositional recurrence of
the preposition; compare, for instance, auf dem Tisch drauf with auf Sylt *drauf. Moreover, the
choice of a pseudo-geometric preposition is heavily influenced by denotational properties of
the noun it co-occurs with (e.g. auf is used with islands, in with countries). The peculiar goal
preposition nach (‘to’), which is obligatorily used with determinerless toponyms, turns out
to be a special instance of a pseudo-geometric preposition. The non-geometric prepositions
bei (‘at’), zu (‘to’), and von (‘from’) form a third class of spatial prepositions. They do not
only impose semantic selection restrictions distinct from geometric and pseudo-geometric
prepositions, but also behave differently with regard to lexical aspect.
The fine-grained syntacticosemantic analysis I present in this thesis does not only make
it possible to spell out PF and LF for spatial prepositions, but it also serves as input to a
morphological case approach (Marantz 1991, McFadden 2004) that accounts for the case
assignment properties of spatial prepositions in German. I show that German prepositions
inherently assign dative case, and that other cases, such as accusative, morphologically derive
from dative case in certain syntacticosemantic contexts. The morphological case approach
proposed in this thesis straightforwardly accounts for the well-known dative/accusative
ix
alternation that manifests itself in (pseudo)-geometric place prepositions co-occurring with
dative case, while (pseudo)-geometric goal prepositions co-occur with accusative case. In
addition, it accounts for the facts that route prepositions exclusively co-occur with accusative
case, and that non-geometric prepositions and all source prepositions exclusively co-occur
with dative case.
Zusammenfassung auf Deutsch
In dieser Arbeit buchstabiere ich die Syntax, Semantik und Morphologie von räumlichen
Präpositionen des Deutschen aus. Dafür nutze ich ein sparsames Grammatikmodell mit nur
einer generativen Komponente, der Syntax. Sie generiert sowohl Phrasen als auch Wörter
(Marantz 1997, Bruening 2016). Ich folge den Prinzipien des Minimalistischen Programms
(MP) (Chomsky 1995) mit Bare Phrase Structure (BPS) als dessen Phrasenstrukturmodul. Ich
zeige, dass eine Kombination aus Distribuierter Morphologie (DM) (Halle und Marantz 1993,
Embick 2015) für die Phonetische Form (PF) und Diskursrepräsentationstheorie (DRT) (Kamp
und Reyle 1993, Kamp et al. 2011) für die Logische Form (LF) es ermöglicht, tiefere und neue
Einsichten in das System deutscher räumlicher Präpositionen zu erlangen.
Ich klassifiziere räumliche Präpositionen gemäß einer weithin akzeptierten Typologie
(Jackendoff 1983, Piñón 1993, Zwarts 2005b, 2008, Gehrke 2008, Svenonius 2010). Place-
Präpositionen denotieren statische Orte (Regionen), während Path-Präpositionen dynami-
sche Orte (räumliche Pfade) denotieren. Ich modelliere von Path-Präpositionen denotierte
räumliche Pfade als geradlinige Liniensegmente. Diese können gerichtet sein, wie im Fall von
Goal- und Source-Präpositionen, oder ungerichtet, wie im Fall von Route-Präpositionen – ein
Gegensatz, der mit Krifkas (1998) gerichteten und ungerichteten Pfadstrukturen modelliert
werden kann. Bezüglich gerichteter Goal- und Source-Präpositionen, welche ich als von Place-
Präpositionen abgeleitet betrachte, folge ich Krifka (1998) und Beavers (2012) in der Annahme,
dass gerichtete räumliche Pfade ihre Richtung von einer Abbildung zwischen Bewegungser-
eignissen und deren räumlicher Projektion erhalten. Ich identifiziere zwei Typen von Goal-
und Source-Präpositionen: (i) (pseudo)-geometrische Goal- und Source-Präpositionen und
(ii) nicht-geometrische Goal- und Source-Präpositionen. Wenn diese beiden Typen mit Ver-
ben kombiniert werden, die die Art und Weise einer Bewegung ausdrücken, so führen
(pseudo)-geometrische Goal- und Source-Präpositionen zu Achievement-Prädikaten, wäh-
rend nicht-geometrische Goal- und Source-Präpositionen zu Accomplishment-Prädikaten
führen. Das heißt, die ersteren denotieren als ausgedehnt konzeptualisierte räumliche Pfade,
während die letzteren als punktuell konzeptualisierte räumliche Pfade denotieren. Route-
Präpositionen – die morphologisch einfachen im Deutschen sind durch, um und über – sind
grundlegend verschieden von Goal- und Source-Präpositionen. Sie sind nicht gerichtet und
erweisen sich als semelfaktivartig. Ich schlage vor, dass sie dreigeteilte räumliche Pfade deno-
tieren. Diese bestehen aus einem nicht-initialen, nicht-finalen Pfad (dem NINF-Pfad), welcher
von zwei Zipfel-Pfaden (tail paths) flankiert wird, einem an jedem Ende. Es kann gezeigt
x Abstracts in English and German
werden, dass Route-Präpositionen nicht richtungsbezogen sind. Aus diesem Grund plä-
diere ich dafür, dass die von Route-Präpositionen denotierten räumlichen Pfade mit Krifkas
(1998: 203) einfacher Pfadstruktur H, welche ungerichtet ist, modelliert werden sollten – einer
algebraischen Struktur, die bislang wenig Aufmerksamkeit erfuhr.
Ferner schlage ich vor, räumliche Präpositionen gemäß einer Klassifikation quer zu der
aus dem vorigen Absatz in drei Klassen einzuteilen: (i) geometrische Präpositionen, (ii)
pseudo-geometrische Präpositionen und (iii) nicht-geometrische Präpositionen. Geometri-
sche Präpositionen referieren auf geometrische Relationen, die sich in einem sparsamen,
perzeptionsgetriebenen Raummodell ausbuchstabieren lassen (Kamp und Roßdeutscher
2005). Typische Präpositionalphrasen mit geometrischen Präpositionen sind: in der Kiste,
in die Kiste, aus dem Haus, an der Wand, und auf dem Tisch. Die geometrischen Präposi-
tionen werden ferner unterteilt in (i) die topologischen Präpositionen in, aus, an und auf ;
sowie (ii) die projektiven Präpositionen hinter, vor, über, unter und neben. Während sich
Route-Präpositionen von sowohl Goal- als auch Source-Präpositionen unterscheiden, so hat
jede Route-Präposition ein geometrisches Konzept mit einer topologischen Goal-Präposition
(abgeleitet von einer topologischen Place-Präposition) gemeinsam und, in einem Fall, mit
einer topologischen Source-Präposition: (i) das Konzept eines Inneren wird von in, aus und
durch geteilt; (ii) das Konzept der Nähe wird von an und um geteilt; und (iii) das Konzept
der Vertikalität wird von auf und über geteilt. Die projektiven Präpositionen werden in
dieser Arbeit nicht behandelt. Die topologischen Präpositionen und die Route-Präpositionen
sind hingegen ein wesentlicher Bestandteil. Pseudo-geometrische Präpositionen sehen wie
geometrische Präpositionen aus, dennoch referieren sie nicht auf geometrische Relationen.
Stattdessen drücken sie funktionale Orte aus. Typische Beispiele von Präpositionalphrasen
mit pseudo-geometrischen Präpositionen sind: in der Schweiz, in die Schweiz und auf Sylt. Es
kann gezeigt werden, dass sich pseudo-geometrische Präpositionen in mehrfacher Hinsicht
anders verhalten als geometrische Präpositionen. Sie erlauben beispielsweise keine postposi-
tionale Wiederholung der Präposition; vergleiche etwa auf dem Tisch drauf mit auf Sylt *drauf.
Außerdem ist die Wahl einer pseudo-geometrischen Präposition in hohem Maße abhängig
von denotationalen Eigenschaften des Nomens, mit welchem die Präposition zusammen auf-
tritt (z.B. auf wird mit Inseln verwendet, in mit Ländern). Die eigentümliche Goal-Präposition
nach, welche beispielsweise mit artikellosen Toponymen obligatorisch ist, stellt sich als eine
spezielle Instanz der pseudo-geometrischen Präpositionen heraus. Die nicht-geometrischen
Präpositionen bei, zu und von bilden eine dritte Klasse räumlicher Präpositionen. Sie erlegen
nicht nur semantische Auswahlbeschränkungen auf, die von geometrischen und pseudo-
gemoetrischen Präpositionen verschieden sind, sondern sie verhalten sich auch anders im
Bezug auf lexialischen Aspekt.
Die feinkörnige syntaktikosemantische Analyse, die ich in dieser Arbeit präsentiere, macht
es nicht nur möglich, PF und LF für räumliche Präpositionen auszubuchstabieren, sondern
sie dient auch als Eingabe für einen morphologischen Kasusansatz (Marantz 1991, McFadden
2004), der die Kasuszuweisungseigenschaften räumlicher Präpositionen im Deutschen erklärt.
xi
Ich zeige, dass deutsche Präpositionen inhärent Dativ zuweisen und dass andere Kasus, wie
zum Beispiel Akkusativ, in bestimmten syntaktikosemantischen Kontexten morphologisch
von Dativkasus abgeleitet sind. Der in dieser Arbeit vorgeschlagene morphologische Kasus-
ansatz erklärt die bekannten Dativ/Akkusativ-Alternation; (pseudo)-geometrische Place-
Präpositionen treten mit Dativ auf, (pseudo)-geometrische Path-Präpositionen mit Akkusativ.
Zusätzlich erklärt der Ansatz warum Route-Präpositionen ausschließlich mit Akkusativ
auftreten, und warum nicht-geometrische Präpositionen und alle Source-Präpositionen mit
Dativ auftreten.
xii Abstracts in English and German
Acknowledgments
This thesis would not have been possible without many people who have helped me in one
way or another. I wish to thank them here.
First and foremost, I want to express my deepest gratitude to my supervisor Antje
Roßdeutscher. She always took the time to listen to my ideas and to discuss them with me. I
would have never reached this point without her. Thank you very much, Antje! I am also very
thankful to Artemis Alexiadou for imparting to me the elegance and beauty of Distributed
Morphology and Minimalism. She always gave me the feeling that I could make it. I am also
extremely grateful to Hans Kamp who has agreed to be on my committee. Thanks for the
valuable comments and the enlightening discussions. In addition, I would like to apologize
to Hans for (ab)using his name in this thesis. I am also very thankful to Jonas Kuhn for being
interested in my work and for his readiness to assist in organizational matters. I feel very
honored that Antje, Artemis, Hans, and Jonas took interest in my work.
I want thank Joost Zwarts and Peter Svenonius, with whom I had the honor and fortune
of discussing my work. I have benefited a lot from their expertise in prepositions. Many
people took the time to offer helpful comments and to raise interesting questions. For all this,
I should like to thank Víctor Acedo Matellán, John Beavers, Pavel Caha, Antonio Fábregas,
Berit Gehrke, Veronika Hegedu˝s, Tomio Hirose, Itamar Kastner, Angelika Kratzer, Terje
Lohndal, Claudia Maienborn, Ora Matushansky, Andrew McIntyre, Marina Pantcheva, Mark
Steedman, Gillian Ramchand, Juan Romeu Fernández, Henk van Riemsdijk, Sten Vikner,
Bonnie Webber, Ronnie Wilbur, Jim Wood, and many more.
I want to thank all the members of the Linguistics Department of University of Stuttgart
who helped me in word and deed: Ellen Brandner, Zeljka Caruso, Daniel P. Hole, Gianina
Iorda˘chioaia, Susanne Lohrmann, Sabine Mohr, Thomas Rainsford, Florian Schäfer, Girogos
Spathas, Anne Temme, Sabine Zerbian, and many more. Special thanks to Marcel Pitteroff
for the fruitful collaboration on prepositional case.
Thanks to all of my colleagues at the Institute for Natural Language Processing of Univer-
sity of Stuttgart, with whom I had the opportunity to work and chat during the course of
my PhD: Anders Björkelund, Stefan Bott, Jagoda Bruni, Marcel den Dikken, Sabine Dieterle,
Grzegorz Dogil, Kurt Eberle, Diego Frassinelli, Gertrud Faaß, Edgar Hoch, Wiltrud Kessler,
Nickolay Kolev, Sybille Laderer, Gabriella Lapesa, Natalie Lewandowski, Sebastian Padó,
Christel Portes, Tillmann Pross, Uwe Reyle, Arndt Riester, Anjte Schweitzer, Kati Schweitzer,
Torgrim Solstad, Sylvia Springorum, Isabel Suditsch, Michael Walsh, and many more. In
xiii
xiv Acknowledgments
particular, I should like to thank Ulrich Heid for his advice and for commenting on various
aspect of this thesis; and I would like to thank Sabine Schulte im Walde for advising me in
many regards.
I would like to thank my office mate Marion Di Marco, not only for not letting our plants
die, but also for the wonderful time. Thanks a lot to the other two members of my PhD
writing group, Kerstin Eckart and Wolfgang Seeker. I also would like to thank the ‘early-bird
Mensa group’ for making sure that I didn’t starve: Fabienne Cap, Markus Gärtner, Sarah
Schulz, and Anita Ramm.
I am thankful to Katie Fraser and Jeremy Barnes for proof-reading parts of this work
and for verschlimmbessering my English. (Of course, any errors that remain are my sole
responsibility!) In addition, I would like to thank Boris Schmitz for letting me use one of his
amazing one-continuous-line-drawings (see Figure 9 on page 124).
I want to thank my friends outside linguistics for supporting me in every way possible
(distraction, affection, advice, judgments, suggestions, chats, beers, discussions, parties, etc.).
Thanks to Sonja Böhm, Stoyka Dachenska, Joschi Gertz, Albrecht Hegener (Danke, echt danke!),
Simone Heusler, Holger Joukl, Martina Joukl, Cordelia Knoch, Christian ‘Homie’ Kohlbach,
Alexandra Maier, Hartwig Maier, Bettina Munimus, Marlene Seckler, and Britta Stolterfoht
(who happens to be a linguist too).
I wish to thank my family. Thanks to my parents Britta and Kurt Haselbach, to my
grandmother Gertrud Strecker, and to my parents-in-law Waltraud and Dieter Thoms. You
always supported me, no matter what. Last but by no means least, I want to thank Uwe
Thoms, die linguistische Wildsau, for encouraging me to enter academia, for bearing with me
through everything, for always being there for me, and for loving me.
This thesis was sponsored by the Deutsche Forschungsgemeinschaft (DFG) via Sonder-
forschungsbereich 732 Incremental Specification in Context.
List of Abbreviations
A adjective
A-P Articulatory-Perceptual
abs absolutive
acc accusative
ADJ Adjacency
AGR agreement
AP adjective phrase
Appl applicative
ApplP applicative phrase
Asp aspect
AspP aspect phrase
BPS Bare Phrase Structure
C complementizer
c-command constituent-command
c-select constituent-select
C-I Conceptual-Intentional
CP complementizer phrase
D determiner
dat dative
def definite
Deg degree
dir directional
DM Distributed Morphology
DP determiner phrase
DRS Discourse Representation Structure
DRT Discourse Representation Theory
Dx deixis
xv
xvi List of Abbreviations
DxP deixis phrase
EI Encyclopedia Item
EPP Extended Projection Principle
erg ergative
expl expletive
F functional
fem feminine
FP functional phrase
FPR Figure/Path Relation
GB Government and Binding
gen genitive
gov governed
HM Head Movement
iff if and only if
imp imparfait (French)
indef indefinite
inf inferior
IPA International Phonetic Alphabet
IPCA Idiosyncratic Prepositional Case Assignment
K case
KP case phrase
LF Logical Form
Lin linearization
loc locative
M morpheme
masc masculine
MCP Movement along Connected Paths
MO Mapping-to-Objects
MSE Mapping-to-Subevents
MSO Mapping-to-Subobjects
MP Minimalist Program
MR Movement Relation
MUSE Mapping-to-Unique-Subevents
xvii
MUSO Mapping-to-Unique-Subobjects
N noun
neut neuter
ninf non-initial, non-final
nom nominative
NP noun phrase
Num number
obj object
occ occupy
obl oblique
P preposition
pass passive
PCA Prepositional Case Assignment
PCI Prepositional Case Impoverishment
PF Phonological Form
pl plural
POSC Primacy of Orthogonality in Spatial Conceptualization
PP preposition phrase (or prepositional phrase)
PPS Primary Perceptual Space
PRO big PRO (silent pronoun)
prog progressive
prox proximity
ps passé simple (French)
Q light preposition Q
QP Q-Phrase (cf. light preposition Q)
refl reflexive
SDeWaC Stuttgart .de-domain Web-as-Corpus
sg singular
SINC Strictly Incremental Relation
SMR Strict Movement Relation
SP spatial path
subj subject
synsem syntacticosemantic
xviii List of Abbreviations
T tense
TH theme vowel
TP tense phrase
UE Uniqueness-of-Events
UG Universal Grammar
UO Uniqueness-of-Objects
unbd unbounded
UT utterance time
V verb
VI Vocabulary Item
VoiceP Voice phrase
VP verb phrase
XbT X-bar Theory (or X¯ Theory)
The following special characters are used:
ℵ Aleph (first letter of the Semitic abjads)
...
ℶ Beth (second letter of the Semitic abjads)
...
ℷ Gimel (third letter of the Semitic abjads)
...
© Copyright symbol
Indicator for Content features
` Script small L
Metasymbol for Encyclopedia Items
℘ Weierstraß p
Metasymbol for Vocabulary Items√
Radical sign
Root
List of Figures
1 Map of Cuba . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 The Y-model of grammar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3 The basic Y-model of grammar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4 Syntax in the Y-model of grammar . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
5 Morphology in the Y-model of grammar . . . . . . . . . . . . . . . . . . . . . . . . 59
6 Semantics in the Y-model of grammar . . . . . . . . . . . . . . . . . . . . . . . . . . 93
7 Spatial path p as a directed curve (cf. Zwarts 2005b: 744) . . . . . . . . . . . . . . 119
8 Euclidean vector space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
9 Primary Perceptual Space (PPS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
10 Left-handed coordinate system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
11 Spatial contact between regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
12 Internal line segment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
13 External line segment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
14 L-shaped line segment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
15 A plumb square from the book Cassells’ Carpentry and Joinery . . . . . . . . . . . 144
16 Plumb-square line segment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
17 Cocktail stick through olive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
18 Spear-like line segment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
19 Toy model of (im)possible paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
20 Initial and final parts of events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
21 MUSO and MUSE properties of SINC relations . . . . . . . . . . . . . . . . . . . . 155
22 Toy model of (im)possible paths (repeated from Figure 19) . . . . . . . . . . . . 158
23 Figure/Path Relation (Beavers 2012: 42) . . . . . . . . . . . . . . . . . . . . . . . . 160
24 Source and goal à la Krifka (1998: 227–228) . . . . . . . . . . . . . . . . . . . . . . . 165
25 Source and goal à la Beavers (2012) . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
26 Non-quantization of SPs to the station . . . . . . . . . . . . . . . . . . . . . . . . . . 167
27 (Non)-divisivity of SPs towards the station . . . . . . . . . . . . . . . . . . . . . . . . 168
28 Non-divisivity of (rectilinear) SPs along the river . . . . . . . . . . . . . . . . . . . 169
xix
xx List of Figures
29 Non-divisivity of fundamentally rectilinear SPs
um den Bahnhof (‘around the station’) . . . . . . . . . . . . . . . . . . . . . . . . . . 170
30 Cumulativity of SPs towards the station . . . . . . . . . . . . . . . . . . . . . . . . . 171
31 Cumulativity of (rectilinear) SPs along the river . . . . . . . . . . . . . . . . . . . . 172
32 Cumulativity of fundamentally rectilinear SPs
um den Bahnhof (‘around the station’) . . . . . . . . . . . . . . . . . . . . . . . . . . 172
33 Support from below . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
34 The basic steady-state force-dynamic patterns (Talmy 2000: 415) . . . . . . . . . 176
35 Typology of spatial prepositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
36 Typology of paths according to Jackendoff (1991) . . . . . . . . . . . . . . . . . . 191
37 Symmetrical typology of paths according to Piñón (1993) . . . . . . . . . . . . . 192
38 um-bar(v, x) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
39 Generalized model of concentric change of direction . . . . . . . . . . . . . . . . 207
40 Historical map of the Greater Antilles . . . . . . . . . . . . . . . . . . . . . . . . . . 219
41 Campaign poster by Green Party (1996 Baden-Württemberg state election) . . 223
42 Transitional goal and source paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
43 Extended goal and source paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
44 NINF-path v′ is a path to deictic reference region r′ in e0 . . . . . . . . . . . . . . 271
45 “w is a path towards region r in e” . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
46 Typology of spatial prepositions (repeated from Figure 35) . . . . . . . . . . . . 295
47 The Y-model of grammar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342
List of Tables
1 Realizations of German Asp[SPACE] (Den Dikken 2010: 101) . . . . . . . . . . . . 22
2 Structures in XbT vs. BPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3 Geometric and non-geometric prepositions in German . . . . . . . . . . . . . . . 184
4 Properties of non-geometric, geometric, and pseudo-geometric prepositions . 190
5 Kracht’s (2002, 2008) classification of paths . . . . . . . . . . . . . . . . . . . . . . 192
6 Bounded and unbounded German path prepositions . . . . . . . . . . . . . . . . 193
7 Categories and features of (pseudo)-geometric and non-geometric prepositions 195
8 Aspectually-relevant features in path prepositions . . . . . . . . . . . . . . . . . . 196
9 Cross-linguistic differences in expressing topological relations
(Bowerman and Choi 2001: 485) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
10 Abstract Content features in P-structures . . . . . . . . . . . . . . . . . . . . . . . . 202
11 Model-theoretic decomposition of durch-bar, um-bar, and ueber-bar . . . . . . . . 256
12 Model-theoretic spell out of route predicates . . . . . . . . . . . . . . . . . . . . . 257
13 Echo extensions of geometric prepositions . . . . . . . . . . . . . . . . . . . . . . . 261
14 Bounded and unbounded non-geometric path prepositions . . . . . . . . . . . . 261
15 Recurrence of geometric prepositions in echo extensions . . . . . . . . . . . . . . 265
16 Deictic elements in echo extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
17 Proximal and distal deictic marking in German postpositions and adverbs . . 269
18 Unbounded non-geometric path prepositions . . . . . . . . . . . . . . . . . . . . . 276
19 Case assignment of spatial prepositions in German . . . . . . . . . . . . . . . . . 296
20 Composite morphological case features . . . . . . . . . . . . . . . . . . . . . . . . . 314
21 Accusative languages vs. ergative languages . . . . . . . . . . . . . . . . . . . . . 318
22 Cross-linguistic examples of alternating adpositions (cf. Caha 2010: 181) . . . . 338
23 Projective prepositions and the axes of the PPS . . . . . . . . . . . . . . . . . . . . 351
24 Grapheme/phoneme mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367
xxi
xxii List of Tables
Chapter 1
Introduction
Prepositions present plenty of puzzling phenomena.1 Focusing on the domain of morpho-
logically simplex, spatial prepositions in German, this thesis identifies the following five
puzzling phenomena:
(I) Semantic interplay of preposition and complement noun:
On the one hand, the choice of a preposition can influence the interpretation of its
complement noun. On the other hand, the interpretation of a complement noun can
also influence the interpretation of the respective preposition.
(II) Morphological interplay of preposition and complement noun:
Morphosyntactic properties of a complement noun can influence the choice of the
respective preposition.
(III) Morphosyntactic properties:
A preposition can have distinct morphosyntactic properties depending on its interpre-
tation.
(IV) Prepositional aspect (Zwarts 2005b):
Some prepositions describing paths in space are unambiguous with regard to preposi-
tional aspect to the effect that they have either a bounded or an unbounded interpre-
tation, while other prepositions describing paths in space are ambiguous between a
bounded and an unbounded interpretation.
(V) Prepositional case assignment:
Prepositions determine the case of their complement nouns in a way that appears to be
arbitrary in some respects, yet systematic in others.
In the following, I will illustrate these puzzling phenomena with respective examples.
1One of these puzzling phenomena concerns the rather marginal question of why the preposition of all
words in the first sentence of this thesis is the only word that does not begin with P.
1
2 1. Introduction
As for the first part of the puzzling phenomenon (I), namely that the choice of a preposition
can influence the interpretation of its complement noun, consider the Twitter tweet in (1) by
the German satire show extra-3 on the occasion of Obama’s Cuba visit in March 2016.2
(1) Wichtiges
important
Detail:
detail:
Obama
Obama
kritisiert
criticizes
Menschenrechtsverletzungen
human rights violations
IN
in
Kuba
Cuba
[...],
nicht
not
AUF
upon
Kuba
Cuba
[...].
When used with the preposition in (‘in’), the toponym Kuba (‘Cuba’) is interpreted as denoting
the state of Cuba, i.e. the Republic of Cuba, but when it is used with the preposition auf
(‘upon’), the toponym is interpreted as denoting the island of Cuba. As a matter of fact, the
state of Cuba and the island of Cuba are not completely coextensive with one another, which
is clarified in Figure 1. So, auf Kuba includes the Guantanamo Bay Naval Base, a place Obama
would like to be silent about.
Figure 1: Map of Cuba
As for the second part of the puzzling phenomenon (I), namely that the interpretation of a
complement noun can also influence the interpretation of the respective preposition, consider
the clause in (2).
(2) Lenny
Lenny
und
and
Carl
Carl
waren
were
auf
upon
dem
the
Standesamt.
civil registry office
‘Lenny and Carl were on top of/at the civil registry office.’
The noun Standesamt (‘civil registry office’) is ambiguous to the effect that it can be interpreted
as a building or as an institution. Depending on the interpretation of the noun Standesamt, the
interpretation of the preposition auf varies. When the noun is interpreted as a building, the
preposition literally means on top of. In this case, Lenny and Carl were on top of the building
of the civil registry office, for instance, because they are roofers. In contrast, when the noun
is interpreted as an institution, the preposition means at. In this case, Lenny and Carl were
at the institution of the civil registry office, for instance, because they were grooms who got
married. Thus, I will refer to this ambiguity as the ‘roofer/groom ambiguity.’
2URL: https://twitter.com/extra3/status/711992190847717376 (30.06.2017)
3As for the puzzling phenomenon (II), namely that morphosyntactic properties of the
complement noun can influence the choice of a preposition, consider the island/state of
Cuba again. In order to express that Cuba – both the island or the state – is the goal of a
motion event, the preposition nach (‘to’) is typically used. This is, in particular, the case
when the noun Kuba occurs without a determiner, as in (3a). If, however, the noun has the
morphosyntactic property of occurring with a determiner, as is the case in (3b), where Kuba is
modified by the adjective schön (‘beautiful’), then the preposition nach is ungrammatical. In
this case, either in (‘in’) for the state reading or auf (‘upon’) for the island reading must be
used; see the first part of the puzzling phenomenon (I).
(3) a. Obama
Obama
reiste
traveled
nach
to
Kuba.
Cuba
b. Obama
Obama
reiste
traveled
in/auf/*nach
in/upon/to
das
the
schöne
beautiful
Kuba.
Cuba
As for the puzzling phenomenon (III), namely that a preposition can have distinct mor-
phosyntactic properties depending on its interpretation, consider the contrast in (4). For
instance, if a preposition such as an (‘on, at’) in (4a) has a geometrically well-defined interpre-
tation (here: spatial contact), then it has the morphosyntactic property of optionally licensing
a postpositional recurrence including a deictic element (here: dr- ‘there’). However, if the
same preposition has a functional interpretation that is not geometrically definable as in (4b),
then the preposition cannot co-occur with a postpositional recurrence.
(4) a. Hans
Hans
war
was
an
on
der
the
Felswand
rock face
(dran)
there.on
‘Hans was at the rock face.’
b. Hans
Hans
war
was
an
on
der
the
Nordsee
North Sea
(*dran)
there.on
‘Hans was at the North Sea.’
As for the puzzling phenomenon (IV), namely that some prepositions describing paths
in space are unambiguous with regard to prepositional aspect (Zwarts 2005b), while others
are ambiguous, consider the contrast between (5) and (6). Both the preposition zu (‘to’) in
(5a) and the circumposition auf ... zu (‘towards’) in (5b) describe directed paths in space to
the effect that they have the park as a goal. In contrast, the preposition durch (‘through’) in
(6) describes paths in space for which the notion ‘goal’ is not applicable. It describes paths
in space that are undirected routes with regard to the park. Applying frame adverbials as a
standard test for telicity, we can see that the ‘goal prepositions’ zu in (5a) and auf ... zu in (5b)
give rise to either a telic (bounded) interpretation or an atelic (unbounded) interpretation. In
contrast, the ‘route preposition’ durch in (6) is ambiguous; it gives rise to a telic (bounded)
and an atelic (unbounded) interpretation (Piñón 1993, Zwarts 2005b).
4 1. Introduction
(5) a. Hans
Hans
rannte
ran
in/*für
in/*for
5
5
Minuten
minutes
zu
to
einem
a
Park.
park
‘Hans ran to the park in/*for 5 minutes.’
b. Hans
Hans
rannte
ran
für/*in
for/*in
5
5
Minuten
minutes
auf
upon
einen
a
Park
park
zu.
to
‘Hans ran towards a park for/*in 5 minutes.’
(6) Hans
Hans
rannte
ran
in/für
in/for
5
5
Minuten
minutes
durch
through
einen
a
Park.
park
‘Hans ran through the park in/for 5 minutes.’
As for the puzzling phenomenon (V), namely that prepositions determine the case of
their complement nouns in a way that appears to be arbitrary in some respects, yet system-
atic in others, we should first look at the systematic aspects. Consider the well-known da-
tive/accusative alternation of German prepositions (Bierwisch 1988, Zwarts 2005a, Van Riems-
dijk 2007, Arsenijevic´ and Gehrke 2009, Caha 2010, Den Dikken 2010). Some prepositions
like in (‘in’) refer to static locations (regions) when co-occurring with a dative complement,
as in (7a), while they refer to dynamic locations (paths in space) when co-occurring with an
accusative complement, as in (7b).
(7) a. Hans
Hans
stand
stood
in
in
einem
a.DAT
Wald.
forest
‘Hans stood in a forest.’
b. Hans
Hans
rannte
ran
in
in
einen
a.ACC
Wald.
forest
‘Hans ran into a forest.’
In addition to the prepositions that alternate like in in (7), there are also prepositions that
do not alternate. Strangely enough, non-alternating prepositions do not uniformly co-occur
with one particular case. For instance, bei (‘at’) in (8), which refers to static locations, does not
alternate and co-occurs with a dative complement. And so do aus (‘out of’) and zu (‘to’) in (9),
which both refer to dynamic locations. However, there are still other prepositions like durch
(‘through’) in (10) that also refer to dynamic locations, but that co-occur with an accusative
complement.
(8) Hans
Hans
stand
stood
bei
at
einem
a.DAT
Wald.
forest
‘Hans stood at a forest.’
(9) Hans
Hans
rannte
ran
aus/zu
out of/to
einem
a.DAT
Wald.
forest
‘Hans ran out of/to a forest.’
(10) Hans
Hans
rannte
ran
durch
through
einen
a.ACC
Wald.
forest
‘Hans ran through a forest.’
5This thesis will show that these puzzling phenomena can be straightforwardly accounted
for by spelling out the syntax, semantics, and morphology of German spatial prepositions in
a parsimonious model of grammar, where only one combinatorial engine generating both
phrases and words is assumed (Marantz 1997, Bruening 2016). In particular, I will show that
combining Minimalist Syntax (Chomsky 1995), Discourse Representation Theory (Kamp and
Reyle 1993, 2011, Kamp et al. 2011), and Distributed Morphology (Halle and Marantz 1993,
Embick 2015), in order to spell out syntax, semantics, and morphology, respectively, enables
us to systematically analyze spatial prepositions, which leads to deeper and new insights
into the system of spatial prepositions in German.
One of these new insights is, for instance, a classification of spatial prepositions along a
geometric dimension. In particular, I will argue that spatial prepositions can be (i) geometric
prepositions, which refer to geometric relations that can be spelled out in a parsimonious,
perception-driven model of space (Kamp and Roßdeutscher 2005); (ii) pseudo-geometric
prepositions, which look like geometric prepositions, but do not refer to geometric relations,
but to functional locative relations; and (iii) non-geometric prepositions, which do not refer to
any locative relations whatsoever. This new classification is orthogonal to a widely accepted
typology, in which spatial prepositions are classified as place and path prepositions, and
in which the latter being further sub-classified into directed path prepositions (goal and
source prepositions) and undirected path prepositions (route prepositions) (Jackendoff 1983,
Piñón 1993, Zwarts 2005b, 2008, Gehrke 2008, Svenonius 2010). This new classification will
contribute to a better understanding and explanation of the puzzling phenomena (I) to (III).
Further, I will exploit Krifka’s (1998: 203, 205) distinction between an undirected path
structure H and a directed path structure D to model route prepositions and goal (and
source) prepositions, respectively. This will contribute to a straightforward explanation of
the puzzling phenomenon (IV); cf. prepositional aspect (Zwarts 2005b).
Spelling out spatial prepositions in the grammatical model described above, makes it also
possible to formulate a morphological case approach (Marantz 1991, McFadden 2004) that
accounts for the case assignment properties of spatial prepositions in German, that is, for the
puzzling phenomenon (V).
As mentioned above, I will spell out the syntax, semantics, and morphology of Ger-
man spatial prepositions in this thesis. I will do this by assuming the Y-model of grammar
(Chomsky 1995, Marantz 1997, Bobaljik 2002, 2008, Embick and Noyer 2007, Embick and
Marantz 2008, Harley 2012, 2014, a.o.), where Syntax is considered to be the only combi-
natorial engine (Marantz 1997, Bruening 2016). Syntactic structures on which no further
syntactic operations are executed constitute Spell-Out. Syntactic structures at Spell-Out
interface with the Articulatory-Perceptual (A-P) systems, on the one hand, and with the
Conceptual-Intentional (C-I) systems, on the other. The interface representation of the A-P
systems is Phonological Form (PF). The operations executed at PF constitute the Morphology.
The interface representation of the C-I systems is Logical Form (LF). The operations executed
at LF constitute the Semantics. The Y-model of grammar is depicted in Figure 2.
6 1. Introduction
The structure of this thesis reflects the Y-model of grammar. Chapter 2 will address the
syntax, Chapter 3 the morphology, and Chapter 4 the semantics. Then, Chapter 5 will spell
out German spatial prepositions with regard to syntax, semantics and morphology. Then,
Chapter 6 will lay out a morphological case approach to spatial prepositions in German that
is based on the syntacticosemantic analyses proposed in Chapter 5. Let us briefly look at
these chapters individually.
Spell-Out
Phonological
Form (PF)
Articulatory-Perceptual
(A-P) systems
Morphology
Logical
Form (LF)
Conceptual-Intentional
(C-I) systems
Semantics
Syntax
Figure 2: The Y-model of grammar
Chapter 2 will present the syntactic module within the Y-model of grammar. In this
thesis, I will adopt the tenets of the Minimalist Program (MP) (Chomsky 1995, Adger 2003).
Section 2.1 will focus on various types of features; features are considered to be the core
building blocks of the grammatical theory adopted here. Section 2.2 will present the principles
and operations according to which structure is generated in the Minimalist Program (MP)
(Chomsky 1995). MP applies Bare Phrase Structure (BPS) as its phrase structure module.
Section 2.3 will clarify the status of Roots in the approach proposed here. I will advocate
an approach that is, in certain respects, comparable to the one proposed by De Belder and
Van Craenenbroeck (2015). Section 2.4 will summarize Chapter 2.
Chapter 3 will explore the morphological branch of the Y-model of grammar, that is Phono-
logical Form (PF). In this thesis, I will adopt the tenets of Distributed Morphology (DM)
(Halle and Marantz 1994, Embick 2015). Section 3.1 will present the operation of Vocabulary
Insertion. In DM, morphophonological exponents are inserted late, i.e. after the syntactic
derivation, into the terminal nodes of syntax. Vocabulary Insertion is controlled by the
7Subset Principle (Halle 1997). Section 3.2 will present the Late Linearization Hypothesis
according to which the elements of a phrase marker are linearized at Vocabulary Insertion
(Embick and Noyer 2001). Section 3.3 will address the notion of ‘ornamental morphology’
(Embick and Noyer 2007: 305), i.e. morphology that is syntacticosemantically unmotivated
and “ornaments” the syntactic representation. Section 3.4 will present morphological opera-
tions on nodes, e.g. Impoverishment, where certain features are deleted from a node under
specified conditions (Bonet 1991, Embick 2015). Section 3.5 will present the morphological
displacement operations Lowering and Local Dislocation (Marantz 1988, Embick and Noyer
2001, 2007). Section 3.6 will present morphophonological Readjustment Rules (Embick 2015).
Section 3.7 will summarize Chapter 3.
Chapter 4 will explore the semantic branch of the Y-model of grammar, that is Logical
Form (LF). In this thesis, I will adopt the tenets of Discourse Representation Theory (DRT)
(Kamp and Reyle 1993, 2011, Kamp et al. 2011) to model LF. As for the model of space, I
will follow Kamp and Roßdeutscher (2005). As for algebraic structures, I will follow Krifka
(1998), Beavers (2012). Section 4.1 will present the semantic construction algorithm at LF,
where each terminal node of a syntactic structure receives a context-dependent interpretation.
Compositionally, the interpretations of the terminal nodes are combined bottom-up along the
syntactic structure by means of unification-based composition rules. As for the representation
of LF, Discourse Representation Theory (DRT) (Kamp and Reyle 1993, 2011, Kamp et al. 2011)
is chosen. One of the features of DRT is that interpretation involves a two-stage process:
(i) the construction of semantic representations referred to as Discourse Representation
Structures (DRSs), i.e. the LF-representation proper; and (ii) a model-theoretic interpretation
of those DRSs. Section 4.2 will briefly address the general conceptualization of ‘Figure’ and
‘Ground’ in language, as introduced by Talmy (1975, 2000). Section 4.3 will focus on the model-
theoretic aspects relevant for the semantic modeling of spatial prepositions. I will present
two models of three-dimensional space: (i) the vector space model of space, as advocated by
Zwarts (1997, 2003b, 2005b), Zwarts and Winter (2000); and (ii) the perception-driven model of
space, as advocated by Kamp and Roßdeutscher (2005), who base their approach on principles
formulated by Lang (1990). In this thesis, I will adopt Kamp and Roßdeutscher’s (2005)
parsimonious, perception-driven model of space, which will be presented in the Sections 4.3.1
to 4.3.6. Section 4.4 will present the algebraic foundations. Section 4.4.1 will present the
mereological structures that will be used in the modeling of spatial paths. In particular,
plain/undirected path structures H (Krifka 1998: 203) and directed path structures D (Krifka
1998: 203) will be presented. Spatial paths can serve as incremental themes measuring out
events (Dowty 1979, 1991, Tenny 1992, Jackendoff 1996, Krifka 1998, Beavers 2012); thus,
Section 4.4.2 will present incremental relations between spatial paths and motion events. I
will briefly present Beavers’ (2012) Figure/Path Relations (FPRs) that account for double
incremental themes. Section 4.5 will focus on spatial paths. I briefly presented two approaches
to spatial paths: (i) an axiomatic approach, where spatial paths are taken as primitives in
the universe of discourse (Piñón 1993, Krifka 1998, Beavers 2012); and (ii) a constructive
8 1. Introduction
approach, where spatial paths are defined as continuous functions from the real unit interval[0, 1] to positions in some model of space (Zwarts 2005b: 748). In this thesis, I will opt for an
axiomatic approach to spatial paths. Section 4.6 will address prepositional aspect, which is
argued to relate to the distinction between bounded and unbounded reference Jackendoff
(1991), Verkuyl and Zwarts (1992), Piñón (1993), Zwarts (2005b). Following Zwarts (2005b), I
will assume that cumulativity is the algebraic property characterizing prepositional aspect.
Section 4.7 will discuss the force-dynamic effect of the German topological preposition auf
(‘upon’), which can be characterized as ‘support form below’. Using Talmy’s (2000: 413, 415)
terms ‘Agonist’ and ‘Antagonist’ for the force entities at issue, I will characterize this force-
dynamic effect such that the complement of the preposition serves as an Antagonist that
prevents the Agonist from falling down. Section 4.8 will summarize Chapter 4.
Chapter 5 will spell out the syntax, semantic, morphology of spatial prepositions in Ger-
man. This chapter is the core of this thesis because it illustrates how spatial prepositions
could be implemented in the Y-model of grammar. First, Section 5.1 will classify spatial
prepositions according to several criteria. Section 5.1.1 will introduce the distinction between
place prepositions, on the one hand, and path prepositions, on the other. Path prepositions
are further subdivided into directed path prepositions (goal and source prepositions) and
undirected path prepositions (route prepositions) (Jackendoff 1983, Piñón 1993, Zwarts 2006,
a.o.). Section 5.1.2 will propose a geometry-based classification of spatial prepositions that
is orthogonal to the place/path typology. I propose that spatial prepositions can be (i) geo-
metric prepositions, (ii) pseudo-geometric prepositions, or (iii) non-geometric prepositions.
Section 5.1.3 will classify path prepositions into bounded and unbounded path prepositions.
Section 5.1.4 will map these classifications to syntactic structure. Then, Section 5.2 will briefly
touch upon the cartographic decomposition of spatial prepositions (Svenonius 2006, 2010,
Pantcheva 2011). Then, Section 5.3 will introduce three abstract Content features that relate
to geometric concepts and that figure in the derivation of the geometric prepositions: [ℵ]
relating to interiority in Section 5.3.1; [ℶ] relating to contiguity in Section 5.3.2; and [ℷ] relating
to verticality in Section 5.3.3. Then, Section 5.4 will derive the lexical structure of spatial
prepositions and spell out PF-instructions for their morphophonological realization and
LF-instructions for their semantic interpretation. Then, Section 5.5 will derive the functional
structure of spatial prepositions and spell out PF-instructions for their morphophonological
realization and LF-instructions for their semantic interpretation. Then, Section 5.6 will illus-
trate how a fully-fledged PP, i.e. a prepositional CP, headed by a spatial preposition can be
integrated in various verbal contexts. Finally, Section 5.7 will summarize Chapter 5.
Chapter 6 will discuss prepositional case in German. I will present (i) the case assignment
properties of (spatial) prepositions in German (Zwarts 2006); (ii) several previous approaches
to prepositional case (Bierwisch 1988, Arsenijevic´ and Gehrke 2009, Caha 2010, Den Dikken
2010); and (iii) a morphological case theory proposed for the verbal domain Marantz (1991),
McFadden (2004). This will pave the way for a proposal of a morphological case approach to
spatial prepositions in German that is based on the syntacticosemantic analyses of spatial
9prepositions presented in Chapter 5.3 First, Section 6.1 will present the case assignment
properties of spatial prepositions in German. Then, Section 6.2 will present four previous
approaches to prepositional case: Den Dikken (2010) in Section 6.2.1; Caha (2010) in Sec-
tion 6.2.2; Arsenijevic´ and Gehrke (2009) in Section 6.2.3; and Bierwisch (1988) in Section 6.2.4.
Then, Section 6.3 will motivate and outline the hypothesis that case is not a phenomenon of
the syntax proper, but of the morphological component of the grammar. This section will
present a morphological case approach spelled out for the verbal domain (Marantz 1997,
McFadden 2007). Then, Section 6.4 will lay out a morphological case theory for simplex
spatial prepositions in German that is based on the syntacticosemantic analysis of spatial
prepositions presented in Chapter 5. Finally, Section 6.5 will summarize Chapter 6.
Chapter 7 will conclude and provide some prospects for future work.
This thesis has the following appendixes. Appendix A will provide synopses of Chapter 5
and Chapter 6. Appendix B will provide proofs that negative non-initial, non-final paths give
rise to bounded route PPs, while positive non-initial, non-final paths give rise to unbounded
PPs. Appendix C will provide a mapping between orthographic (graphemic) representations
and phonemic IPA-representations used in this thesis. Appendix D will list the picture credits
for the images used in this thesis.
3The morphological case approach to prepositions proposed by Haselbach and Pitteroff (2015) presents
an early stage of the morphological case theory developed in Section 6.4. The morphological case approach
presented in Haselbach and Pitteroff (2015) was jointly developed by Boris Haselbach and Marcel Pitteroff.
At that stage, however, the approach was syntacticosemantically not as elaborated as it is here. Moreover,
Sections 6.2 and 6.3 overlap with Haselbach and Pitteroff (2015), to some extent. For the most part, this work
was carried out by me.
10 1. Introduction
Chapter 2
Syntax
In this thesis, I advocate a parsimonious model of grammar (Marantz 1997, Bruening 2016,
a.o.) with only one combinatorial component – syntax – that is capable of generating both
phrases and words. Adopting the theoretical tenets of the Minimalist Program (MP) (Chom-
sky 1995, Adger 2003, Hornstein et al. 2005, Boeckx 2006, a.o.), I assume the common Y-model
of grammar (Chomsky 1995, Marantz 1997, Bobaljik 2002, 2008, Embick and Noyer 2007,
Embick and Marantz 2008, Pfau 2009, Harley 2012, 2014, a.o).4 The basic Y-model is sketched
in Figure 3 below. Each derivation of a linguistic unit starts out with the Numeration, a
set of intentionally-selected items capable of generating structure. Numeration feeds the
derivational workspace where syntactic operations (Merge, Adjoin, Agree, and Move) are
carried out, in order to build structure in the module termed Syntax. Syntactic structures on
which no further syntactic operations are executed constitute Spell-Out. Syntactic structures
at Spell-Out interface with the Articulatory-Perceptual (A-P) systems on the one hand, and
with the Conceptual-Intentional (C-I) systems on the other. The representational interface
level between Spell-Out and the A-P systems is termed Phonological Form (PF). The set
of operations that are executed in order to arrive at PF are morphological operations. This
set of morphological operations constitutes the module Morphology. The representational
interface level between Spell-Out and the C-I systems is termed Logical Form (LF). The set
of operations that are executed in order to arrive at LF are semantic operations. The set of
semantic operations constitutes the module Semantics.
By assumption, several lists feed the Y-model of grammar. Building on Halle and Marantz
(1993), Marantz (1997), Harley (2012), a.o., I assume List 1, List 2, and List 3. List 1 is assumed
to comprise the “syntactic primitives, both interpretable and uninterpretable, functional and
contentful” (Harley 2014: 228). In this thesis, I suggest to split List 1 into (i) the Lexicon
and (ii) the Content. The Lexicon contains (bundles of) functional primitives, viz. category
and syntacticosemantic/morphosyntactic features, taken from the initial state of grammar
termed Universal Grammar (UG) (Chomsky 1995: 14), while the Content contains (bundles of)
contentful primitives that are not relevant to Syntax but potentially relevant to Morphology
4A model akin to the Y-model is the T-model; see Bobaljik (2002) for a discussion.
11
12 2. Syntax
Numeration
Spell-Out
Phonological
Form (PF)
A-P
system
Morphology
Logical
Form (LF)
C-I
system
Semantics
Syntax
List 1:
Syntactic primitives,
functional and contentful
List 2
(Vocabulary):
Instructions for
pronouncing
terminal nodes
in context
List 3
(Encyclopedia):
Instructions for
interpreting
terminal nodes
in context
Figure 3: The basic Y-model of grammar
and Semantics. The fundamental distinction between Lexicon and Content is that the former
is generative (i.e. capable of generating structure), while the latter is not generative. Being the
only generative module, the Lexicon corresponds to what Marantz (1997: 201) terms the “pure
lexicon.” Notwithstanding cross-linguistic patterns, the substance and the feature bundling
in the Lexicon and the Content are assumed to be language-specific. Following Harley
(2014: 228), I assume that List 2, termed Vocabulary, contains “instructions for pronouncing
terminal nodes in context”, and that List 3, termed Encyclopedia, contains “instructions for
interpreting terminal nodes in context.”
(11) a. Lexicon (subset of List 1):
The generative (syntactic) items of a language.
b. Content (subset of List 1):
The non-generative, contentful items of a language.
c. Vocabulary (List 2):
Instructions for pronouncing terminal nodes in context.
d. Encyclopedia (List 3):
Instructions for interpreting terminal nodes in context.
2.1. Features 13
In this chapter, I lay out the syntactic module within the Y-model of grammar, as sketched
in Figure 4. The syntactic building blocks are features, which are the subject of Section 2.1.
Then, Section 2.2 discusses the principles according to which syntactic structure is built. Then,
Section 2.3 clarifies the status of Roots in the approach that is proposed here.
Numeration
Spell-Out
Phonological
Form (PF)
A-P
system
Morphology
Logical
Form (LF)
C-I
system
Semantics
Syntax
Lexicon:
The generative items
of a language
Content:
The non-generative,
contentful items
of a language
(List 2)
Vocabulary:
Instructions for
pronouncing
terminal nodes
in context
(List 3)
Encyclopedia:
Instructions for
interpreting
terminal nodes
in context
. . . . .(List. . .1)
Figure 4: Syntax in the Y-model of grammar
2.1 Features
Features are the core building blocks of the grammatical model assumed in this thesis. We
can think of features as abstract properties of linguistic units. For instance, if we consider a
word as a morphosyntactic unit, then “a morphosyntactic feature [...] is a property of a word”
(Adger 2003: 26). Features are essential in linguistic theory because they help to determine the
linguistic behavior of the respective carrier. For instance, features may determine the syntactic
operations that the carrier may undergo or how the carrier is phonologically realized and
semantically interpreted.
Let me first clarify the theoretical status of features. There are two opposing views
on features. On the one hand, features can be seen as part of a description language for
grammatical theory. On this view, “feature theory does not constrain the objects of linguistic
14 2. Syntax
theory but merely describes them” (Adger and Svenonius 2011: 28). For example, Head-
driven Phrase Structure Grammar (Pollard and Sag 1987, 1994) takes this view. On the other
hand, features can be seen as “properties of syntactic atoms and hence [they] are directly
objects of the theory” (Adger and Svenonius 2011: 28). In this sense, features can enter into
relationships with each other to form structure. This view means that the feature theory
and the theory of grammar correlate such that constraining the former implies constraining
the latter. This makes the feature theory central in the overall theory of grammar and thus
characteristic for a given syntactic theory. This thesis takes the latter view on features, namely
that they are primitives of the grammar. Adger and Svenonius (2011: 28) further point out that
the Minimalist framework (Chomsky 1995) is “a set of guidelines which constrain the general
hypothesis space within which these various theories can be entertained.” Anticipating the
syntactic operation Merge, which is the core operation for structure building (cf. Section 2.2),
Adger and Svenonius (2011: 31) give an informal definition of feature.
(12) Features:
a. Syntax builds structure through recursive application of Merge.
b. The smallest element on which Merge operates is a syntactic atom.
c. A syntactically relevant property of a syntactic atom which is not shared by all
syntactic atoms and which is not derivable from some other property is a feature.
(Adger and Svenonius 2011: 31)
Note that I typically indicate (bundles of) features by means of square brackets; that is, I
indicate that X is a feature by writing [X].
2.1.1 Types of features
This section addresses feature systems and where to allocate features in the Y-model of
grammar advocated in this thesis. Three types of feature systems figure in linguistic theory:
(i) privative features, (ii) binary features, and (iii) multi-valent features. This section discusses
each of these systems in turn. Privative features consist of attributes only. Attributes are
atomic symbols. Adger (2010: 187) defines privative features as given in (13).
(13) Privative feature (preliminary version):
An atomic symbol drawn from the set F = {A, B, C, D, E, ...} is a feature.
(Adger 2010: 187)
One useful extension of (privative) features is to assume uninterpretability as a formal
property capturing structural dependencies. One disadvantage of simple privative features,
as defined in (13), is that they are not powerful enough to state structural dependencies.
For this, we would need a separate system including rules that state which features may
or may not combine to form complex syntactic objects. Entertaining two such systems is
2.1. Features 15
undesirable. Avoiding this situation motivates the notion of uninterpretability as a formal
property of features that captures syntactic dependencies (Chomsky 1995). In particular,
the feature prefix u, which indicates uninterpretability, sets up structural dependencies in
the syntactic derivation. This is achieved by making the “syntactic structure building rules
sensitive to the presence of the u-prefix, ensuring that when a feature bears such a prefix,
there must be another feature in the structure which is exactly the same, but lacks the prefix.
This implements Chomsky’s notion of checking” (Adger 2010: 189). In this sense, the u-prefix
does a purely formal job ensuring syntactic dependencies. At this point, I refer to Section 2.2,
which addresses the uninterpretability of features in the context of the syntactic operation
Merge. Adger extends the definition of privative features by uninterpretability as given in
(14).
(14) Privative feature (final version):
a. An atomic symbol drawn from the set F = {A, B, C, D, E, ...} is a feature.
b. An atomic symbol drawn from the set F = {A, B, C, D, E, ...} and prefixed by u is
a feature.
(Adger 2010: 188)
A more complex feature system involves binary features. A disadvantage of privative
features is that it soon becomes clumsy, though not impossible, to cope with agreement
phenomena ubiquitous in natural language. One way to enrich a feature system such that
it can account for these phenomena is to equip features with a value. That is, each feature
attribute is assigned a certain feature value. A basic step is to allow values drawn from a
binary set. Typically, the binary values are positive (plus, +) and negative (minus, −) (Jakobson
1932, Bierwisch 1967, Adger 2003, 2010). Adger defines a binary feature as a combination of
an attribute and a value, as given in (15). Note that I represent binary features with the value
prefixed to the attribute, e.g. [+X], instead of the pair notation ⟨X,+⟩.
(15) Binary feature:
A feature is an ordered pair ⟨Att, Val⟩ where
a. Att is drawn from the set of attributes {A, B, C, D, E, ...}, and
b. Val is drawn from the set of values {+,−}.
(Adger 2010: 191)
A further enrichment of the feature system is to allow a larger set of possible feature
values, i.e. not only binary values. Adger refers to such systems as multi-valent feature
systems. In this thesis, I refrain from using multi-valent features. An even more complex
feature system allows the recursive embedding of features as values. I also refrain from this
kind of feature system. Note, however, that Functional Unification Grammars commonly
implement recursive features. For example, Lexical Functional Grammar (Bresnan 2001)
exploits a recursive feature system for its so-called F-structure (i.e. functional structure).
16 2. Syntax
The choice of the adequate feature system is, of course, an empirical question. However,
on a theoretical level, we can say that one should prefer, according to the law of parsimony
(Occam’s razor), the simplest system or the most economic feature system. As mentioned
above, a privative feature system using only atomic features hardly copes with the agreement
phenomena in natural language. Thus, I also use binary feature systems in this thesis.
However, I eschew more complex systems. As a consequence, the grammar implemented
here comprises a mixture of a privative and binary features.
Here, I make use of Svenonius’ (2007b) distinction between interface features and module-
internal features: Interface features are those features that figure across grammatical modules,
while module-internal features figure only in one grammatical module. In the Y-model of
grammar advocated in this thesis, there are three modules, (i) syntax, i.e. the branch from
Numeration to Spell-Out, (ii) morphology, i.e. the PF-branch from Spell-Out to the A-P
interface, and (iii) semantics, i.e. the LF-branch from Spell-Out to the C-I interface. On this
view, interface features that figure across modules can only be those that have repercussions
in syntax. I assume that two lists feed the syntax. The Lexicon list feeds the Numeration,
while the Content list feeds Spell-Out. On the one hand, the features in the Lexicon are
universal and generative. In line with Chomsky (1995), Alexiadou (2001, 2004), a.o., I take
the view that UG provides a universal set of features. A given language picks out a subset
of these features and stores (bundles of) them in its Lexicon. These features can generate
syntactic structure. Generally, I assume two types of features in the Lexicon, (i) category (or
categorial) features, which are addressed in Section 2.1.2, and (ii) syntacticosemantic (synsem)
features, which are addressed in Section 2.1.3. On the other hand, the features in the Content
are language-specific and non-generative. Content features are addressed in Section 2.1.4.
Note at this point that features referring to the grammatical notion of case are often
also subsumed under the syntactically-relevant features. That is, they are considered to be
interface features. In this thesis, I do not take this perspective. Adopting a morphological
case approach (Zaenen et al. 1985, Yip et al. 1987, Marantz 1991, McFadden 2004, Bobaljik
2008, Schäfer 2012, a.o.), I propose in Section 6.4 that – from a prepositional perspective – case
features do not need to be assumed in the syntax proper. Thus, I consider case features to
be PF-internal features. This contrasts with Adger (2003), for instance, who conceives case
as a syntactic category. Putting case into the syntax proper, Adger assumes that functional
heads may bear uninterpretable case features that must be checked by nominal elements.
In particular, Adger models case by means of a multi-valent feature system comprising an
attribute ‘CASE’ and possible values such as ’NOM’ (for nominative), ‘ACC’ (for accusative),
etc. For example, in order to assign nominative to subjects, Adger (2003: 211) assumes that
a finite tense head bears an uninterpretable case feature [uCASE ∶ NOM]. Furthermore, he
assumes that a finite tense head values nominative on a DP in its specifier under Agree. As
already mentioned, I part company with Adger (2003) with respect to case features. First, I do
not assume that case features figure in syntax proper. Instead, I assume that case feature are
PF-internal features, the value of which is determined post-syntactically at the morphology
2.1. Features 17
interface, on the basis of the output from syntax. Second, in line with Bierwisch (1967), Halle
and Vaux (1997), McFadden (2004), a.o., I assume that the morphological realizations of case,
i.e. nominative, accusative, etc., do not correspond to primitive features or feature values in the
system, but that they are the realizations of more abstract case features; cf. Section 6.3.2.
2.1.2 Category features
Category features are syntactically-relevant interface features. Generally, we can identify (i)
features for lexical categories, (ii) features for functional categories, and (iii) features for light
categories. They are discussed in the following paragraphs.
Lexical categories
The major category features are those relating to the traditional word classes verb (V),
noun (N), adjective (A), and preposition (P) (e.g. Adger 2003: 36).5 These four categories are
often referred to as lexical categories. The lexical categories figure in structure building. The
syntactic operation Merge is sensitive to categories by exploiting the formal feature property
of uninterpretability. Uninterpretable category features can also be referred to as c-selectional
(categorial selectional) features or as subcategorization features (Adger 2003: 84). I assume, as
commonly accepted, that these four lexical categories form four syntactic domains.
In principle, the four lexical categories can be decomposed into more abstract features.
Several scholars assume a decomposition of the lexical categories into abstract binary features
(e.g. Chomsky 1970, Jackendoff 1977, Bresnan 1982, Hengeveld 1992, Déchaine 1993, Wun-
derlich 1996, Hale and Keyser 1997, Baker 2003). While all approaches differ fundamentally
with respect to the kind and motivation of these abstract features – as well as the distribution
of the feature values – all approaches share the idea that the four lexical categories can be
decomposed by means of two binary features. For example, Hale and Keyser (1997: 207)
propose that the four major categories can be defined in structural and predicational terms.
Hale and Keyser assume the feature [±COMPLEMENT], which states whether a category “nec-
essarily combines with another category which stands in the structural relation ‘immediate
sister’ to it”. Additionally, they assume the feature [±SUBJECT], which states whether or not
a category “projects a predicate and must, therefore, have a subject”. Equipped with these
two binary features, Hale and Keyser decompose the lexical categories N, V, A, and P as
follows. The feature [+COMPLEMENT] groups the categories verb and preposition together,
because these categories normally take a structural complement; the feature [−COMPLEMENT]
groups the categories noun and adjective together, because these categories normally do not
take a structural complement. The feature [−SUBJECT] groups the categories noun and verb
together because these categories normally do not project a predicate requiring a (semantic)
5Note that some scholars (e.g. Grimshaw 2000, Baker 2003) do not consider P to be a lexical category on par
with V or N. Grimshaw (2000), for example, treats prepositions as a functional part of the extended projection of
N. This thesis, however, treats P as a lexical category on par with V, N, and A.
18 2. Syntax
subject; and the feature [+SUBJECT] groups the categories adjective and preposition together
because these categories normally project a predicate requiring a (semantic) subject. That
is, nouns are specified as [−COMPLEMENT,−SUBJECT], verbs as [+COMPLEMENT,−SUBJECT],
adjectives as [−COMPLEMENT,+SUBJECT], and prepositions as [+COMPLEMENT,+SUBJECT].
Note, however, that I do not implement such a decomposition of the lexical category features
in this thesis, even though it is, in principle, feasible. Instead, I use the privative features N,
V, A, and P for the four lexical categories.
Functional categories
In addition to lexical categories, functional categories are identified for each of the four
categorial domains (e.g. Fukui 1986, Speas 1986, Abney 1987, Van Riemsdijk 1990, Ritter
1993, a.o.). The traditional distinction between lexical and functional categories concerns the
assumption that lexical categories may assign thematic roles (Higginbotham 1985), while
functional categories may not do so (Fukui 1986, Speas 1986). Note that this does not mean
that functional categories may not have semantic content. In fact, the semantic content of
functional categories is said to be functional in nature, rather than conceptually involving the-
matic relations. Structurally, functional categories are generally assumed to project syntactic
structure and to surmount the lexical categories.
Let us now very briefly look at the functional categories commonly assumed in the verbal,
nominal, and adjectival domain; then we will look at the functional categories in the preposi-
tional domain in more detail. For the verbal domain, the following functional categories are
typically assumed: C (for complementizer) for words like that or for (Rosenbaum 1965), T
(for tense) hosting tense information (Pollock 1989), and Asp (for aspect) hosting aspectual
information (Borer 1994). Their typical hierarchical order above the lexical category V is
given in (16).
(16) Functional categories in the verbal domain:
C > T > Asp > V
For the nominal domain, the following functional categories are typically assumed: D
(determiner) for determiners like the or a (Abney 1987), and Num (number) hosting number
information (Ritter 1991, 1993) are commonly assumed. For the functional structure of noun
phrases, see also Valois (1991), Longobardi (1994), Szabolcsi (1994), Alexiadou (2001), to
mention a few. The typical hierarchical ordering of the functional categories above the lexical
category N is given in (17).
(17) Functional categories in the nominal domain:
D > Num > N
For the adjectival domain, Abney (1987) proposes the functional category Deg (degree) for
elements like so or too, as in so/too big (Abney 1987: 189); see also Adger (2003: 347), Radford
2.1. Features 19
(2004: 79), a.o. As in the verbal and the nominal domain, the functional category in the
adjectival domain is assumed to be hierarchically above the lexical category A, as given in
(18).
(18) Functional categories in the adjectival domain:
Deg > A
One of the first proposals for an additional functional category in the prepositional domain
comes from Van Riemsdijk (1990). He proposes the functional category ‘little p’, hierarchically
above the lexical category P. With the functional category little p, Van Riemsdijk (1990)
accounts for German postpostional and circumpositional phrases as in (19). In particular, he
proposes that elements like nach (‘according to’) in (19a) or unten (‘down’) in (19b) occupy
the functional category little p, while an element like in of the fused form im (in plus dem, ‘in
the.DAT’) in (19b) occupies the lexical category P.
(19) a. meiner
my.DAT
Meinung
opinion
nach
according-to
‘in my opinion’
b. im
in.the.DAT
Tal
valley
unten
down
‘down in the valley’
(Van Riemsdijk 1990: 233)
For German, Van Riemsdijk (1990: 239) assumes the surface realization as given in (20); that
is, the lexical category P precedes the nominal phrase while the functional category little p
follows it.6
(20) [pP [PP P○ NP ] p○ ]
(Van Riemsdijk 1990: 239)
Building on Koopman (2000, 2010), Den Dikken (2003, 2006, 2010) proposes a more
articulated functional structure dominating the lexical category P. Establishing a range of
functional categories, both Koopman and Den Dikken decompose Van Riemsdijk’s (1990)
functional category little p. Distinguishing between a locative lexical category Ploc and a
directional lexical category Pdir, Den Dikken (2010) assumes the functional categories and
their respective hierarchical ordering in (21a) and (21b).7 Generalizing over locative [PLACE]
6Interestingly, Van Riemsdijk (1990: 240–241) observes that the surface realization of the functional category
little p and lexical category P in Hungarian seems to be the mirror image of that in German, namely that the
functional category little p precedes the nominal phrase, while the lexical category P follows it. For Hungarian,
he (1990: 240–241) thus proposes the structure [pP p○ [PP NP P○ ] ].
7Note that Koopman and Den Dikken sometimes use different labels for the functional categories of the
prepositional domain. In particular, C[PLACE] equals C(Place), Dx[PLACE] equals Deg(Place), Asp[PLACE] equals
Place, C[PATH] equals C(Path), Dx[PATH] equals Deg(Path), and Asp[PATH] equals Path. Note also that Noonan
(2010) and other scholars who propose comparable functional categories for the prepositional domain use again
other labels.
20 2. Syntax
and directional [PATH], the functional categories for spatial prepositions in (21c) can be
assumed.
(21) Functional categories in the prepositional domain:
a. Locative prepositions
C[PLACE] > Dx[PLACE] > Asp[PLACE] > Ploc
b. Directional prepositions
C[PATH] > Dx[PATH] > Asp[PATH] > Pdir
c. Spatial prepositions (generalized)
C[SPACE] > Dx[SPACE] > Asp[SPACE] > P
(Den Dikken 2010: 100, 104)
At this point, we should look at a detail that remains implicit in Den Dikken’s approach,
but that will become important in this thesis. In order to distinguish between the lexical cate-
gories Ploc and Pdir, we can (or maybe have to) assume additional features that may combine
with the lexical category feature P constituting prepositional heads. Let me be more precise:
In Chapter 5, I argue that several syntacticosemantic features are characteristic for spatial
prepositions: the features [LOC] and [AT], which can co-occur with the directional feature[±TO], and the feature [±NINF], which is characteristic of route prepositions. Prepositions that
contain only the feature [LOC] or the feature [AT] correspond to Den Dikken’s Ploc. Preposi-
tions that contain the feature [±TO] or the feature [±NINF] correspond to Den Dikken’s Pdir.
Note that I assume that both these features are not categorial in nature, but syntacticosemantic;
see Section 2.1.3.
Let us come back to Den Dikken’s approach and look first at the functional category
Dx[SPACE]. The basic motivation for assuming Dx[SPACE] is the proper treatment of measure
phrases. Focusing on Dutch, both Koopman and Den Dikken assume that spatial measure
phrases are hosted in the specifier of Dx[SPACE]. Consider the locative PP in (22); where the
measure phrase tien meter (‘ten meter’) modifies the preposition naast (‘next to’).
(22) [PP tien
ten
meter
meter
naast
next to
de
the
deur
door
] heeft
has
Jan
Jan
gezeten
sat
‘Jan sat ten meters away from the door’
Den Dikken analyzes this as in (23). The locative functional category Dx[PLACE] hosts the
measure phrase in its specifier, while Ploc realizes the preposition naast. The complement of
the preposition follows the lexical category.
(23) [ ... [ tien meter Dx[PLACE] [ ... [ Ploc=naast DP=de deur ]]]]
ten meter next.to the door
(Den Dikken 2010: 79)
2.1. Features 21
Let us now look at C[SPACE] and Asp[SPACE]. One of the main arguments for both concerns
the possible placement of so-called “r-pronouns” in Dutch. In Dutch, r-pronouns such as
er (‘there’) occur in the prepositional domain when the complement of the preposition is
pronominal. Crucially, r-pronouns do not appear in the canonical complement position to
the right of the lexical category P, but somewhere left to it. Consider the locative PPs in (24),
showing that an r-pronoun may appear both in front of and after a potential measure phrase.
This is presumably hosted by the functional category Dx[SPACE], and it occurs, in any case, in
front of the lexical preposition naast.
(24) a. [PP er
there
tien
ten
meter
meter
naast
next to
] heeft
has
Jan
Jan
gezeten
sat
b. [PP tien
ten
meter
meter
er
there
naast
next to
] heeft
has
Jan
Jan
gezeten
sat
both: ‘Jan sat ten meters away from it.’
(Den Dikken 2010: 79)
Den Dikken analyzes this as in (25). He claims that r-pronouns originate, as expected, in the
complement position of the lexical category Ploc and obligatorily move to either the specifier
of Asp[PLACE] or further up to the specifier of C[PLACE]. In (25), the symbol ti (for trace)
indicates the base position of the r-pronoun er. Furthermore, the trace and the r-pronoun are
co-indexed, as indicated by the subscript i. For details on the movement operation, I refer the
reader to Section 2.2.2.
(25) [ ⟨eri⟩ C[PLACE] [ tien meter Dx [ ⟨eri⟩ Asp[PLACE] [ Ploc=naast ti ]]]]
(Den Dikken 2010: 79)
Further motivation for the functional category Asp[SPACE] comes from deictic particles in
German. In German, unlike in English or Dutch, postpositional elements may involve a
deictic particle like hin (‘thither’) or her (‘hither’) in the case of directional prepositions (see
Van Riemsdijk and Huijbregts 2007, Noonan 2010, for instance; see also Roßdeutscher 2009
for a semantic analysis of German hin and her). Consider the data in (26).
(26) a. auf
on
das
the.ACC
Dach
roof
hin-auf/-über/-unter
thither-on/-over/-under
‘up/over/down/ onto the roof’
b. aus
out.of
dem
the.DAT
Haus
house
her-aus
hither-out.of
‘out of the house’
(Den Dikken 2010: 101)
Den Dikken argues that the functional category Asp[SPACE] may host deictic particles such as
hin and her. In particular, he (2010: 101) presents the potential morphological realizations of
Asp[SPACE] in German, given in Table 1. The two versions of Asp, i.e. the locative Asp[PLACE]
22 2. Syntax
and the directional Asp[PATH], pair with two orientational features: [PROXIMAL] meaning
‘toward the speaker’ and [DISTAL] meaning ‘away from the speaker’.
[PROXIMAL] [DISTAL]
Asp[PLACE] hier da/dort
Asp[PATH] her hin
Table 1: Realizations of German Asp[SPACE] (Den Dikken 2010: 101)
In order to derive a directional PP such as auf das Dach hinüber (‘over onto the roof’), we can
further assume that C[PATH] may host a prepositional element like über (‘over’), while the
lexical category Pdir hosts the prepositional element auf (‘upon’). Assuming that Asp[PATH]
head-moves to C[PATH], we arrive at the ultimate surface form in (26a). Section 5.5 discusses
the functional structure of spatial PPs in more detail.8
(27) [ C[PATH]=über [ ... [ Asp[PATH]=hin [ Pdir=auf DP=das Dach ]]]]
over thither on the roof
A further assumption in Den Dikken’s approach is that the directional lexical category
Pdir may embed the locative lexical category Ploc, with potential locative functional categories
intervening. The full-fledged hierarchy of functional and lexical categories of the domain
of spatial prepositions according to Den Dikken is given in (28). While I principally assume
a functional prepositional structure as presented above, I do not assume that a lexical Pdir
embeds functional prepositional structure.
(28) C[PATH] > Dx[PATH] > Asp[PATH] > Pdir > C[PLACE] > Dx[PLACE] > Asp[PLACE] > Ploc
(adapted from Den Dikken 2010: 99)
Some scholars (e.g. Alexiadou 2010a,b, Alexiadou et al. 2010) hypothesize a parallelism
of functional categories across the lexical domains V, N, A, and P. That is, the hierarchy of
functional categories is supposed to be structured parallel to one another. With regard to
the verbal, nominal, and prepositional domains, Den Dikken (2010) is explicit about this
assumption by claiming the parallelism in (29).
(29) Parallelism of functional categories:
a. C[FORCE] > Dx[TENSE] > Asp[EVENT] > V
(= C) (= T) (= Asp)
b. C[DEF] > Dx[PERSON] > Asp[NUM] > N
(= D) (= Num)
c. C[SPACE] > Dx[SPACE] > Asp[SPACE] > P
(adapted from Den Dikken 2010: 100)
8For Head Movement, I refer the reader to Matushansky (2006)
2.1. Features 23
The description of the categories in (29) also serves as a recapitulation of the functional cate-
gories for the domains presented above. The functional category C[FORCE], known simply as C
in the verbal domain, finds its matching pieces in C[DEF], known as D in the nominal domain,
and in C[SPACE] in the spatial prepositional domain. The functional category Dx[TENSE], known
as T in the verbal domain, finds its matching piece in Dx[SPACE] in the spatial prepositional
domain. For the nominal domain, Den Dikken assumes that Dx[PERSON] hosts information on
person. The functional category Asp[EVENT], known simply as Asp in the verbal domain, finds
its matching pieces in Asp[NUM], known as Num in the nominal domain, and in Asp[SPACE] in
the spatial prepositional domain.
Light categories
In addition to the lexical and functional categories discussed above, we can identify a third
type of category features that is neither clearly lexical nor clearly functional. Items of the
lexical categories normally contribute conceptually-grounded lexical-semantic information,
and they may establish thematic relations. Items of the functional categories, on the other
hand, contribute functional semantic information, for example tense in the verbal domain.
Crucially, functional categories are characterized by the fact that they do not establish thematic
relations. However, the categories that are subject of this section typically do establish
thematic relations, i.e. they behave more like lexical categories; but, unlike genuine lexical
categories, they do not contribute conceptually-grounded lexical-semantic information. Such
categories are typically referred to as light categories (e.g. Folli and Harley 2007) or semi-
lexical categories (e.g. Alexiadou 2005: 20, Meinunger 2006: 90, Harley 2013a: 34).9 I refer to
categories of this type as light categories.
First, let us look at light categories commonly assumed in the verbal domain. Recall
from the discussion on lexical categories that the lexical category V can take a complement.
The complement is often referred to as the internal argument. However, unlike the internal
argument, it is often assumed that external arguments of verbs are not introduced by the
verb itself, i.e. the lexical category V, but by an additional light category (Chomsky 1995,
Kratzer 1996, Harley 1995, 2013a, Marantz 1997, a.o.). This light category is often referred to
as little v (Chomsky 1995) or Voice (Kratzer 1996). Marantz (1984: 25) observes that the choice
of the external argument normally does not influence the interpretation of a verb, unlike the
choice of the internal argument. Consider the examples of the verb kill in (30), where the
interpretation of the verb depends on the choice of the internal argument.
(30) a. kill a cockroach = cause the bug to croak
b. kill a conversation = cause the conversation to end
c. kill an evening watching TV
= while away the time span of the evening
9I have nothing to say about the discussion concerning semi-lexicality in the sense of Van Riemsdijk (1998).
For this, see the contributions in Corver and Van Riemsdijk (2001).
24 2. Syntax
d. kill a bottle = empty the bottle
e. kill an audience = entertain the audience to an extreme degree
(Kratzer 1996: 114, glosses by Harley 2011)
Based on this observation, Chomsky (1995) proposes that a separate light verb dubbed little v,
rather than the lexical category V introduces the external argument. Kratzer (1996) relates
this light category to the voice of the verb, which is why she labels it Voice. I adopt the term
Voice for this light category.
Structurally, Voice, if present, is assumed to be hierarchically above the lexical category V,
but below the functional categories of the verbal domain. Normally, active Voice licenses an
external argument in its specifier position, whereas passive voice does not. See also Bruening
(2013) for a recent account on passive voice. External arguments are often interpreted as
agents or causers. See, e.g., Harley (2013a) for a recent discussion on the role of Voice and its
distinctness from other (semi)-lexical categories in the verbal domain.
In addition to Voice, many scholars (Marantz 1993, Collins 1997, McGinnis 1998, Pylkkänen
2000, 2002, Anagnostopoulou 2001, Cuervo 2003, McFadden 2004, McIntyre 2006, 2009,
Miyagawa and Tsujioka 2004, Lee-Schoenfeld 2006, a.o.) assume a light category for verbal
applicatives, i.e. Appl (or with various other labels, such as vappl). Pylkkänen (2002: 17)
adduces the data from the Bantu language Chaga in (31), originally discussed by Bresnan
and Moshi (1990: 148–149), to motivate the category Appl. Unlike, for example, English
or German, where applicatives are normally not morphologically marked on verbs, Chaga
shows morphological marking on a verb when a benefactive argument is licensed in an
applicative structure. Consider the examples in (31), where the morpheme -í- on the verb
indicates an applicative construction with an additional argument (in boldface).
(31) a. N-a˝-ı˝-lyì-í-à
FOC-1S-PR-eat-APPL-FV
m-kà
1-wife
k-élyá
7-food
‘He is eating food for his wife.’
b. N-a˝-ı˝-zrìc-í-à
FOC-1S-PR-run-APPL-FV
mbùyà
9 friend
‘He is running for a friend.’
(Bresnan and Moshi 1990: 148–149)
One crucial applicative property, with respect to argument structure, is that applicatives
introduce a further argument – the applied argument – in their specifier position. Semantically,
applied arguments can serve, a.o., as benefactives or malefactives of the respective verb
(Pylkkänen 2002, Lee-Schoenfeld 2006, McIntyre 2006, 2009).10 An example of an applicative
construction in English is given in (32).
(32) I baked him a cake.
(Pylkkänen 2002: 17)
10Note that McIntyre uses the term “ficiaries” to cover both beneficiaries and maleficiaries.
2.1. Features 25
Examples from German, where applied arguments are usually marked with dative case, are
given in (33) and (34).11 Sometimes, an (additional) possessive interpretation between the
applied argument and the direct object is possible, as in (34).
(33) a. Ihm
him.DAT
ist
is
ein
a.NOM
Hund
dog
gestorben.
died
‘He had a dog die.’
b. Jemand
someone
hat
has
mir
me.DAT
das
the
Auto
car
geklaut.
stolen
‘I had someone steal my car.’
(McIntyre 2006: 186)
(34) Mein
my
Bruder
brother
hat
has
der
the.DAT
Mami
mom
das
the
Auto
car
zu
to
Schrott
scrap
gefahren.
driven
‘My brother totaled mom’s car (totaled the car on mom).’
(Lee-Schoenfeld 2006: 104)
Basically two distinct positions for applicatives are identified: one hierarchically above
and one hierarchically below the lexical category V.12 This gives rise to the terms high
applicative and low applicative, respectively. High applicatives are located between Voice
and V, while low applicatives are located below V. These distinct positions are justified
semantically. High applicatives relate an applied argument to the event denoted by the
verb (event-related applicative). Low applicatives relate an applied argument to the internal
argument of the verb (entity-related applicative). McIntyre (2006, 2009) assumes that German
shows both high and low applicatives, although some authors reject this view. Pylkkänen
(2002), for example, treats all German applicatives as low ones. I follow McIntyre in assuming
that German shows indeed both high and low applicatives. (35a) is an instance of a high
applicative, as the individual denoted by the applied argument (i.e. him) is affected by the
event denoted by the verb (i.e. the breaking of the plate), not only by the entity denoted by
the internal argument of the verb (i.e. the plate). (35b) is an instance of a low applicative as
the individual denoted by the applied argument (i.e. him) receives the entity denoted by the
internal argument (i.e. a book), establishing a possession relation between the two.
(35) a. (weil)
since
Anne
Anne
ihm
him.DAT
den
the.ACC
Teller
plate
zerbrach
broke
‘since Anne broke his plate’
b. (weil)
since
ich
I
ihm
him.DAT
ein
a.ACC
Buch
book
gab
gave
11McIntyre (2006, 2009) labels the applicative category Vdat because he predominantly discusses German
data where this category is assumed to introduce an applied argument with dative morphology.
12Note that some scholars assume more (or less) structural types of applicatives. Cuervo (2003), for instance,
argues for three main types of applicatives. Next to the commonly assumed high and low applicatives, she
assumes a so-called “affected applicative,” which embeds under a dynamic verb and requires a stative predicate
in its complement.
26 2. Syntax
‘since I gave him a book’
(McIntyre 2006: 186–187)
Let us summarize the light categories for the verbal domain presented above. In addition
to the lexical category V, we can assume the light category Voice introducing external argu-
ments and the category Appl introducing applied arguments. While Voice is hierarchically
above all other (semi)-lexical categories in the verbal domain, Appl may be above (Applhigh)
or below (Appllow) the lexical category V. (36) summarizes this picture.
(36) Light categories in the verbal domain:
Voice > Applhigh > V > Appllow
Let us now look at a light category proposed for the prepositional domain by Svenonius
(2003). Svenonius hypothesizes an external-argument-introducing light category hierarchi-
cally above the lexical category P. Adopting the term from Van Riemsdijk (1990), Svenonius
labels this light category little p. However, in terms of the classification of categories applied
in this thesis, Van Riemsdijk’s (1990) little p and Svenonius’ (2003) little p do not have the
same status. In particular, Van Riemsdijk’s little p is a functional category, because it is
not assumed to establish any thematic relation; while Svenonius’ little p is a light category,
because it is in fact assumed to establish a thematic relation.13
Prepositions often serve to express spatial relations between entities. A cognitive notion
that is relevant in the context of spatial relations is the relation between Figure and Ground
as defined by Talmy (1975, 2000) (cf. Section 4.2). With respect to prepositions, Svenonius
(1994, 2003) observes an uneven behavior of the argument denoting the Ground, on the one
hand, and the argument denoting the Figure, on the other. First, a preposition may select the
Ground, but not the Figure. In particular, he (2003: 435) posits the generalizations in (37).
(37) a. P c-selects the Ground
b. P does not c-select the Figure
(Svenonius 2003: 435)
Second, a preposition may place selection restrictions on the Ground, but not on the Figure.
Third, in languages with morphological case, a preposition may case-mark the Ground
argument but not the Figure argument; see Haselbach and Pitteroff (2015) and Section 6.4
of this thesis for a morphological case approach to prepositions. Svenonius (2003) proposes
that the Figure argument is introduced in the specifier of a light category called little p, while
the Ground argument is introduced in the complement position of the lexical category P.
Assuming that the cognitive relation between Figure and Ground is reflected in prepositional
syntax, Svenonius (2003: 435) draws a parallelism between the prepositional and verbal
domain by stating that “the close relationship between P and the Ground on the one hand,
13This thesis distinguishes the two categories under discussion by representing Van Riemsdijk’s (1990) little
p with an upright character and Svenonius’ (2003) little p with an italic character.
2.1. Features 27
and the more distant relationship between P and the Figure on the other, is reminiscent of the
asymmetric relationship a verb has with its two canonical arguments, the Agent and Patient
[...].” Furthermore, he (2003: 436) concludes that “the Figure is the ‘external’ argument of the
preposition.” Building on these considerations, Svenonius (2003) formulates the so-called
Split P Hypothesis, stating that a separate prepositional light category, little p, introduces an
external argument in its specifier position, in parallel to Voice in the verbal domain (Kratzer
1996). In (38a), for example, hay is the Figure and the wagon is the Ground. Svenonius analyzes
the prepositional structure as in (38b), where the Ground appears as the complement of the
lexical category P, while the Figure appears in the specifier of little p.
(38) a. We loaded hay on the wagon.
b. [ DP=hay little p [ P=on DP=the wagon ]]
(adapted from Svenonius 2003: 436)
Note that this thesis does not dwell on the Split P Hypothesis any further, even though it
could be incorporated here in principle. In Chapter 5, I propose a prepositional light category
in order to account for goal and source prepositions derived from locative prepositions. I
label this light preposition as Q. Hierarchically, Q is between little p and P. (39) shows the
light category little p hierarchically above the lexical category P.
(39) Light categories in the prepositional domain:
little p > Q > P
Let us summarize the discussion on light categories. Next to the fundamental split of
categories into lexical categories (V, N, A, and P), on the one hand, and functional categories
(e.g. C, T, or D), on the other hand, we identified so-called light categories, which are struc-
turally in the middle. Like lexical categories, light categories may introduce arguments and
establish thematic relations. Unlike lexical categories, however, light categories normally do
not contribute conceptually-grounded lexical-semantic information. For the verbal domain,
we can identify two light categories. First, the light category Voice (Kratzer 1996) is assumed
to introduce external arguments interpreted as agents or causers. Second, the light category
Appl for applicatives (cf. Pylkkänen 2000, a.o.) is assumed to introduce applied arguments
interpreted as benefactor or malefactors. Appl comes in two versions: one above (Applhigh)
and one below (Appllow) lexical category V. For the prepositional domain, Svenonius (2003)
proposes the light category little p, in analogy to Voice, that is supposed to introduce an
external argument, which may be interpreted as a Figure with respect to a Ground (Talmy
1975, 2000).
28 2. Syntax
2.1.3 Syntacticosemantic features
This section briefly addresses the class of syntacticosemantic (synsem) features (40); that
is, those features from the universal inventory of features that have both a syntactic and a
semantic impact.
(40) Syntacticosemantic (synsem) features:
Features from the universal inventory of syntacticosemantic features [...].
(Embick 2015: 6)
One group of synsem features are the so-called “φ-features” (phi-features) which normally
comprise features for person, number, and gender (e.g. Adger and Harbour 2008: 2, Bobaljik
2008: 295). One characteristic of φ-features is that they are motivated by semantic and
morphological facts (Adger 2003: 45).14 Furthermore, φ-features are typically subject to
predicate-argument agreement, such as subject-verb agreement. For example, the Russian
verbs in (41a) agree with the singular subjects in gender (feminine), while the verbs in (41b)
agree with the plural subjects in number (plural).
(41) a. Devocˇk-a
girl-FEM
poigral-a
played-FEM
v
in
komnate.
room
Potom
then
on-a
PRON-FEM
pospal-a.
slept-FEM.
‘The girl played in the room. Then she slept.’
b. Devocˇk-i
girl-PL
poigral-i
played-PL
v
in
komnate.
room
Potom
then
on-i
PRON-PL
pospal-i.
slept-PL
‘The girls played in the room. Then they slept.’
(Bobaljik 2008: 295)
Focusing on German, I will briefly present in the following the commonly assumed φ-
features for number, gender, and person. German shows singular and plural number. That is,
regarding the category number, we can assume the binary features [±SG] for singular and[±PL] for plural. Even though, at first glance, they seem to be complementary, that is, [+SG]
seems to equal [−PL] and vice versa, we should assume both of them. Consider a language
that has dual next to singular and plural number, such as the Uto-Aztecan language Hopi.
With a binary feature system involving a singular and a plural feature, we can account for
dual number by stating that dual number is specified as [+SG,+PL]. In fact, dual number in
Hopi seems to be constructed by means of singular and plural morphology in combination,
as illustrated in (42c).
(42) a. Pam
that
taaqa
man.SG
wari
ran.SG
‘That man ran.’
14Note that φ-features and other synsem features often relate to a language’s inflectional morphology, which
is why they are alsp referred to as morphosyntactic features (Stump 2005: 50). In this thesis, I occasionally use
the term ‘morphosyntactic’ in order to refer to both morphology and syntax at the same time.
2.1. Features 29
b. Puma
those
taPtaq-t
man.PL
yuPti
ran.PL
‘Those men ran.’
c. Puma
those
taPtaq-t
men.PL
wari
ran.SG
‘Those two men ran.’
(Adger 2003: 28)
We can conclude from the Hopi data in (42) that [±SG] and [±PL] are in fact not in comple-
mentary distribution. See also a similar discussion on this topic in Adger (2010: 192–193). For
the sake of consistency, I assume – also for German, which does not have dual, but obviously
singular and plural – both number features [±SG] and [±PL]. Considering the category of
grammatical gender, German has feminine, masculine, and neuter. Using a binary feature
system, we have, in principle, several options to express this. A natural way to account
for this three-way gender distinction is to assume a binary feature [±FEM] for feminine and
a binary feature [±MASC] for masculine. In this way, we can define feminine gender as[+FEM,−MASC], masculine gender as [−FEM,+MASC], and neuter gender as [−FEM,−MASC].
Considering the category of grammatical person, German has first person, second person,
and third person. In order to account for this, we can assume the binary features [±1] and[±2]. From a semantic point of view, it makes sense to assume that these features correlate
with the two interlocutors ‘speaker’ and ‘hearer’. With the two person-features, we can
represent the tripartite of person in German as follows. For first person, the speaker, we can
assume the feature bundle [+1,−2], for second person, the hearer, the feature bundle [−1,+2],
and for the third person, neither speaker nor hearer, the feature bundle [−1,−2].
Let’s turn away from the discussion on φ-features and, instead, take a brief look at
the synsem features proposed in Chapter 5, for the domain of spatial prepositions. I will
argue that, considering German, we have evidence for at least two locative synsem features.
I label them [LOC] and [AT]. Anticipating a classification of spatial prepositions along
a geometric dimension (cf. Section 5.1.2), I argue that the feature [LOC] underlies locative
pseudo-geometric and locative geometric prepositions. Both geometric and pseudo-geometric
prepositions can derive goal and source prepositions. Therefore, I will argue that the synsem
feature [LOC] can be dominated by the directional synsem feature [±TO]: [+TO] derives goal
prepositions, while [−TO] derives source prepositions. Furthermore, the locative synsem
feature [AT] is characteristic for non-geometric prepositions, which can also derive goal
and source prepositions. Thus, I assume the directional synsem feature [±TO] that can also
dominate [AT]. I will argue additionally that the feature [±NINF] (for non-initial, non-final
paths) is characteristic for route prepositions.
30 2. Syntax
2.1.4 Content features
Let us now look at Content features, that is, at the features that make up the Content list. By
assumption, Content features are inserted into derivations after the syntactic computation is
accomplished, but before structures are sent off to the interfaces. In particular, I assume that
Content features are inserted into Root positions (cf. Section 2.3) at Spell-Out. By insertion
into Root positions, Content features become Roots. On these assumptions, much of the
discussion in the literature on roots is also relevant for Content features (e.g. Marantz 1997,
Embick 2000, Harley and Noyer 2000, Pfau 2000, 2009, Arad 2003, 2005, Borer 2005a,b, 2013,
Acquaviva 2009a,b, Siddiqi 2009, Acquaviva and Panagiotidis 2012, Haugen and Siddiqi
2013, the contributions in Alexiadou et al. 2014, as well as Harley 2014 and the commentaries
thereon).
It is sometimes argued that prepositions are functional (e.g. Grimshaw 1991, 2000, 2005,
Baker 2003, Botwinik-Rotem 2004), which would ultimately mean that prepositions do not
involve Roots. However, Svenonius (2014: 442) states “that at least some functional items
must have conceptual content [...]”. In particular, he (2014: 442) argues that the English
prepositions
[...] in and on [...] behave identically, just like cat and mouse do. But unlike[PLURAL] or [DEFINITE], the distinction between in and on is not an independently
motivated syntactically relevant feature. For some pairs, such as over and under,
there is enough crosslinguistic data to suggest that the distinguishing feature is
never syntactically relevant (that is, no language has a grammatically significant
distinction between [UP] and [DOWN] like the one observed for [±DEFINITE]).
The distinguishing feature Svenonius alludes to in his statement can be attributed to Content
features (Roots) inasmuch as they are supposed to represent idiosyncratic differences that
are irrelevant to the computational system of grammar (Marantz 1995, 1996). Hence, I take
Svenonius’ statement as an invitation to assume that – at least some – prepositions can involve
Content features.
Generally, Content features are (i) language-specific, (ii) conceptually grounded, and (iii)
non-generative features that (iv) receive a semantic interpretation at LF and a morphological
realization at PF. I briefly discuss these four claims in the following.
Regarding the claims that Content features are language-specific and conceptually grounded,
let me point to Adger’s (2003: 37–38) statement concerning semantic features, the conception
of which comes close to my own conception of Content features.
It seems likely that semantic features are universal, common to us all, but that
different languages group semantic features in different ways so as to reflect the
artefacts and concepts that are important to the culture in which the language
is spoken. Of course, this cultural variation should not be over-emphasized: an
2.1. Features 31
enormous amount of what we think, perceive, taste, hear, etc. is common to
all human beings as a result of our shared cognitive and physical limitations,
and similar or identical collocations of semantic features will be involved in all
languages for the lexical items that correspond to these concepts. It may even be
the case that it is the universal aspect of our mental capacities that give rise to
basic semantic features.
Regarding the claim that Content features are conceptually grounded, I take the view
that Content features are like indexes (Pfau 2000, 2009, Acquaviva 2009a, Harley 2014). In
particular, I assume that Content features serve as abstract differential indexes to the effect
that they differentiate various concepts, which are not grammatical in nature. That is, Content
features encode that piece of information that differentiates two distinct grammatical entities
(e.g. phrases or clauses), with all else being equal, i.e. when all bits of grammatically-
relevant information have been abstracted away. In this sense, my conception of Content
features comes close to Acquaviva’s (2009a) conception of Roots as differential indexes. He
(2009a: 16) states that “the root DOG acts as an index that makes the noun dog different from
nouns based on other roots [e.g. from the noun cat]. In the abstract syntactic representation
before Vocabulary insertion, roots do not mean anything by themselves, but act as name-tags
which define identity and difference. Their function is differential, not substantive.” That is,
Acquaviva’s roots are like the indices 1 and 2 in (43).
(43) He1 likes broccoli, but he2 doesn’t.
(Acquaviva 2009a: 16)
Consider the two clauses in (44). Arguably, the two clauses are syntactically, semantically,
and morphologically parallel except for the choice of head noun of the direct object. It is cat
in (44a), while it is dog in (44b); the difference between which is – I think – not a grammatical
one. I assume that this kind of this difference is expressed by Content features. That is, the
direct object DP in (44a) contains the Content feature [©CAT], while the direct object DP in
(44b) contains the Content feature [©DOG] instead.15 Apart from that, everything else in the
two clauses is arguably the same.
(44) a. John petted a fluffy cat.
b. John petted a fluffy dog.
In my approach, Content features are conceptually grounded not to the effect that they
have substantive semantic meaning – in fact, I assume that a Content feature is meaningless
in and of itself – but to the effect that they differentiate concepts. The question whether
Roots – which in a way correspond to my Content features – are contentful is by no means
uncontroversial. Some scholars hypothesize that Roots inherently relate in some (under-
specified) way or another to conceptual (or semantic) features, while other scholars reject
15In general, I indicate Content features with the prefix ©.
32 2. Syntax
this hypothesis. For instance, Siddiqi (2009: 18) states that “roots are abstract morphemes
linked to a basic concept (the root for cat is
√
CAT)”, while Borer (2014: 356) states that Roots
“never have Content it goes without saying that they have no formal semantic properties of
any kind.” I think that this opposition reveals two fundamentally different conceptions of
Roots. In principle, scholars advocating contentful Roots take a semantics-based conception
of Roots, while scholars rejecting contentful Roots take a morphology-based conception of
Roots. By advocating the conception of Content features, I follow those scholars who take a
semantics-based view of Roots.
Consider Rappaport Hovav’s (2014) argument in favor of contentful Roots based on
homonymy. In particular, she discusses a textbook example of homonymy, viz. the two
English words bank (‘riverside’) and bank (‘financial institution’). Even though the two nouns
might be etymologically related, they synchronically do not share a single index-identified
Root. Rather, they only share a single morphophonological exponent, namely /bæNk/. This
is because the morphosyntactic contexts, in which the two words/Roots appear, do not
disambiguate the respective meanings. All else being equal, the sentence (45) is ambiguous
only with respect to the lexical ambiguity of bank.
(45) He went to the bank.
(Rappaport Hovav 2014: 433)
The fact that the sentence (45) preserves exactly the lexical ambiguity under discussion shows
that the two instances of bank are in contrastive distribution. This leads Rappaport Hovav
(2014: 434)
[...] to the conclusion that there is a single string of phonemes – a single VI –
which represents two distinct roots. But this is really just another way of saying
that these two roots are individuated semantically. Thus [...] the criterion for
individuation in this case is purely semantic.
The semantic individuation criterion that Rappaport Hovav alludes to in her statement is
best captured in terms of differential indexes on conceptual structure, i.e. Content features.
Regarding the claim that Content features are non-generative, I take the view that they
have no bearing on syntactic computation. In particular, I assume that Content features do
not project syntactic structure and, thus, they do not take arguments (Alexiadou and Lohndal
2013, 2014, Alexiadou 2014, Borer 2014, De Belder and Van Craenenbroeck 2015). Content
features do not affect the syntactic derivation in any way. Assuming that Roots are defined
derivationally (cf. Section 2.3), I take the view that De Belder and Van Craenenbroeck’s (2015)
operation Primary Merge generates an insertion site for Content features. The structural
position generated by Primary Merge is the Root position, which has the property that
whatever is in it cannot project.
Regarding the claim that Content features can affect the semantic interpretation at LF
and the morphological realization at PF, I follow Rappaport Hovav (2014: 432) in assuming
2.1. Features 33
that roots, i.e. Content features, qua abstract morphemes are “identified by their bipartite
nature” and that they are “individuated by a link between sound (a VI) and meaning (an
instruction for interpretation).” That is, Content features are associated with Encyclopedia
Items at LF and with Vocabulary Items at PF.16 In that sense, Content features are not different
from universal Lexicon features.
In this thesis, I assume two kinds of Content features. For one, I assume that idiosyncratic
Content features express the arbitrary (morphological and semantic) differences between
two grammatical entities, with all else being equal. For instance, the Content features [©CAT]
and [©DOG] discussed above are instances of idiosyncratic Content features.17 In a nominal
context, they give rise to the nouns cat and dog. Idiosyncratic Content features are what
Arad (2005: 99) alludes to by stating that “each root [i.e. Content feature] specifies some
idiosyncratic core that differs from other cores, or roots.” In addition to idiosyncratic Content
features, I assume highly abstract Content features.18 I assume that the function of abstract
Content features is (at least) twofold. On the one hand, they can relate to general perceptually-
grounded concepts like ‘verticality’ or ‘interiority’, while, on the other hand, they can bundle
with idiosyncratic Content features and thereby give rise to particular aspects of meaning
of the idiosyncratic Content features. Even though this bundling seems to be systematic
to some extent, it can be – from a grammatical point of view – arbitrary. Before I illustrate
this kind of bundling, let us first look at a case where abstract Content features relate to
perceptually-grounded concepts.
Content features can become Roots (cf. Section 2.3), and so can abstract Content features.
Abstract Content features can become Roots as singletons; or they can become Roots as
feature bundles together with idiosyncratic Content features. Let me flesh out these two
possibilities with an example. Let us first look at the case where abstract Content features
become Roots as singletons. I claim that the abstract Content feature [ℵ] as a singleton relates
to the concept of interiority when being inserted into a Root position of a spatial preposition.
However, it can give rise to different LF-interpretations in different structural environments.
In particular, the abstract Content feature [ℵ] gives rise to the LF-predicate ‘in’ in the Root
position of a locative preposition, while it gives rise to the LF-predicate ‘durch-bar’ in the Root
position of a route preposition. Anticipating the precise interpretation algorithm at LF, I
claim that German has an Encyclopedia Item that provides the LF-instructions for P in (46);
cf. Section 5.4.
16Exceptions of the general rule that Content features have both a semantic interpretation at LF and a
morphological realization at PF are, e.g., Harley’s (2014) caboolde items (aka cran-morphemes). I do not discuss
such mismatches here, but refer to the respective literature, especially the comments on Harley (2014).
17Note that I indicate idiosyncratic Content features with the prefixed symbol ©. Note also that the labeling
of Content features is arbitrary – as it is, in principle, the case for all features. Instead of labeling a Content
feature [©DOG], one could have labeled it [©5S43FY] without any difference. Nevertheless, for the sake of
comprehensibility, I generally choose transparent feature labels.
18I represent abstract Content features by means of Hebrew characters, e.g. ℵ (aleph), ℶ (beth), ℷ (gimel), etc.
34 2. Syntax
(46) LF-instructions for P (sketch):
a. P ↔ [durch-bar(v, x)∧ ...] / “[ℵ] in Root position of route P”
b. ↔ [in(r, x)] / “[ℵ] in Root position of locative P”
Both the predicate in, which denotes a relation between a region r and a material object x,
to the effect that r is the interior of x; and the predicate durch-bar, which denotes a relation
between a spatial path v and a material object x, to the effect that v is a path through x, relate
to the concept of interiority. I refer the reader to Section 5.3.1 for a model-theoretic definition
of the LF-predicates in and durch-bar.
Let us now look at a case where abstract Content features become Roots as feature bundles,
together with idiosyncratic Content features. I claim that, in such cases, an abstract Content
feature can give rise to a certain aspect of meaning of the concept that is differentiated by the
respective idiosyncratic Content feature it bundles with. That is, various abstract Content
features can bring out various aspects of meaning of idiosyncratic Content features in the
very same structural context. Across idiosyncratic Content features, this can be systematic
to some extent, but, in general, the bundling of abstract and idiosyncratic Content features
is more or less arbitrary, from a grammatical point of view. For instance, the idiosyncratic
Content feature [©CUBA] relates to the geographic entity Cuba. The German noun Kuba
(‘Cuba’), however, can be interpreted as a state, i.e. the state of Cuba; or as an island, i.e. the
island of Cuba. This difference is clearly not a grammatical difference. Thus, I do not attribute
this difference to a (synsem or category) feature from the Lexicon. Instead, I claim that the
idiosyncratic Content feature [©CUBA] can bundle with abstract Content features, e.g. [ℵ]
and [ℷ], and thereby the various interpretations of Kuba can arise. Both the Content feature
bundle [©CUBA,ℵ] and the Content feature bundle [©CUBA, ℷ] can be interpreted in the very
same nominal Root position as the noun Kuba. But while the feature bundle [©CUBA,ℵ]
is interpreted as the Cuban state (47a), the feature bundle [©CUBA, ℷ] is interpreted as the
Cuban island (47b). That is, German has the Encyclopedia Items that provide the respective
LF-predicates in (47); cf. Section 5.4 and, in particular, (362) on page 220.
(47) LF-instructions for the noun Kuba (sketch):
a. N ↔ [State-of-Cuba(x)] / “[©CUBA,ℵ] in Root position of N”
b. ↔ [Island-of-Cuba(x)] / “[©CUBA, ℷ] in Root position of N”
This kind of Content-feature bundling is arguably systematic across comparable idiosyn-
cratic Content features. Consider the German noun Malta, which behaves identical to Kuba.
That is, the Content feature bundles [©MALTA,ℵ] and [©MALTA, ℷ] are LF-interpreted as the
Maltese state and the Maltese island, respectively. This is simply due to the fact that Malta can
be (conceptionalized as) both a state and an island. However, this kind of systematicity finds
its limitations in the state of affairs of the world. In the first place, there is no grammatical
reason why Content feature bundles such as [©HAITI, ℷ] or [©HISPANIOLA,ℵ], for instance,
2.2. Building structure 35
should not exist. I claim that the respective interpretations are simply not available (indicated
with #), because a state of Hispaniola (48c) and an island of Haiti (48d) do not exist in the
(actual) world.19 Hispaniola is an island (48a) and Haiti is a state (48b). See also Section 5.4
and, in particular, (359) on page 218.
(48) LF-instructions for the nouns Hispaniola and Haiti (sketch):
a. N ↔ [Island-of-Hispaniola(x)] / “[©HISPANIOLA, ℷ] in N’s Root pos.”
b. ↔ [State-of-Haiti(x)] / “[©HAITI,ℵ] in N’s Root position”
c. ↔ #[State-of-Hispaniola(x)] / “[©HISPANIOLA,ℵ] in N’s Root pos.”
d. ↔ #[Island-of-Haiti(x)] / “[©HAITI, ℷ] in N’s Root position”
The interpretation of abstract Content features depends on the idiosyncratic Content
feature it bundles with. In particular, I do not claim that bundling with the abstract Content
feature [ℵ] always yields a state reading and that bundling with [ℷ] always yields an island-
reading. This is a peculiarity in the domain of idiosyncratic Content features relating to
geographic entities. In other conceptual domains, the abstract Content features [ℵ] and [ℷ]
can give rise to other aspects of meaning. In fact, I claim that abstract Content features form
classes in particular conceptual domains (more or less) systematically. Staying within the
domain of geographic entities, I assume that the abstract Content feature [ℵ] is not exclusively
characteristic of state readings. Combined with the other idiosyncratic Content features it
can also be characteristic of city readings, territory readings, region readings, etc. Likewise,
the abstract Content feature [ℷ] is not exclusively characteristic of island readings. It can also
be characteristic of mountain readings, square readings, etc. Furthermore, even though the
bundling of abstract and idiosyncratic Content features is systematic to some extent, it is
arbitrary from a grammatical point of view. There is no grammatical reason for why bundling
with [ℵ] can yield state readings, for instance, but not island readings; nor for why, the other
way round, [ℷ] can yield island readings, but not state readings. Such generalizations are
language-specific and not universal.
2.2 Building structure
This thesis builds on principles of the Minimalist Program (MP) proposed by Chomsky (1995).
MP applies Bare Phrase Structure (BPS) as its phrase structure module. Section 2.2.1 lays
out the tree-structural relations and projection principles of BPS; Section 2.2.2, the major
operations of BPS. Based on insights from that, Section 2.2.3 derives the notions complement,
specifier, and adjunct. Then, that section also discusses briefly the differences between
19Note that this might, of course, change. For instance, between 1804 and 1844, the island of Hispaniola had
the name Haiti. (Thanks to Kerstin Eckart (pc) for pointing that out to me.) In fact, at that time, the name Haiti
denoted both an island and a state, like Kuba and Malta today.
36 2. Syntax
BPS and X-bar Theory (XbT), which is the phrase structure module of Government and
Binding (GB) (Chomsky 1981, Haegeman 1994, a.o.), MP’s predecessor.
2.2.1 Tree-structural relations and projection
Let us begin with two basic tree-structural relations, namely motherhood and sisterhood. In
(49), Z is the ‘mother’ or ‘mother node’ of X and Y. Conversely, X and Y are ‘daughters’ or
‘daughter nodes’ of Z. X is the ‘sister’ or ‘sister node’ of Y and vice versa.
(49) Z
YX
Another important tree-structural relation is constituent-command (c-command). In
general parlance, c-command gives one for every node its sisters and the descendants of the
sisters. I adopt the definition of c-command put forth by Adger (2003: 117) in (50).
(50) C-command:
A node α c-commands a node β if and only if α’s sister either
a. is β, or
b. contains β.
(Adger 2003: 117)
With this straightforward definition of the structural relation of c-command, we can identify
the following c-command relations in the exemplary tree in (51). The node X c-commands
the nodes Y, V, and W. The node Y c-commands the node X and the node V c-commands the
node W which itself c-commands the node V. The node Z does not c-command any other
node.
(51) Z
Y
WV
X
It is generally assumed in MP that syntactic nodes consist of features. This thesis straight-
forwardly adopts the notion of projection “where features from a daughter node project on to
the mother node in a syntactic object” (Adger 2003: 76). In this context, it is worth noting that
I consider a syntactic object to be either an element taken from the Numeration (normally a
head) or a complex element that is the output of a syntactic operation. Assume the category
X merges with the category W. One of the categories projects. Let us assume here, that X
projects. The new complex syntactic object is therefore also of category X. We will further
assume that this complex syntactic object merges with the category Y. Assume again that X
2.2. Building structure 37
projects. Assume also that now no further merge takes place where X projects. The respective
structure is represented by the tree diagram in (52).
(52) X
X
WX
Y
A crucial property of BPS is that the phrasal status of distinct levels of projection is
derived when the structure has been built; unlike in X-bar Theory (cf. Section 2.2.3), where
the phrasal status is representationally given in a template predetermining the respective
levels of projection. In the tree in (52), we find distinct levels of projection of X. Chomsky
(1995) defines them as in (53).
(53) Levels of Projections:
a. A minimal projection X○ (or X) is a functional head selected from the numera-
tion.
b. A maximal projection XP (or X”) is a syntactic object that does not project.
c. An intermediate projection X’ is a syntactic object that is neither an X○ nor an
XP.
(Chomsky 1995: 242–243)
Let us now apply the definitions of the levels of projection to our exemplary tree in (52),
which yields the tree in (54).
(54) X
X
WX
Y
→ interpreted as XP
→ interpreted as X’
interpreted as X○ ←
(Boeckx 2006: 176)
According to (53b), the syntactic objects Y and W are interpreted as phrases, i.e. YP and
WP, respectively, because they do not project here.20 In our example, the lowest X node
is interpreted as a minimal projection X○, the highest X node is interpreted as a maximal
projection, and the middle X node is interpreted as an intermediate projection X’. We obtain
the customary tree structure diagram in (55).
20Note that, in this exemplary tree, Y and W can also be interpreted as minimal because they are items
selected from the numeration. Later, I will use the notation Y○/YP for this configuration.
38 2. Syntax
(55) XP
X’
WPX○
YP
Under this perspective, the terms ‘maximal projection’ and ‘minimal projection’ are derived
properties in BPS. A minimal projection is simply any node which does not dominate a copy
of itself, and a maximal projection is any node which is not dominated by a copy of itself
(Harley 2013b: 66).
2.2.2 Syntactic operations
Let us now look at the syntactic operations for structure building in Bare Phrase Structure
(BPS). We can identify the syntactic operations Merge, Adjoin, Agree, and Move. This section
presents them in turn.
Recall from Section 2.1.1 that we identified uninterpretability as a property of features. In
particular, uninterpretable features, which are prefixed with u, figure in syntactic structure
building. Adger (2003) assumes that uninterpretable features may not be present in the
structure when the structure is sent off to the interfaces, i.e. at Spell-Out. In particular, he
formulates the general constraint of Full Interpretation as given in (56).
(56) Full Interpretation:
The structure to which the semantic interface rules apply contains no uninterpretable
features.
(Adger 2003: 85)
Hence, all uninterpretable features must be deleted in the course of the syntactic derivation
before the structure is sent off to the interfaces at PF. An uninterpretable feature [uF] is
deleted by checking it with a matching interpretable feature F.21 Therefore, Adger formulates
the checking requirement in (57).
(57) Checking Requirement:
Uninterpretable features must be checked, and once checked, they delete.
(Adger 2003: 91)
One tree-structural relation under which checking can take place is sisterhood, as formulated
in (58).
(58) Checking under Sisterhood:
An uninterpretable c-selectional feature [uF] on a syntactic object Y is checked when
21Note that the function of the u-prefix is similar to the function of Sternefeld’s (2007: 35) star features: Ein
Baum ist wohlgeformt, wenn jedes Merkmal [∗α∗] des Baumes (genau) ein lokales Gegenstück der Form [α] hat (A tree is
well-formed, if each feature [∗α∗] of the tree has (exactly) one local counterpart of the form [α]).
2.2. Building structure 39
Y is sister to another syntactic object Z which bears a matching feature F.
(Adger 2003: 85)
Merge
For building a binary tree structures, Chomsky (1995) formulates the core recursive syntactic
operation Merge, which inputs two syntactic objects and outputs one syntactic object con-
taining the two. In (59), I adopt Adger’s (2010) definition of Merge, which follows the one by
Chomsky (1995: 243–244).
(59) Merge:
a. Lexical items are syntactic objects.
b. If A is a syntactic object and B is a syntactic object,
then Merge of A and B, K = {A,{A, B}}, is a syntactic object.
(Adger 2010: 186)
The reason why I adopt Adger’s definition instead of Chomsky’s original definition is that
it already includes the notion of projection. Chomsky (1995: 243) defines K = {γ,{α, β}},
with γ being the outputted label of K. Chomsky (1995: 244) then argues that one of the two
constituents α or β necessarily “projects and is the head of K”. Projection means ‘percolation’
or ‘handing over’ of features to the label. Consider Chomsky’s original definition of Merge
and suppose that α projects. In this case, we can substitute γ with α, arriving at Adger’s
definition. K, as defined above, is usually represented in bracket notation (60a) or as a
tree-diagram (60b).
(60) a. [X X Y ]
b. X
YX
With the checking requirement formulated in (57) and with the idea that checking can take
place under sisterhood (dubbed as ‘pure checking’ by Adger 2003: 168), as formulated in
(58), we can motivate the syntactic operation Merge. Adger describes the syntactic operation
Merge, as in (61).
(61) a. Merge applies to two syntactic objects to form a new syntactic object.
b. The new syntactic object is said to contain the original syntactic objects, which
are sisters, but which are not linearized.
c. Merge only applies to the root [i.e. topmost] nodes of syntactic objects.
d. Merge allows the checking of an uninterpretable [...] feature on a head, since it
creates a sisterhood syntactic relation.
(Adger 2003: 90–91)
40 2. Syntax
Feature checking under Merge can be represented as in (62).
(62) X
YX[uY]
The operation Merge is restricted such that it can only target the topmost node of a
syntactic tree.22 Adger formulates this condition as the Extension Condition given in (63).
Chomsky (1995: 190) refers to this condition as ‘Extend Target’.
(63) Extension Condition:
A syntactic derivation can only be continued by applying operations to the root [i.e.
topmost] projection of the tree.
(Adger 2003: 95)
Suppose a configuration as in (64), where the node X merges with the node Y, and X projects.
The Extension Condition restricts the derivation such that any other node W can only Merge
with the structurally higher node X, but not with the lower instance of X or with Y.
(64) X
YX
Merge W →
☇ Merge W → ←Merge W ☇
If at least one syntactic object that is input to Merge is taken from the Numeration, we
speak of external Merge. The reason for referring to this as external Merge is the following.
If the two syntactic objects α and β merge and one (suppose β) is taken from the Numeration,
it is essentially external, i.e. not contained in one of the two. External Merge contrasts with
internal Merge, which amounts to the syntactic operation Move which we will discuss below.
I usually refer to external Merge simply as Merge.
Unlike Adger, who defines an argument “as a constituent in a sentence which is assigned
a θ-role by a predicate” (Adger 2003: 81), I consider an argument to be the syntactic object
selected under the operation Merge. In turn, the syntactic object that selects in any Merge
operation is referred to as the head (Adger 2003: 91). This definition of a head leads to a
mismatch of the term head in BPS, as compared to X-bar Theory. In X-bar Theory, minimal
projections are defined as heads, while in BPS intermediate and maximal projections can also
serve as heads.
22Adger (2003) and others use the term ‘root’ to refer to the topmost node in a syntactic tree. In this thesis,
however, I will use the term root/Root to refer to a different grammatical concept (cf. Section 2.3). In order to
avoid confusion, I will use the term ‘topmost’, rather than ‘root’, when referring to the highest node in a tree.
2.2. Building structure 41
Note that I assume that syntactic structures are abstract representations without a com-
mitment to their surface linearization. That is, the two structures in (65) are syntactically
identical. Following Embick and Noyer (2007), I assume that structures are linearized by a
morphological operation after the syntactic derivation. I refer the reader to Section 3.2 for a
more detailed discussion.
(65) Z
YX
= Z
XY
Adjoin
We can identify another syntactic operation with which it is possible to generate structure,
namely Adjoin. In contrast to Merge, which is triggered by the checking requirement of
uninterpretable features, “Adjoin [...] does not need to be triggered. [...]. Adjoin inserts a
phrasal object into another phrasal object at its outermost level. It does not create a new
object, it expands one of the old ones by stretching its outermost layer into two parts and
inserting the adjoined object between them” (Adger 2003: 112). Adjoin, like Merge, follows
the Extension Condition given in (63). The syntactic operation Adjoin can be schematized as
in (66), where the constituent YP (the adjunct) adjoins to the constituent XP (the adjunction
site).
(66) XP
XPYP
One property of the operation Adjoin that follows from its non-triggered nature is that the
distributional behavior of adjunction sites is the same whether or not they have and adjunct
(Adger 2003: 112).
Agree
At the beginning of this section, the syntactic operation Merge has been defined as checking
under sisterhood. As the relation of sisterhood can be considered to be a local instance
of the c-command relation (Adger 2003: 169), we can additionally assume a more general
(i.e. not sisterhood-based, but c-command-based) relation of feature checking. This relation
is referred to as Agree. Adger (2003) provides the definition of Agree in (67).
(67) Agree:
An uninterpretable feature [uF] on a syntactic object Y is checked when Y is in a
c-command relation with another syntactic object Z which bears a matching feature
F.
(Adger 2003: 168)
42 2. Syntax
Agree as checking under c-command gives rise to a more general (and thus possibly more
distant) checking of uninterpretable features in configurations such as those sketched in (68).
The interpretable feature F on Z checks the uninterpretable feature [uF] on Y. The structural
condition that holds between Y and Z is c-command, no matter which of the two nodes
dominates the other.
(68) a. ...
...
Z[F]...
Y[uF]
b. ...
...
Y[uF]...
Z[F]
Checking under sisterhood, as defined in (58), is a subtype of Agree (i.e. checking under
c-command), because sisterhood can be reduced to a more local version of c-command, i.e.
sisterhood is contained in c-command (Adger 2003: 169). In fact, Sigurðsson (2004, 2006)
considers Agree to be a precondition on the syntactic operation Merge, which builds on
checking under sisterhood (“Agree Condition on Merge”).
At this point of the discussion, it is crucial to distinguish the syntactic operation Agree
from morphological agreement, which I assume to take place in morphology (Bobaljik 2008).
Sigurðsson (2004) claims that whenever Merge applies, the possibility of morphological
agreement arises. The actual morphological realization of syntactic Agree is then considered
to be a parameter of a given language. Sigurðsson substantiates this claim by presenting
data from various Germanic languages, showing that morphological agreement is subject
to immense variation, and that it seems to be impossible to generalize over all instances
(Sigurðsson 2004). Consider the patterns of predicate argument agreement sketched in (69),
i.e. finite verb agreement and predicate agreement. While English is poor in agreement
morphology, as having almost none (except for third person singular -s), Icelandic is rich in
agreement morphology. German and Swedish are in the middle, as they have more agreement
morphology than English, but less than Icelandic. In German, the finite verb agrees with the
subject (which is also known as subject-verb agreement), whereas in Swedish, an adjectival
predicate agrees with the subject.
(69) a. They would-∅ be rich-∅. (English)
2.2. Building structure 43
b. They would-AGR be rich-∅. (German)
c. They would-∅ be rich-AGR. (Swedish)
d. They would-AGR be rich-AGR. (Icelandic)
(Sigurðsson 2004)
Move
Besides the syntactic operations Merge, Adjoin, and Agree, I assume a fourth syntactic
operation, called Move. Informally, we can say that Move is an operation that changes the
position of syntactic objects. However, Move is not a primitive operation, but the result of
the interaction between two operations, one of which is Merge. The general idea is that,
under Move, (a copy of) some syntactic object Y that is contained in another syntactic object X
(re)-merges with X.23 With respect to the other operation involved in Move, we basically find
two approaches: (i) the Trace Theory of movement (Chomsky 1973, Haegeman 1994: 309–313)
and (ii) the Copy Theory of movement (Chomsky 1993: 34–35, Nunes 1995, 2011).24 These two
approaches differ fundamentally with respect to the second operation constituting Move –
next to Merge – and ultimately with respect to the theoretical status of the moved element and
its in-situ position. Within a Trace Theory, the syntactic object targeted by Move is physically
displaced, leaving behind an empty category, or trace t, before is it re-merged. That is, the
second operation constituting Move is a displacement operation. The Copy Theory stands
in contrast to that. Here, the syntactic object targeted by Move is copied to the effect that
the master copy remains in situ (and becomes phonologically silent), while the copy merges.
That is, the second operation constituting Move is a copy operation.25
In the following, I briefly sketch both approaches to the operation Move. Like the op-
eration Merge, the operation Move is triggered by some uninterpretable feature that must
be checked locally. Assume a projecting syntactic object X bearing an uninterpretable fea-
ture [uF] that has to be checked locally. Instead of selecting an external constituent with
a matching feature, X (the probe) scans its c-command domain for an internal syntactic
object with a matching feature F. Let’s further assume that X finds a matching feature on the
downstairs-embedded, non-projecting syntactic object Y (the goal), as in (70).
23The fact that a syntactic object is (initially) contained in another syntactic object gives rise to the term
internal Merge.
24See also Boeckx (2006: 105–106).
25Hornstein (2001), Hornstein et al. (2005) argue that a copy operation seems to be independently needed
to build up a Numeration from List 1. In particular, they (2005: 215) argue that List 1 does not shrink like a
bag of marbles when an item of it is taken to build up a Numeration, but that items of List 1 are copied into a
Numeration.
44 2. Syntax
(70)
X[uF]
...
Y[F]...
X[uF]
Within a Trace Theory approach, the probe X attracts the goal Y into its local domain, thereby
checking the uninterpretable feature [uF] locally. The displaced syntactic object Yi leaves
behind a trace ti. The displaced constituent and the trace are co-indexed. (71) illustrates Move
within a Trace Theory approach.
(71) X
X[uF]
...
ti
...
X[uF]
Yi[F]
Within a Copy Theory approach, the goal Y is copied under co-indexation (72a) and then
merged with the probe X – obeying the Extension Condition in (63) – and thereby checking
the uninterpretable feature [uF] locally (72b).
2.2. Building structure 45
(72) a. Copy goal:
X[uF]
...
<Yi>[F]...
X[uF] → Yi[F]
b. Merge goal with probe:
X
X[uF]
...
<Yi>[F]...
X[uF]
Yi[F]
The master copy of Yi, i.e. its lower instance, ultimately undergoes phonological deletion,
which means that it is not pronounced (Nunes 1999, 2004, Boeckx 2006: 165–167). Phonological
deletion is indicated by angle brackets. Note that it is argued, in favor of the Copy Theory,
that there are instances where the master copy in fact receives a phonological realization.
Consider, for example, the Afrikaans data in (73), where the intermediate instances of met wie
(‘with who’) are in fact overtly realized (Hornstein et al. 2005: 215).
(73) Met
with
wie
who
het
have
jy
you
nou
now
weer
again
gesê
said
met
with
wie
who
het
did
Sarie
Sarie
gedog
thought
met
with
wie
who
gaan
go
Jan
Jan
trou?
marry
‘Who(m) did you say again that Sarie thought Jan is going to marry?’
(Du Plessis 1977: 725)
Note that the so-called Copy Construction in German (Höhle 1996, Fanselow and Mahajan
2000, Fanselow and C´avar 2001), exemplified in (74), can be analyzed along the same lines as
in the Afrikaans example.
(74) a. wer
who
denken
think
Sie
you
wer
who
sie
you
sind
are
‘who do you think you are’
b. wen
who
denkst
think
Du
you
wen
who
sie
she
meint
believes
wen
who
Harald
Harald
liebt
loves
46 2. Syntax
‘who do you think that she believes that Harald loves’
(Fanselow and Mahajan 2000: 219)
With regard to the question Trace Theory vs. Copy Theory, I have nothing more to say
than the following. The Copy Theory has the theoretical advantage that we do not have
to stipulate a new theoretical primitive, i.e. an empty category or trace. Hornstein et al.
(2005: 213) note that “a copy [...] is not a new theoretical primitive; rather, it is whatever the
moved element is, namely, a syntactic object built based on features of the numeration”.
The sequence of the positions occupied by a constituent undergoing the operation Move
is referred to as the (movement) chain. For example, (72b) constitutes the movement chain
[Yi,<Yi>]. Chomsky (1995: 253) argues that a movement chain is subject to the condition that
all members of a movement chain have the same phrase structure status. He formulates the
Chain Uniformity condition in (75).
(75) Chain Uniformity:
A chain is uniform with regard to phrase structure status.
(Chomsky 1995: 253)
Chain Uniformity rules out configurations where a projecting syntactic object moves into
a position where it cannot project. Assume a derivation as in (76a), where the projecting
terminal node Y moves into the local domain of X, i.e X projects. Let us determine the phrasal
structure status of the nodes in (76b). According to the principles formulated in (53), the
lower copy of Y is interpreted as a minimal projection (Y○i ) because it projects in this position,
while the higher copy of Y is interpreted as a maximal projection (YPi) because it does not
project in this position.
(76) a.
X
X
...
Y
...<Yi>
...
X
Yi
2.2. Building structure 47
b.
XP
X’
...
YP
...<Y○i >
...
X○
YPi
The configuration in (76b) gives rise to the movement chain [YP,<Y○>]. Its elements have
different phrasal statuses ([maximal projection,<minimal projection>]), which violates Chain
Uniformity.
2.2.3 Complements, specifiers, and adjuncts
This section elaborates on the notions complement, specifier, and adjunct as structural
notions. Strictly speaking, we can identify two instances of Merge (59) that are technically
the same, but that generate different levels of projection. On the one hand, there is the Merge
operation that Adger (2003: 105–108) dubs First Merge. The characterization of First Merge
is that the projecting syntactic object inputted to the Merge operation is interpreted as a
minimal projection. The non-projecting syntactic object that undergoes First Merge next to
the projecting one is called complement. On the other hand, there is Second Merge (Adger
2003: 109–110) that is characterized such that the projecting syntactic object is not interpreted
as a minimal projection. The non-projecting syntactic object undergoing Second Merge next
to the projecting one is called specifier.26 The syntactic object undergoing Adjoin that is
not expanded is called the adjunct. The operation Adjoin is also sometimes referred to as
adjunction (Adger 2003: 110–114). These considerations give rise to the relational definition of
complement, specifier, and adjunct in (77). Hence, these notions refer to structural positions.
(77) a. Complement: Sister of minimal projection
b. Specifier: Sister of intermediate projection
c. Adjunct: Sister of maximal projection
(Adger 2003: 110–111)
In a tree diagram, this looks as depicted in (78).
26The terms Spec-X, Spec,X or SpecX refers to a specifier position of X.
48 2. Syntax
(78) XP
XP
X’
complementX○
specifier
adjunct
The specifier position and the complement position are argument positions because they
are generated by the operation Merge. They contrast with adjuncts, which are not selected
by Merge, but undergo the operation Adjoin. The relation between X○ and its complement,
as well as the relation between X○ and its specifier are considered to be local. This follows
from the definition of Merge, which involves checking under sisterhood – arguably a local
tree-structural relation (Adger 2003: 169).
Bare Phrase Structure vs. X-bar Theory
At this point, it is helpful to say something about the differences between Bare Phrase
Structure (BPS) and X-bar Theory (XbT). Note that this comparison is only a brief overview
of the differences between XbT and BPS; for a more detailed discussion on this topic, I refer
the reader to Adger (2003), Hornstein et al. (2005), Boeckx (2006), Lohndal (2012). XbT, first
proposed by Chomsky (1970) and further developed by Jackendoff (1977), states a hierarchical
segmentation of phrases. Each phrase is segmented into a maximal projection, at least one
intermediate projection, and a minimal projection. Recall the tree in (55) illustrating the levels
of projection, which I repeat here in (79). As this exemplary phrase comprises two arguments,
namely YP in a specifier position and ZP in the complement position, the XbT tree and the
BPS tree of this phrase basically look alike.
(79) XP
X’
ZPX○
YP
However, there is a crucial difference between XbT and BPS concerning the theoretical status
of the levels of projection. XbT is representational, that is, structure is built in one fell
swoop. The items and arguments are then inserted into the structure. BPS, on the other
hand, is derivational; that is, structure is built bottom up bit by bit. This difference in the
conceptualization of phrase structure gives rise to the hypothesis that in XbT each and all
phrases comprise all levels of projection regardless of the amount of arguments. In BPS, on
the contrary, no such preconceived phrase structure is assumed, but the respective levels of
projection are set up as required.
2.2. Building structure 49
Another difference between XbT and BPS is that the former permits binary and unary
branching, while the latter only permits binary branching. Consider now the different
argument-structural configurations in Table 2 below.
XbT BPS
(i)
XP
X’
ZPX○
YP
XP
X’
ZPX○
YP
(ii)
XP
X’
X○
YP
XP
X○YP
(iii)
XP
X’
ZPX○
XP
ZPX○
(iv)
XP
X’
X○
X○/XP
(v)
XP
X’
X’
...X○
WP
...
XP
XPWP
Table 2: Structures in XbT vs. BPS
Apart from the theoretical status of the projections (representational in XbT vs. deriva-
tional in BPS), a transitive structure such as in row (i) looks identical in both XbT and BPS.
With ZP in complement position and YP in specifier position, X projects a minimal projection
X○, an intermediate projection X’, and a maximal projection XP. However, the differences
become visible when a phrase contains fewer than two arguments. If a phrase contains only
one argument, as in the rows (ii) and (iii) in Table 2, XbT structurally distinguishes between
the argument in the specifier position and the argument in complement position. Under
the assumption of linearization outlined above, i.e. that the order of items in the structure
50 2. Syntax
is irrelevant, no such distinction between a specifier and a complement can be made in
BPS. This is because the structures in row (ii) and (iii) in Table 2 are identical, i.e. YP and
ZP are both in complement position of X○. Chomsky (1995: 247–248) points to a potential
problem if the distinction between specifier and complement cannot be made; see also Boeckx
2006: 175–176 and Harley 2011: 17–19. The X-bar-theoretical distinction between the specifier
and complement in the rows (ii) and (iii) is often exploited in order to capture an empirically
well-motivated distinction of two classes of intransitive verbs, dubbed ‘unergative’ and
‘unaccusative’ verbs.27 While unergative verbs like in John dances are assumed to project only
a specifier, unaccusative verbs like in John arrives are assumed to project only a complement.
Both positions then are assumed to surface as the subject. In BPS, both structures collapse in
one and we lose this theoretical generalization about argument structure.
However, we can solve this problem by assuming light categories, for instance. Unac-
cusative verbs are assumed to project only a complement of V, while the single argument of
unergative verbs is assumed to be projected by a light category such as Voice. Now consider
the case that a phrase contains no argument at all, like in row (iv). Here, XbT assumes
the full range of projections from minimal projection X○ over intermediate projection X’ to
maximal projection XP. In contrast, BPS assumes only one node in this case. According to
BPS’s principles of projection, such mono-node structures are interpreted as minimal and
maximal projections at the same time. Thus, a phrase without any argument is represented
by X○/XP (or XP/X○) in BPS.
Another difference between XbT and BPS concerns the status of adjuncts, such as WP in
row (v). Both XbT and BPS consider adjuncts as optional, but while adjuncts are considered
to be endocentric in XbT – adjuncts occur within maximal projections as sisters and daughters
of intermediate projections –, adjuncts are considered to be exocentric in BPS – adjuncts occur
as sisters of maximal projections.
2.3 Roots
In this section, I propose that Root is a derivational notion, just like the notions ‘complement’,
‘specifier’, and ‘adjunct’, which are discussed in Section 2.2.3. That is, Roots are identified
derivationally. In particular, I propose that a Root position is a sister and, at the same time, a
daughter of a minimal projection – a structural configuration that can be achieved by means
of De Belder and Van Craenenbroeck’s (2015) operation Primary Merge.28 A Root is what is
inserted in a Root position. The structural position that is indicated with the Root symbol “
√
”
in (80) qualifies as a Root position.
27For instance, German unergative verbs normally co-occur with the auxiliary haben (‘have’), while unac-
cusatives co-occur with sein (‘be’).
28Note that this proposal ultimately requires a redefinition of complements as sisters, not daughters, of
minimal projections.
2.3. Roots 51
(80) X○
X○√
When generated by Primary Merge, Root positions are empty∅. That is, Root positions are
like place holders in their initial state. I suggest that Root positions can be filled at Spell-Out.
Typically Content items (cf. Section 2.1.4) are inserted into Root positions and thereby become
Roots. However, De Belder and Van Craenenbroeck (2015) argue that feature bundles from
the Lexicon, e.g. bundles of synsem features, can also occur in Root positions. In Chapter 5,
I argue that the Root position of certain prepositions (pseudo-geometric prepositions and
non-geometric prepositions) can also remain empty.
Alexiadou and Lohndal (2013, 2014), Alexiadou (2014) argue that, when a Root combines
with a categorizer, it is always the categorizer that projects, never the Root. In particular,
they argue that Roots are always modifiers of functional categorizing heads, i.e. they are
supposed to be like adjuncts to functional material (81a). Configurations where roots project
are excluded (81b).
(81) a. X
X
√
b. *
√
X
√
In order to account for this structural restriction, I adopt De Belder and Van Craenenbroeck’s
(2015) operation Primary Merge to generate insertion sites for Roots. Their (2015: 629) leading
thought is that
there are specific positions in the syntactic structure that will serve as the insertion
site for roots [...]. These positions are characterized by the absence of grammatical
features and therefore do not play any active role in the syntactic derivation.
One of De Belder and Van Craenenbroeck’s empirical arguments for a structural account
to Roots is based on the observation that functional Vocabulary Items can occupy positions
that are normally occupied by non-functional Vocabulary Items. Consider the Dutch data in
(82), where functional Vocabulary Items behave like nouns or like verbs.
(82) a. Ik
I
heb
have
het
the
waarom
why
van
of
de
the
zaak
case
nooit
never
begrepen.
understood
‘I have never understood the motivation behind the case.’
b. In
in
een
a
krantenartikel
newspaper.article
komt
comes
het
the
wat/hoe/wie/war
what/how/who/where
altijd
always
voor
before
het
the
waarom.
why
52 2. Syntax
‘In a newspaper the what/how/who/where always precedes the why.’
c. De
the
studenten
students
jij-en
you-INFINITIVE
onderling.
amongst.one.another
‘The students are on a first-name basis with each other.’
d. Martha
Martha
is
is
mijn
my
tweede
second
ik.
I
‘Martha is my best friend.’
e. Niets
nothing
te
to
maar-en!
but-INFINITIVE
‘Don’t object!’
f. Paard
horse
is
is
een
a
het-word.
the.NEUTER.DEFINITE-word
‘Paard takes a neuter article.’
(De Belder and Van Craenenbroeck 2015: 630)
In particular, De Belder and Van Craenenbroeck observe that functional Vocabulary Items do
not project their functional features if they surface in the position of a lexical Vocabulary Item.
Consider the Dutch example in (83), where the functional Vocabulary Item ik (‘I’) in subject
position behaves like a common noun and not like a functional Vocabulary Item. In particular,
we would expect that the functional Vocabulary Item ik with the φ-features specification for
first person singular enters into an agreement relation with the verb, that is, that the copula
verb wezen (‘be’) should surface as ben (‘be.1.SG’). However, ben in (83) is ungrammatical and
the copula verbs shows third person singular agreement morphology, that is, it surfaces as is
(‘be.3.SG’).
(83) Mijn
my
tweede
second
ik
I
{*ben/is}
am/is
ongelukkig.
unhappy
‘My best friend is unhappy.’
(De Belder and Van Craenenbroeck 2015: 632)
De Belder and Van Craenenbroeck conclude that the functional Vocabulary Item ik in (83)
occupies a structural position where it cannot project its functional features and thereby
trigger morphological agreement.
With regard to the syntactic operation Merge, De Belder and Van Craenenbroeck observe
that there is a technical imbalance when Merge is applied for the first time in a derivation;
that is, when the derivational workspace is empty. In this case, an item is selected from the
Numeration, but – unlike in successive selection operations – it is not fed to the operation
Merge. Instead, the item is simply put into the derivational workspace. Any other item
that is selected afterwards, but before the structure is finalized and sent off to the interfaces,
undergoes Merge with an existing syntactic object in the derivational workspace. De Belder
and Van Craenenbroeck eliminate this imbalance by proposing that the first item selected from
the Numeration is indeed fed to the operation Merge (e.g. as defined in (59) in Section 2.2.2).
However, as the very first item selected from Numeration cannot merge with an existing
2.3. Roots 53
syntactic object, it simply merges with the empty set. The empty set is arguably present
if nothing else is present in the derivational workspace. Assume that we have an empty
derivational workspace and select the item X from the Numeration. It merges with the empty
set into the derivational workspace. As the empty set innately does not contain any features,
it naturally follows that only X projects its features. The resulting structure in (84) depicts
Primary Merge as outlined above.
(84) Primary Merge:
X
X∅
(adapted from De Belder and Van Craenenbroeck 2015: 637)
This structure straightforwardly explains why functional Vocabulary Items do not affect the
derivation when they behave like roots. De Belder and Van Craenenbroeck propose that the
functional Vocabulary Item ik in (83) is inserted in an empty set position generated by Primary
Merge. Material in this position cannot project. It follows that morphological agreement does
not take place. Anything in this position is ‘encapsulated’.
It is crucial to point to a fundamental difference between Primary Merge and other Merge
operations, such as First Merge or Second Merge, cf. Section 2.2.3. While First Merge and
Second Merge have a clear trigger, namely an uninterpretable (category) feature, Primary
Merge does not have such a trigger. For example, take a verb with an internal argument.
Initially, such a verb comprises the feature bundle V[uD]. The category V determines the
category verb and the u-prefixed feature [uD] triggers First Merge with a DP. What is the cor-
responding counterpart that triggers Primary Merge? One could think of an uninterpretable
empty set feature [u∅] or a bare uninterpretable feature [u]. However, this does not conform
with the definition of uninterpretable features as given in (14b), because the empty set is not a
feature.29 Uninterpretability is typically conceived of as a property of features. Thus, Primary
Merge has to be triggered differently. In this thesis, I assume that Primary Merge is triggered
by selection from the Numeration.
I assume that Root Insertion happens at Spell-Out. I follow De Belder and Van Craenen-
broeck, who suggest that the empty set position generated by Primary Merge constitutes
an insertion site for Roots. At Spell-Out, the syntactic derivation is accomplished, and the
phrase structure status can be determined. The lower X-node in (84) is clearly a minimal
projection because it is an item taken from the Numeration. Thus, it is labeled as X○. What
about the higher X-node? As it is completely identical to the lower X-node – it does not
contain any further features whatsoever – it is reasonable to also label the higher X-node as a
minimal projection. Note that we additionally have to consider the question of whether X
29Even if we would assume an uninterpretable empty set feature or a bare uninterpretable feature, this is still
fundamentally different from an uninterpretable category feature.
54 2. Syntax
further projects. If X projects further structure, then the higher X-node is merely a minimal
projection (X○); this case is illustrated in (85). If X does not project further structure, then
the higher X-node is both a minimal and a maximal projection (X○/XP); this case is ignored
in (85). What is crucial here is that both the higher and the lower X-node have the status
of a minimal projection. The empty set position ∅, which is the sister and the daughter of
a minimal projection, serves as the insertion site for Roots. I assume that this happens at
Spell-Out.
(85) Root Insertion at Spell-Out:
X○
X○∅
Root
Let me illustrate these considerations with a simplified derivation. Take the DP a dog.
Abstracting away from the functional structure (e.g. NumP), we can assume the simplified
structure in (86) to begin with.
(86) DP
N○/NP
dog
D○
a
We can assume that the Root
√
dog – or, to be precise, the Content feature [©DOG] (cf.
Section 2.1.4) in a Root position – underlies this derivation. First, N is taken from the
Numeration and fed to the operation Primary Merge. It merges with the empty set (87a).
Subsequently, D[uN] merges with the ‘complex’ N (87b). At Spell-Out, the phrasal status of
the nodes can be determined along the definitions in (53). The lower N-node is a minimal
projection (N○) because it is an item selected from the Numeration. As the higher N-node is
equivalent to the lower node – it is equivalent to an item selected from the Numeration – is
can also be considered to be a minimal projection. In addition, it is also a maximal projection
(N○/NP), because it is a syntactic object that does not project. Similarly, the lower D-node is
a minimal projection (D○), as it is an item selected from the Numeration, while the higher
D-node is a maximal projection (DP), because it does not project (87c). When the phrasal
status is determined at Spell-Out, we can insert material into the Root position ∅. In this
2.3. Roots 55
example, we insert the Content feature [©DOG] (87d). In this position, the Content feature[©DOG] is interpreted as the Root √dog (87e).30
(87) a. N
N∅
b. D
N
N∅
D
c. DP
N○/NP
N○∅
D○
d. DP
N○/NP
N○∅
[©DOG]
D○
e. DP
N○/NP
N○√dog
D○
Root positions are determined derivationally. In BPS, the notions of complement, specifier,
and adjunct are derivational. Recall (77) from Section 2.2.3, where we defined complements
as sisters of minimal projections, specifiers as sisters of intermediate projections, and adjuncts
as sisters of maximal projections. I suggest that we can define Root positions along the
same lines. Like complements, Root positions are sisters of minimal projections, but unlike
complements, Root positions are additionally also dominated by minimal projections; recall
(85). In particular, I propose (88), which is basically an extension of (77).
30From a phrase-structural point of view, items in Root positions have, by definition, the status of a maximal
projection because they do not project, cf. (53b). However, I refrain from labeling Root material as phrasal (e.g.
dogP). Instead, I use the common notation with the Root symbol (e.g.
√
dog).
56 2. Syntax
(88) a. Root position: Sister and daughter of minimal projection
b. Complement: Sister but not daughter of minimal projection
c. Specifier: Sister of intermediate projection
d. Adjunct: Sister of maximal projection
extension of (77); (Adger 2003: 110–111)
This can be displayed as in the tree-diagram in (89).
(89) XP
XP
X’
ComplementX○
X○Root position
Specifier
Adjunct
I propose that Root positions are characteristic for Roots. Put differently, we can identify
Roots as the (Content) material inserted into Root positions (90).
(90) Root:
A Root is what is inserted into a Root position.
Typically, (bundles of) Content features (cf. Section 2.1.4) are inserted into Root positions
and thus become Roots. In (87), this is presented for the Content feature [©DOG] that
becomes the Root
√
dog. However, we can also find other types of features in Root positions.
Reconsider the examples in (82) where arguably functional features occur in Root positions
(De Belder and Van Craenenbroeck 2015). In (82d), for instance, ik (‘I’) serves as a common
noun. That is, we can assume that the synsem feature bundle [+1,+SG] from the Lexicon is
inserted into a nominal Root position and thus becomes the Root
√
ik. However, I do not
discuss such cases any further, because they fall outside the scope of this thesis. Instead, I will
propose in Section 5.4 that, in the domain of spatial prepositions, Root positions can either be
filled with Content features (geometric prepositions) or remain empty (pseudo-geometric
prepositions and non-geometric prepositions).
Let me close this section with a brief note on the question of how to account for more
than one Root in a given derivation. Primary Merge basically allows one root per derivation,
because a Root position is generated only when the workspace is empty and the first item
from the Numeration is merged into the empty derivational workspace. De Belder and
Van Craenenbroeck (2015: 642) refer to this as One Derivational Workspace, One Root (“In
every derivational workspace, there is exactly one root, and for every root there is exactly one
2.4. Summary 57
derivational workspace”). However, a derivation typically involves more than one Root. One
possibility to account for this is to assume a layered derivation to the effect that derivations
are, in principle, readmitted to the Numeration. Following Zwart (2009: 161), De Belder and
Van Craenenbroeck propose that “the output of a previous derivation [can appear] as an atom
in the numeration for the next derivation”. This means that a derivation is cleared from the
workspace and inserted back into the Numeration. With a cleared derivational workspace,
Primary Merge can generate a further Root positions.
2.4 Summary
This chapter laid out the syntactic module within the Y-model of grammar. In this thesis, I
adopt the tenets of the Minimalist Program (MP) (Chomsky 1995, Adger 2003).
Section 2.1 addressed the notion of ‘feature’; features are considered to be the core building
blocks of the grammatical theory adopted here. Section 2.1.1 presented the two types of
feature systems that are relevant in this thesis: (i) privative features, where features are
considered to be attributes; and (ii) binary features – features, that are considered to be
pairs consisting of an attribute and a value drawn form a binary domain. Focusing on
prepositions, Section 2.1.2 discussed category features. A general division into three types of
category features was made: (i) the lexical categories V (verb), N (noun), A (adjective), and P
(preposition); (ii) the functional categories C (complementizer) > Dx (deixis) > Asp (aspect);
and (iii) light categories such as verbal Voice (Kratzer 1996) or Appl (applicative) (Pylkkänen
2002, McIntyre 2006) and prepositional ‘little p’ (Split P Hypothesis) (Svenonius 2003). The
functional categories dominate the lexical categories. Light categories are considered to
be in between functional and lexical categories. The Parallelism Hypothesis states that
the functional categories, which dominate the lexical categories, are structured in parallel
across the lexical domains; cf. Den Dikken (2010: 100 104). Section 2.1.3 briefly addressed
syntacticosemantic (synsem) features, i.e. those feature that are drawn from the universal
inventory of syntacticosemantic features (Embick 2015: 6). In Section 2.1.4, I introduced
Content features, which I consider to be language-specific, conceptually grounded, and
non-generative. They can affect the semantic interpretation at LF and the morphological
realization at PF. I identified two types of Content features: (i) idiosyncratic Content features,
which relate to the arbitrary differences between two grammatical entities, with all else being
equal (e.g. the difference between cat and dog); and (ii) abstract Content features, the function
of which is at least two-fold. On the one hand, they can relate to general perceptually-
grounded concepts like ‘interiority’ or ‘verticality’, while, on the other hand, they can bundle
with idiosyncratic Content features and thereby give rise to particular aspects of meaning
of the idiosyncratic Content features. This was illustrated with the toponym Kuba (‘Cuba’),
which can denote the island of Cuba or the state of Cuba. Depending on the abstract Content
feature the idiosyncratic Content feature bundles with, either of these interpretations is
promoted at LF.
58 2. Syntax
Section 2.2 presented the principles according to which structure can be generated in the
Minimalist Program (MP) (Chomsky 1995). MP applies Bare Phrase Structure (BPS) as its
phrase structure module. Section 2.2.1 laid out the tree-structural relations and projection
principles of BPS; Section 2.2.2, the major operations of BPS. Section 2.2.3 derived the notions
complement, specifier, and adjunct. Then, that section also discussed the differences between
BPS and X-bar Theory (XbT), which is the phrase structure module of Government and
Binding (GB) (Chomsky 1981, Haegeman 1994, a.o.), MP’s predecessor.
Section 2.3 clarified the status of Roots in the approach proposed here. Adopting the
operation Primary Merge (De Belder and Van Craenenbroeck 2015), I defined a Root position
as the position that is a sister and a daughter of a minimal projection; cf. (88) on page 56.
Consequently, I defined a Root as what is inserted into a Root position; cf. (90) on page 56.
Chapter 3
Morphology
This chapter explores the branch from Spell-Out to the Articulatory-Perceptual (A-P) system
in the Y-model of grammar (Morphology), as depicted in Figure 5 below.
Numeration
Spell-Out
Phonological
Form (PF)
A-P
system
Morphology
Logical
Form (LF)
C-I
system
Semantics
Syntax
Lexicon:
The generative items
of a language
Content:
The non-generative,
contentful items
of a language
(List 2)
Vocabulary:
Instructions for
pronouncing
terminal nodes
in context
(List 3)
Encyclopedia:
Instructions for
interpreting
terminal nodes
in context
. . . . .(List. . .1)
Figure 5: Morphology in the Y-model of grammar
This thesis adopts the tenets of Distributed Morphology (DM) (Halle and Marantz 1993,
1994, Halle 1997, Harley and Noyer 2000, Embick and Noyer 2001, 2007, Embick and Marantz
59
60 3. Morphology
2008, Siddiqi 2009, Harley 2012, Matushansky and Marantz 2013, Embick 2015, a.o.). 31 DM
endorses the Separation Hypothesis (Beard 1987, 1995), stating that derivations, including
their syntacticosemantic formatives, are distinct from their morphological realizations. That
is, form and function are separate in DM. The concrete morphophonological realizations are
dissociated from the abstract syntactic representations until a later stage of the derivation.
Only at PF, the abstract structures are provided with concrete realizations. Bobaljik (2015: 7)
gets to the heart of it by stating that “morphology interprets, rather than projecting, syntactic
structure.” In fact, both the PF-branch and the LF-branch are considered to be interpretative
components of the grammar that receive syntactic input from Spell-Out and tailor it to
interfaces (Chomsky 1970, Adger 2003: 60).
Let us look at the key features of DM. First, DM assumes late insertion of morphophono-
logical exponents. That is, morphophonological features are not assumed to be present in
derivations before the PF-branch. In particular, the syntactic module does not operate on
morphophonological features. Second, DM assumes syntactic structures all the way down.
That is, words – take it as a pretheoretical term here – can be structurally decomposed,
according to the same structural principles as phrases and clauses. In particular, DM ex-
plicitly rejects the Lexicalist Hypothesis (e.g. Di Sciullo and Williams 1987), according to
which “words are created in the Lexicon, by processes distinct from the syntactic processes
of putting morphemes/words together. Some phonology and some structure/meaning
connections are derived in the lexicon, while other aspects of phonology and other aspects
of structure/meaning relations are derived in (and after) the syntax” (Marantz 1997: 201).32
In DM, there is no separate lexicon that builds words out of morphemes and gives them
to the syntax that then builds phrases out of these words.33 Syntax is the only generative
engine in the grammar. It forms words, as well as phrases and clauses. Furthermore, Bobaljik
(2015: 2) notes that “the functions of morphology in other approaches, and of the Lexicon in
particular, are in DM distributed (hence the name) over multiple points in the architecture.”
Third, DM assumes that the morphophonological exponents, which are inserted late into the
structure, are typically underspecified, as compared to the matching features of the insertion
site. This kind of underspecification is based on three other principles, (i) feature decomposi-
tion, (ii) the Subset Principle (Halle 1997), and (iii) specificity. As for feature decomposition,
it is typically assumed that (complex) features are decomposed into the smallest plausible
feature bundles serving as atoms. As for the Subset Principle, it is assumed that the feature
specification of a morphophonological exponent must meet only a subset of the feature
specification of the terminal node where the exponent is to be inserted. Or, put the other
way around, the features specified on a terminal node can be a superset of the features
specified on the morphophonological exponent that is to be inserted. A major advantage of
31In addition, I refer the reader to the DM-website; cf. URL: http://www.ling.upenn.edu/~rnoyer/
dm/ (27.06.2017)
32See also Bruening (2016) for a recent discussion against the Lexicalist Hypothesis.
33This sentence was written during the partial solar eclipse (≈ 71 % coverage) on March 20, 2015; 10:37 UTC+1;
48○44’47.4”N, 9○06’29.4”E (Pfaffenwaldring 5b, Stuttgart, Germany).
3.1. Vocabulary Insertion 61
the Subset Principle is that many syncretisms can straightforwardly be derived from it.34 As
for specificity, it is assumed that, if several morphophonological exponents meet a subset
of the feature specification of a terminal node, then the most specific exponent is inserted
into that terminal node. In the context of Vocabulary Insertion (cf. Section 3.1), the principles
related to underspecification are discussed in more detail.
At PF, several processes are typically assumed in DM. The core operation at PF is
Vocabulary Insertion, i.e. the insertion of morphophonological exponents into syntactic
terminals, and thereby realizing them. These exponents are assumed to be stored in a list
often referred to as the Vocabulary (or List 2). Section 3.1 addresses Vocabulary Insertion.
Concomitant to Vocabulary Insertion, syntactic structures are assumed to be linearized
(Embick and Noyer 2001). Section 3.2 addresses Linearization. There are also morphological
processes assumed before Vocabulary Insertion and Linearization. For instance, ornamental
morphology, i.e. morphological material that is syntactico-semantically unmotivated and
only ornaments a syntactic representation, is assumed to be processed early in the PF-branch.
Ornamental morphology typically involves the insertion of purely morphological nodes and
features into the derivation (e.g. case and agreement). Section 3.3 addresses ornamental
morphology. In DM, several operations on nodes are assumed. They are addressed in
Section 3.4. In line with Embick and Noyer (2001) and others, I assume morphological
movement operations (Morphological Merger), one taking place before and one taking place
after Vocabulary Insertion and Linearization. The morphological movement operation prior
to Vocabulary Insertion and Linearization is referred to as Lowering, the one after Vocabulary
Insertion and Linearization as Local Dislocation. Section 3.5 addresses Lowering and Local
Dislocation, i.e. the two instances of Morphological Merger. The morphophonological
exponents can be subject to contextually-triggered Readjustment. Morphophonological
Readjustment rules are typically assumed to apply late in the PF-branch. Section 3.6 addresses
Readjustment rules.
3.1 Vocabulary Insertion
By assumption, the features handed over from Spell-Out to Phonological Form (PF) do not
underlyingly have phonological features. Instead, they receive their phonological form at PF,
via the operation Vocabulary Insertion (Halle and Marantz 1993, 1994, Marantz 1995, Harley
and Noyer 1999, Embick and Noyer 2007, Embick 2015, a.o.).35 Consider the Late Insertion
Hypothesis in (91), as formulated by Halle and Marantz (1994).
34Note that Nanosyntax (cf. Starke 2009) is in this respect the direct opposite of DM, as it assumes the
Superset Principle, instead of the Subset Principle. See also Lohndal (2010) for a brief comparison of DM and
Nanosyntax.
35Note that I assume, unlike Embick (2015) for instance, that this holds for the generative features from the
Lexicon and for non-generative, but contentful features from the Content. In fact, Embick (2015: 7) assumes that
functional morphemes that are composed of syntacticosemantic (synsem) features do not have a phonological
representation, while Roots do have a phonological representation. Embick’s synsem features correspond to my
Lexicon features and his Roots correspond to my Content features.
62 3. Morphology
(91) Late Insertion:
The terminal nodes that are organized into the familiar hierarchical structures by
the principles and operations of the syntax proper are complexes of semantic and
syntactic features but systematically lack all phonological features. The phonological
features are supplied – after the syntax – by the insertion of Vocabulary Items into the
terminal nodes. Vocabulary Insertion [...] adds phonological features to the terminal
nodes, but it does not add to the semantic/syntactic features making up the terminal
node.
(Halle and Marantz 1994: 275–276)
In DM, syntactic terminals are typically referred to as (abstract) morphemes. Vocabulary
Insertion is the process of phonologically (or morphologically) realizing such abstract mor-
phemes. In DM, it is generally assumed that Vocabulary Insertion applies only to abstract
morphemes that are syntactic terminals. This is different from Nanosyntax, for instance,
where also phrasal spell-out is assumed. Note also at this point that Halle and Marantz
(1993: 118) assume that Vocabulary Insertion takes place only after the application of all
morphological operations that modify the trees generated in the syntax.
Each language has a particular set of phonological exponents stored in the Vocabulary of
that language.36 Technically, it is assumed that a phonological exponent is inserted into an
abstract morpheme, i.e. into a feature bundle serving as a syntactic terminal. In particular, I
assume that a phonological exponent ℘ can be added to an abstract morpheme M. That is, I
operationalize Vocabulary Insertion as an additive process as sketched in (92).37
(92) Vocabulary Insertion:
M[] → M[℘]
For the sake of illustration, consider the examples in (93). Note that these examples are
adapted from Embick (2015: 88). The structure in (93a) shows the morphologically-relevant
structure of the past tense of the English verb play. The structure consists of the Root
√
play,
the abstract verb morpheme V, and the abstract tense morpheme T that is specified as
past [+PAST]. None of the abstract morphemes in (93a) contain phonological information.
Ignoring the contextual conditions of Vocabulary Insertion for the moment, we can assume
that Vocabulary Insertion adds the respective phonological exponents to the effect that they
are integrated into the respective feature bundles (93b). The Root receives the exponent
36Note that the instructions for pronouncing features stored in VIs are considered language-specific. In fact,
the VIs of a language are (or: must be) acquired and memorized by the speakers of that language.
37Alternatively, Vocabulary Insertion can be operationalized as a replacive process (Halle 1990, Embick 2015).
Here, each feature bundle comes inherently with a place-holder that is replaced by a phonological exponent.
3.1. Vocabulary Insertion 63
/pleI/, the abstract verb morpheme receives the null exponent ∅, and the abstract past tense
morpheme receives the exponent /d/. This ultimately yields the verb played, viz. /pleId/.38
(93) a. feature structure of past tense of play prior to insertion:
T[+PAST]
V[]√play[©PLAY]
b. feature structure of past tense of play after insertion:
T[+PAST,/d/]
V[∅]√play[©PLAY,/pleI/]
Let us now look at the contextual conditions for inserting phonological exponents into an
abstract morpheme. By assumption, the Vocabulary is a list of instructions for pronouncing
abstract morphemes, and thus the contextual conditions for inserting phonological exponents
into abstract morphemes are stored in the Vocabulary Items (VIs) of a language. In line with
Embick (2015: 83), I define a VI as given in (94).
(94) Vocabulary Item (VI):
A Vocabulary Item is a pairing between a phonological exponent and a set of [...]
features that determine the privileges of occurrence of that exponent.
(Embick 2015: 83)
Ideally, the pairing between a phonological exponent and a set of features determining
its insertion site should have the form of one-to-one mapping, i.e. one particular abstract
morpheme would correspond to one particular phonological exponent, and vice versa.
However, this ideal scenario is rarely or even never the case. In fact, natural languages
exhibit a phenomenon that is typically referred to as (contextual) allomorphy (e.g. Halle
and Marantz 1993, Marantz 2001, 2011, Embick 2003, 2010, 2012, 2015, Embick and Marantz
2008). Contextual allomorphy describes a situation where several exponents are potential
realizations for a particular abstract morpheme and where the choice of the exponent depends
on the local environment. We could also say that contextual allomorphy describes a situation
where several exponents compete for insertion into a particular abstract morpheme and the
winner is determined by the local environment. Consider the case of the past tense formation
38For representing phonological exponents, I use the International Phonetic Alphabet (IPA); cf. URL: https:
//www.internationalphoneticassociation.org/ (27.06.2017). Appendix C provides a phoneme-
grapheme mapping of the prepositions that are focused on in this thesis.
64 3. Morphology
in English. All past tense verbs arguably comprise the abstract past tense morpheme T[+PAST].
This feature bundle is not uniformly realized by one particular exponent. In most cases, it is
realized by the exponent -ed.39 Nevertheless, there are verbs that form the past tense with
the exponent -t, such as lef-t (leave) or ben-t (bend). Yet, other verbs form the past tense with
the null exponent ∅. Examples are hit-∅ (hit) or sang-∅ (sing).40 As the exponents -t and ∅
co-occur only with a limited set of verbs, while the exponent -ed co-occurs with the majority
of verbs, we can say that -t and ∅ are inserted into past tense morphemes in specific contexts,
while -ed is inserted into past tense morphemes in all unspecified contexts, as a so-called
elsewhere exponent (or elsewhere form). Only certain verbs trigger the insertion of the
special exponents instead of the elsewhere exponent. The difference between the respective
verbs can be broken down into different Roots (or, ultimately into different Content features).
In a VI, this is expressed such that various contexts triggering a special exponent are listed.
The typical notation of a VI is illustrated in (95), which represents the VI for the English past
tense morpheme.
(95) VI for the English past tense morpheme:
a. T[+PAST] ↔ -t / {√bend,√leave, ...} __
b. ↔ ∅ / {√hit,√quit, ...} __
c. ↔ -ed elsewhere
(adapted from Embick 2015: 93)
This is to be read as follows. The exponent -t is inserted into the past tense morpheme
T[+PAST] iff it occurs in the context of the Roots √bend, √leave, etc. The null exponent ∅ is
inserted into the past tense morpheme T[+PAST] iff it occurs in the context of the Roots √hit,√
quit, etc. If none of these context are present, the elsewhere exponent -ed is inserted into
the past tense morpheme T[+PAST].41 The order of listing the contexts is crucial. The more
specific ones must precede the less specific ones, and the generic context for the elsewhere
39For the sake of illustration, I use the orthographic forms of the exponents instead of the actual phonological
exponents. Ultimately, this does not change anything.
40Note that ‘irregular’ past tense formation in English is often accompanied by morphophonological read-
justment, e.g. sing → sang. Section 3.6 discusses such readjustment processes from a DM perspective.
41The VI for the English past tense morpheme in (95) is stated such that the ‘entire’ morpheme is looked
at. An alternative would be to ‘outsource’ the past feature [+PAST] to the context side, which leads to a more
general VI of the tense morpheme. This is illustrated in (96), which I consider here to be tantamount to (95).
(96) VI for tense morpheme:
a. T ↔ -t / {√bend,√leave, ...} __ [+PAST]
b. ↔ ∅ / {√hit,√quit, ...} __ [+PAST]
c. ↔ -ed / __ [+PAST]
d. ↔ ...
Note, however, that the exponent -ed in (96) is not a real elsewhere exponent. Nevertheless, it could then
be considered to be the ‘elsewhere’ exponent for past contexts. The choice between (95) and (96) relates to
the question of how general a VI should/could be formulated. This is, of course, a question concerning the
architectural design of the grammar.
3.1. Vocabulary Insertion 65
exponent must come last. By checking the more specific contexts first, it is guaranteed that
the less specific exponents and the elsewhere exponent are blocked in the respective context,
which is what we want.
The VI schema given for the English past tense morpheme in (95) can be generalized
as given in (97). The exponent ℘1 is inserted into the morpheme M in the context C1; the
exponent ℘2 is inserted into the morpheme M in the context C2; etc. The exponent ℘n is the
elsewhere exponent, and it is inserted into the morpheme M when all specified contexts (C1
to Cn−1) are not present. The order of the contexts is such that C1 is the most specific context,
while Cn−1 is the least specific context.
(97) General schema of a VI:
a. M ↔ ℘1 / C1
b. ↔ ℘2 / C2
c. ⋮
d. ↔ ℘n−1 / Cn−1
e. ↔ ℘n elsewhere
The context specified on an exponent can, of course, be broader than the very local
morphemic context. The size of a contextual domain is a question of locality. In this thesis, I
do not want make a specific claim concerning the locality domain of contextual allomorphy.
Instead, I refer the reader to Marantz (1997, 2013), Embick (2010), Anagnostopoulou (2014).
As a working hypothesis, I assume that categorial domains qualify as interpretative domains.
Exponents are inserted into abstract morphemes according to the Subset Principle (Halle
1997). It is given in (98).
(98) Subset Principle:
The phonological exponent of a Vocabulary Item is inserted into a morpheme [...] if
the item matches all or a subset of the grammatical features specified in the terminal
morpheme. Insertion does not take place if the Vocabulary Item contains features not
present in the morpheme. Where several Vocabulary Items meet the conditions for
insertion, the item matching the greatest number of features specified in the terminal
morpheme must be chosen.
(Halle 1997: 128)
Let us look at three aspects of the Subset Principle in more detail. First, an exponent must
match all or a subset of the grammatical features specified in the terminal morpheme. Consider an
abstract morpheme M with the feature specification M[α, β,γ] and a respective VI with the
exponent ℘ specified for [α,γ]. Assuming there is no other exponent in M’s VI specified as[α, β,γ], the exponent ℘ is inserted into M, as it matches a subset of the features specified in
M. This scenario is outlined in (99).
66 3. Morphology
(99) a. Abstract morpheme M:
M[α, β,γ]
b. Vocabulary Item:
M ↔ ℘ / [α,γ]
c. Specification of exponent ℘ matches a subset of M’s features:
α γ
β
℘M
d. Insertion of exponent ℘ into morpheme M:
M[α, β,γ,℘]
Second, insertion does not take place if the VI contains features not present in the morpheme. Assume
again the same morpheme M and the respective VI containing again the exponent ℘. Now
assume that ℘ is additionally specified for the feature [δ], i.e. [α,γ, δ]. In this case, the
exponent ℘ cannot be inserted into the morpheme M, because ℘ contains a feature in its
specification, namely [δ], not present in the morpheme M. Inserting ℘ into M would lead to
ungrammaticality. This scenario is outlined in (100).
(100) a. Abstract morpheme M:
M[α, β,γ]
b. Vocabulary Item:
M ↔ ℘ / [α,γ, δ]
c. Feature specification of exponent ℘ contains feature missing in M:
α γ
β
δ
*℘M
d. Insertion of exponent ℘ into morpheme M does not take place.
Third, where several VIs meet the conditions for insertion, the item matching the greatest number
of features specified in the terminal morpheme must be chosen. Consider again the morpheme
M[α, β,γ]. Let us assume that two exponents, e.g. ℘1 and ℘2, are listed in the respective
VI and are thus potential candidates for insertion into M. Assume that the exponent ℘1 is
specified as [β,γ] and that the exponent ℘2 is specified as [γ]. In this situation, the exponent℘1 is inserted, because it matches more features in the morpheme M than the exponent ℘2. In
particular, the specification of ℘1 contains the feature β which is absent in the specification of℘2. This scenario is outlined in (101).
3.1. Vocabulary Insertion 67
(101) a. Abstract morpheme M:
M[α, β,γ]
b. Vocabulary Item:
(i) M ↔ ℘1 / [γ, β]
(ii) ↔ ℘2 / [γ]
c. Exponents ℘1 and ℘2 compete for insertion.
Feature specification of exponent ℘1 matches more features in M:
α γ
β ℘1
*℘2M
d. Insertion of exponent ℘1 into morpheme M:
M[α, β,γ,℘1]
Another possible situation, although not covered by the Subset Principle, is that two
exponents in a VIs match the same number of distinct features in a morpheme. Consider
again the morpheme M with the feature specification M[α, β,γ]. Let us assume again two
exponents in the respective VI, namely the exponent ℘1 with the feature specification [α],
and the exponent ℘2 with the feature specification [β]. As neither exponent comprises more
matching features in their specifications than the respective other one, we face a standstill. A
possible solution to this problem builds on the assumption of a hierarchical ordering of the
respective features. If we have evidence to assume that one feature is hierarchically above the
other, we can constrain Vocabulary Insertion such that the VI with the hierarchically higher
feature wins. Let us assume in this example that the feature [α] is hierarchically above [β], i.e.[α] > [β]. In this case, the exponent with the higher ranked feature in its specification wins,
i.e. ℘1 is inserted into the morpheme M.
(102) a. Abstract morpheme M:
M[α, β,γ]
b. Feature hierarchy:[α] > [β]
c. Vocabulary Item:
(i) M ↔ ℘1 / [α]
(ii) ↔ ℘2 / [β]
d. Exponents ℘1 and ℘2 compete for insertion and match the same number of
distinct features in M. The specification of ℘1 consists of a feature that is hierar-
chically higher than the feature in the specification of ℘2:
68 3. Morphology
α
β
γ ℘1
*℘2
M
e. Insertion of exponent ℘1 into morpheme M:
M[α, β,γ,℘1]
Let us flesh out the considerations about Vocabulary Insertion with a concrete example.
Take the agreement morphology of the German (weak) past tense conjugation illustrated in
(103) with the verb sag-en (‘say-INFINITIVE’). The suffix -te (/t@/) is arguably the realization
of the past tense morpheme specified as T[+PAST].42 With regard to person and number
agreement, we can identify four different suffixes (exponents): (i) the null suffix ∅ for the first
and third person singular, (ii) the suffix -st (/st/) for the second person singular, (iii) the suffix
-n (/n/) for the first and third person plural, and (iv) the suffix -st (/t/) for the second person
plural.
(103) German (weak) past tense agreement (sagen ‘say’):
singular plural
first person sag-te-∅ sag-te-n
second person sag-te-st sag-te-t
third person sag-te-∅ sag-te-n
(Bobaljik 2015: 6)
A potential structural analysis of the verbs in (103) is sketched in (104). This complex head
structure, which is parallel to Embick and Noyer’s (2007: 316) structure of Huave verbs,
involves the underlying Root
√
sag, the verb morpheme V, the past tense morpheme T,
and the agreement morpheme AGR.43 T contains the feature [+PAST] and AGR contains
φ-features.
42 Note that the ‘e’ on the past tense morpheme -te is typically assumed to be phonologically conditioned.
The underlying realization is assumed to be -t (/t/). In traditional German linguistics, this is referred to as
e-Erweiterung (‘e-extension’), see Eisenberg et al. (1998). In this example, e-Erweiterung yields the realization -te
(/t@/). In DM, e-Erweiterung can be modeled as a readjustment rule (Section 3.6).
43Note that the morpheme AGR is syntactically unmotivated. In fact, this morpheme is assumed to be a
purely morphological feature-bundle. In DM, such types of morphemes are referred to as ‘ornamental’ or
‘dissociated’ morphology (Embick and Noyer 2007: 305) (cf. Section 3.3).
3.1. Vocabulary Insertion 69
(104)
T
AGR[φ]T
T[+PAST]V
V
√
sag
(adapted from Embick and Noyer 2007: 316)
Focusing on the agreement morpheme and its potential φ-feature manifestations, we could
list the respective exponents as given in (105).
(105) a. AGR[+1,−2,−PL] ↔ ∅
b. AGR[−1,+2,−PL] ↔ /st/
c. AGR[−1,−2,−PL] ↔ ∅
d. AGR[+1,−2,+PL] ↔ /n/
e. AGR[−1,+2,+PL] ↔ /t/
f. AGR[−1,−2,+PL] ↔ /n/
The listing in (105) is formed as full specification of the exponents. In particular, it contains
two syncretisms, i.e. cases where the form-function relation is one-to-many. The null exponent∅ realizes the first and third person singular; and the exponent /n/ realizes the first and third
person plural. Listing these exponents multiple times leads to redundancy. Let us eliminate
this in the following. The exponent /t/ is the most specific one, because it is specified for
the second person and for plural number [+2,+PL]. The exponent /n/ is not specified for the
second person, and it is also not specified for the first person, because it occurs with the first
and the third person. This leads to the assumption that the exponent /n/ is specified only for
plural number [+PL]. The exponent /st/ is not specified for number, but it is specified for the
second person [+2]. The exponent ∅ is the least specific exponent. It is specified neither for
person, nor for number. That is, we can consider the null exponent as being the elsewhere
form. Eliminating redundancy in this way, we can restate the exponents for German (weak)
past tense agreement as given in (106).
(106) German (weak) past tense agreement (AGR) exponents:
a. AGR ↔ /t/ / [+2,+PL]
b. ↔ /n/ / [+PL]
c. ↔ /st/ / [+2]
d. ↔ ∅ elsewhere
(adapted from Bobaljik 2015: 6)
In German, the AGR-morpheme can have the possible φ-feature specifications in (107).
70 3. Morphology
(107) Possible specifications of the AGR-node, prior to Vocabulary Insertion:
singular plural
first person AGR[+1,−2,−PL] AGR[+1,−2,+PL]
second person AGR[−1,+2,−PL] AGR[−1,+2,+PL]
third person AGR[−1,−2,−PL] AGR[−1,−2,+PL]
With regard to the VI in (106), the Subset Principle regulates Vocabulary Insertion as follows.
The exponent /st/, which is specified for [+2], qualifies as a potential realization for the
second person singular and plural. However, as there is a more specific exponent, namely /t/
specified for [+2,+PL], /st/ is not inserted. Instead, /t/ is inserted for second person plural.
The exponent /t/, on the other hand, is too specific for second person singular, which is why
/st/ is inserted here. We are now left with the first and third person. Both exponents /t/ and
/st/ are specified for [+2]; and as such, they are too specific. They cannot be inserted. The
exponent /n/ serves to realize the positive plural feature. It is thus inserted for first and third
person plural. Finally, there are no further exponents that match the feature specifications
of the first and third person singular. Ergo, the elsewhere exponent ∅ is inserted in order to
realize AGR. After Vocabulary Insertion, the AGR-morpheme has the possible forms in (108).
(108) Possible specifications of the AGR-node, after Vocabulary Insertion:
singular plural
first person AGR[+1,−2,−PL,∅] AGR[+1,−2,+PL,/n/]
second person AGR[−1,+2,−PL,/st/] AGR[−1,+2,+PL,/t/]
third person AGR[−1,−2,−PL,∅] AGR[−1,−2,+PL,/n/]
Enriched with the phonological exponents as given in (108), the AGR-morpheme can be
processed at PF, that is, it can be pronounced respectively.
3.2 Linearization
In Minimalist Syntax, as well as in Distributed Morphology, it is typically assumed that
linear order is not a property of the narrow syntax, but that an operation at PF linearizes
hierarchically-organized syntactic structure to the effect that it can be processed serially at the
A-P system (e.g Chomsky 1995, Embick and Noyer 2001, 2007, Hornstein et al. 2005, Bobaljik
2015). The hierarchical phrase structures generated by syntax are two-dimensional objects,
as their buildings blocks are organized in terms of (i) dominance and (ii) sisterhood. Linear
order, however, is not assumed to be a property of syntactic structures. For example, the two
minimal structures given in (109) are identical at the level of narrow syntax, because in both
structures Z directly dominates X and Y, and X is the sister of Y and vice versa.44
44Note that the sisterhood relation does not impose a linear order.
3.2. Linearization 71
(109) a. Z
YX
b. Z
XY
The A-P system, however, requires a linear order, because the linguistic units must be
processed in real time as a serial chain, which means that the output of PF must be a one-
dimensional string of sounds or signs. Embick and Noyer (2001: 562) claim that “linear
ordering is not a property of syntactic representations but is imposed at PF in virtue of the
requirement that speech be instantiated in time (see Sproat 1985). It is therefore natural to
assume that linear ordering is imposed on a phrase marker at the point in the derivation
when phonological information is inserted, that is, at Vocabulary Insertion.” In particular,
they formulate the Late Linearization Hypothesis given in (110).
(110) The Late Linearization Hypothesis:
The elements of a phrase marker are linearized at Vocabulary Insertion.
(Embick and Noyer 2001: 562)
In order to flatten a two-dimensional syntactic structure into a one-dimensional string,
Embick and Noyer (2007: 562) propose an operation at PF, dubbed Lin (for linearization).
This operation takes two syntactic sister nodes as input and imposes a binary concatenation
operator on them. For the concatenation operator, I use the symbol ⌢.45 The relationship
established by the concatenation operator is to be understood as immediate precedence (Embick
2015: 73). So, when Lin applies to the two sister nodes X and Y, then the result is either that X
immediately precedes Y, or that Y immediately precedes X (111). Subsequent applications of
Lin to all pairs of sister nodes in a binary branching tree results in a sequential ordering of all
terminal nodes (Marantz 1984, Sproat 1985, Embick and Noyer 2007).
(111) Linearization:
Lin [ X Y ] → ( X ⌢ Y ) or ( Y ⌢ X )
(Embick and Noyer 2007: 294)
Each language has a set of PF-rules that determine the linear order in which the syntactic
objects are spelled out. Consider, as an example, the English sentence in (112a) and the
Japanese sentence in (112b), both of which arguably have a comparatively parallel structure
at the level of narrow syntax. However, the sentences are different with regard to the linear
order of the constituents within the VP. In English, the verb precedes the direct object, while
in Japanese the verb follows the direct object.
45Note that Embick and Noyer (2007) use the symbol ∗. In line with Embick (2015: 73), I represent concatena-
tion with the symbol ⌢.
72 3. Morphology
(112) a. Norbert [VP ate bagels ].
b. Jiro-ga
Jiro-NOM
[VP sushi-o
sushi-ACC
tabeta
ate
].
‘Jiro ate sushi.’
(Hornstein et al. 2005: 218)
Henceforth, I will represent syntactic structures – in particular in Chapter 5 – in the order
as they are ultimately linearized. This is not a commitment to linear order in syntax, but
rather for the sake of intelligibility.
3.3 Ornamental morphology
A fundamental assumption within Distributed Morphology (DM) is that syntactic structures
are sent off from Spell-Out to PF, where they receive a phonological realization. So, ideally
all morphemes would be syntactico-semantically grounded. However, there is apparently
morphological material that is syntactico-semantically unmotivated. In particular, there is
morphological material for which there is no reason to assume that its respective features are
already present in the syntactic derivation. This means that some morphemes are added to a
structure at PF – potentially due to language-specific well-formedness conditions. Embick
and Noyer (2007: 305) refers to this kind of morphological material as ornamental, because
it “merely introduces syntactico-semantically unmotivated structure and features which
‘ornament’ the syntactic representation.” In particular, Embick and Noyer propose two
types of insertion processes for inserting ornamental morphological material at PF: (i) the
insertion of nodes and (ii) the insertion of features. Embick (1997, 1998), Embick and Noyer
(2007) refer to nodes and features that are inserted at PF as dissociated (113). This term
is supposed to emphasize “that such material is an indirect reflection of certain syntactic
morphemes, features, or configurations, and not the actual spell-out of these” (Embick and
Noyer 2007: 309).
(113) a. Dissociated nodes:
A node is dissociated if and only if it is added to a structure under specified
conditions at PF.
b. Dissociated features:
A feature is dissociated if and only if it is added to a node under specified
conditions at PF.
(Embick and Noyer 2007: 309)
Before I present examples of dissociated nodes and features, let me point to the distinction
between copying (or sharing) of features and the introduction (or insertion) of features (114).
3.3. Ornamental morphology 73
(114) a. Feature copying:
A feature that is present on a node X in the narrow syntax is copied onto another
node Y at PF.
b. Feature introduction:
A feature that is not present in narrow syntax is added at PF.
(Embick and Noyer 2007: 309)
Features subject to morphological agreement or concord processes are typically copied, while
case features – in morphological case theories (e.g. Marantz 1991, McFadden 2004, Bobaljik
2008, cf. Section 6.3.3) – are assumed to be introduced at PF. Note also that both copying and
introducing features, which leads to ornamental morphology, are assumed to take place prior
to Vocabulary Insertion (Section 3.1).
Dissociated nodes
Let us now look at an example of a dissociated node, i.e. a node that is added under specified
conditions at PF (Embick and Noyer 2007: 309). In many languages, the finite verb agrees
with one of its arguments. In Latin, for example, the finite verb agrees with the subject, which
is why this phenomenon is often referred to as subject-verb agreement. Consider the inflected
form of the Latin verb laudo¯ (‘praise’) in (115), which comprises (i) the verb stem laud-, (ii) the
theme vowel -a¯, (iii) the imperfective past tense suffix -ba¯, and (iv) the person and number
agreement suffix -mus for first person plural.
(115) laud-a¯-ba¯-mus
praise-TH-PAST-1.PL
‘We were praising.’
(Embick and Noyer 2007: 305)
With regard to the suffix -mus for finite verb agreement, we can assume that this is hosted
by a so-called AGR-node or AGR-morpheme (cf. also Section 3.1). In DM, however, it is
commonly assumed that verbal AGR-morphemes are absent at the level of syntax – because
they are syntacticosemantically unmotivated – and that they are inserted into the structure
only at PF. A similar point can be made for the theme vowel morpheme TH hosting the suffix
-a¯. In (116), the complex head structure for the verb in (115) is given. It has the form as when
it is sent off from Spell-Out to PF. The structure involves (i) the Root
√
laud, (ii) the verb
morpheme V, (iii) and the past tense morpheme T[+PAST]. Crucially, the AGR-morpheme
and the theme vowel morpheme TH are missing in (116). Note that the complex head is
arguably derived via Head Movement (cf. Matushansky 2006 for a morphological approach
to Head Movement that is compatible with Bare Phrase Structure).
74 3. Morphology
(116) T
T[+PAST]V
V
√
laud
(Embick and Noyer 2007: 306)
Embick and Noyer (2007) propose that the AGR-morpheme is inserted into the derivation at
PF. This can be formulated by the insertion rule in (117), stating that finite T is structurally
extended by the agreement morpheme AGR. Embick and Noyer take the view that this
process has the same properties as adjunction.
(117) Insertion of AGR:
Tfinite → [ T AGR ]
(Embick and Noyer 2007: 306)
Embick and Noyer further propose that the verb morpheme V is structurally extended in the
same way by the theme vowel morpheme TH. The resulting structure is given in (118).
(118) T
AGR[+1,+PL]T
T[+PAST]V
V
THV
√
laud
(Embick and Noyer 2007: 306)
The AGR-morpheme is then the target of finite verb agreement (Sigurðsson 2004, Bobaljik
2008). This means that the φ-features of the controller of finite verb agreement (here: the
subject) are copied to – or shared with – the AGR-morpheme. In this example, the AGR-
morpheme exhibits the φ-features for the first person plural. After Vocabulary Insertion has
taken place (cf. Section 3.1), we obtain the feature structure in (119). Note that the exponents
in (119) are represented orthographically and not phonologically, as usual.
3.3. Ornamental morphology 75
(119)
AGR[+1,+PL, -mus]
T[+PAST, -ba¯]
TH[-a¯]V[∅]
√
laud[laud]
(adapted from Embick and Noyer 2007: 306)
Dissociated features
Let us now look at an example of dissociated features, i.e. features that are added under
specified conditions at PF (Embick and Noyer 2007: 309). In line with Marantz (1991), Mc-
Fadden (2004), Embick and Noyer (2007), Bobaljik (2008), I assume that case does not have
a repercussion in narrow syntax, but that it is a purely morphological phenomenon that is
built on syntax; cf. Section 6.3.3. This basically means that case features are not assumed to be
contained in structures sent off from Spell-Out. Instead, it is assumed that case features are
inserted into structures at PF. Consider the the dative plural form of the Latin noun fe¯mina
(‘woman’), which is fe¯minı¯s (120). The nominal stem is fe¯min-, and the suffix -ı¯s marks plural
dative.
(120) fe¯min-ı¯s
woman-PL.DAT
‘for (the) women’
For this item, we can assume the complex head structure depicted in (121). Crucially, there
are no case features in this structure at the point when it is sent off from Spell-Out to PF. We
only have (i) the Root, (ii) the noun morpheme N, and (iii) the plural number morpheme
Num[+PL].
(121) Num
Num[+PL]N
N
√
femin
(Embick and Noyer 2007: 307)
As in the verbal example above, the theme vowel morpheme TH is added to the morpheme
hosting the Lexical category feature.
76 3. Morphology
(122) Num
Num[+PL]N
N
THN
√
femin
(Embick and Noyer 2007: 307)
Suppose that the DP in which this sub-structure is embedded receives dative case features,
viz. [+INF,+OBL].46 Embick and Noyer (2007: 308) propose that case features are added to D.
The respective morphological rule is depicted in (123).
(123) Insertion of case features:
D → D[case features]
(Embick and Noyer 2007: 308)
The addition of the dative case features [+INF,+OBL] to D yields the configuration in (124).
(124) ..
...
...Num
Num[+PL]N
N
THN
√
femin
D[+INF,+OBL]
In Latin, case and number are typically realized in the same position. One way of dealing
with this is to assume that the case features are copied to Num (Embick and Noyer 2007: 308),
e.g. via DP-internal concord (Sigurðsson 2004, Kramer 2010, Norris 2014). Num is then
augmented by the case features to Num[+PL,+INF,+OBL]. After Vocabulary Insertion has
taken place, the respective feature structure looks as given in (125).
46Note that Embick and Noyer (2007) assume a slightly different set of morphological case features (Halle
1997). However, for the point being made here, this does not make a difference.
3.4. Operations on nodes 77
(125)
Num[+PL,+INF,+OBL, -ı¯s]
TH[∅]N[∅]
√
femin[fe¯min]
The Root
√
femin receives the exponent fe¯min. N receives the null exponent ∅. Simi-
larly, the morphological theme vowel TH receives the null exponent ∅.47 And finally,
Num[+PL,+INF,+OBL] receives the exponent -ı¯s.
3.4 Operations on nodes
This section discusses several operations on terminal nodes at PF that are assumed to take
place prior to Vocabulary Insertion. The following two sections discuss three of these oper-
ations. Section 3.4.1 discusses the operation Impoverishment, an operation where features
are deleted from a morpheme within a certain context. Section 3.4.2 discusses the operations
Fusion and Fission; these two operations respectively fuse or split terminal nodes in certain
contexts.
3.4.1 Impoverishment
The morphological operation Impoverishment, which was first proposed by Bonet (1991),
targets the feature content of a morpheme, i.e. terminal node, such that it deletes certain
features from the respective morpheme. In order to constrain its application, Impoverishment
is contextually conditioned. Typically, the effect of Impoverishment is that a more general (or
less specific) exponent is inserted into a morpheme, which would otherwise be realized by a
more specific (or less general) exponent. Impoverishment rules apply prior to Vocabulary
Insertion. Embick (2015: 140) formalizes Impoverishment as given in (126), where the feature[α] deletes in the context C.
(126) Impoverishment:[α] → [] / C
(Embick 2015: 140)
47Meyer (1992: 10) assumes that the dative (and also the ablative) plural forms of nouns belonging to the
First Declension (a), e.g. fe¯min-ı¯s, derive from forms involving a theme vowel, i.e. fe¯min-a-is.
78 3. Morphology
Let us now look at an example of Impoverishment. Take strong/week adjectival inflection
in Norwegian as an example.48 Consider the adjectival suffixes in the Norwegian DPs in (127)–
(130). All examples contain the adjective stor (‘big’) in prenominal position. The examples in
(127) and (128) are indefinite (indef), while the examples in (129) and (130) are definite (def).
The examples in (127) and (129) are singular (sg), while the examples in (128) and (130) are
plural (pl). The a.-examples contain the noun bil (‘car’) that has masculine (masc) gender,
while the b.-examples contain the noun vindu (‘window’) that has neuter (neut) gender.
(127) a. en
a.SG.MASC
stor
big.SG.MASC
bil
car
‘a big car’
b. et
a.SG.NEUT
stor-t
big-SG.NEUT
vindu
window
‘a big window’
(128) a. stor-e
big-PL
bil-er
car-INDEF.PL
‘big cars’
b. stor-e
big-PL
vindu-er
window-INDEF.PL
‘big windows’
(129) a. den
the.SG.MASC
stor-e
big-SG.MASC
bil-en
car-DEF.SG.MASC
‘the big car’
b. det
the.SG.NEUT
stor-e
big-SG.NEUT
vindu-et
window-DEF.SG.NEUT
‘the big window’
(130) a. de
the.PL
stor-e
big-PL
bil-ene
car-DEF.PL
‘the big cars’
b. de
the.PL
stor-e
big-PL
vindu-ene
window-DEF.PL
‘the big windows’
The indefiniteness/definiteness distinction in Norwegian DPs normally follows the distinc-
tion between strong/weak adjectival inflection. The prenominal position in an indefinite DP
normally constitutes an environment for strong adjectival inflection, while the prenominal
position in a definite DP normally constitutes an environment for weak adjectival inflection.
In the strong singular pattern in (127), the adjectival suffixes are ∅ for non-neuter and -t for
neuter. In the strong plural pattern in (128), the adjectival suffix is -e for both non-neuter and
neuter. In the weak pattern in (129) and (130), the adjectival suffix is also always -e. This is
summarized in (131).
48Many Germanic languages show the phenomenon of strong/weak adjectival inflection. For German,
however, the picture is much more complex than for Norwegian.
3.4. Operations on nodes 79
(131) a. Norwegian strong adjectival suffixes:
non-neuter neuter
singular ∅ -t
plural -e -e
b. Norwegian weak adjectival suffixes:
non-neuter neuter
singular -e -e
plural -e -e
(Sauerland 1996: 28)
In order to account for this, we can assume the plural number feature [±PL], and – for the sake
of simplicity – the neuter gender feature [±NEUT]. We can further assume the dissociated
AGR-morpheme that realizes adjectival inflection. The strong inflection pattern can be
accounted for with the VI in (132). The exponent -t is inserted into neuter, non-plural AGR-
morphemes, the null exponent ∅ is inserted into non-neuter, non-plural AGR-morphemes,
and the elsewhere exponent -e is inserted into all other AGR-morphemes.
(132) Exponents of Norwegian adjectival inflection:
a. AGR ↔ -t / [−PL,+NEUT]
b. ↔ ∅ / [−PL,−NEUT]
c. ↔ -e elsewhere
(adapted from Sauerland 1996: 28)
The weak inflection pattern can also be accounted for with this VI, if we assume an Impover-
ishment rule operating on the adjectival AGR in weak contexts. The Impoverishment rule
on AGR-morphemes, as formulated in (133), deletes the gender feature [±NEUT] in weak
contexts. Note that I simply use ‘weak’ here as a cover term for such weak contexts. One of
these is the prenominal position after a definite article.49
(133) Norwegian adjectival AGR-Impoverishment:[±NEUT] → [] / ‘weak’
With this Impoverishment rule, both the exponents -t and ∅ are too specific for insertion
into the adjectival AGR-morpheme in weak contexts. Instead, the elsewhere exponent -e is
inserted in weak contexts.
3.4.2 Fusion and Fission
Ideally, the correspondence between the syntactico-semantic/morphosyntactic structure and
the surface realization is such that each abstract morpheme in the structure corresponds
to one exponent on the surface. This idealization is weakened by several morphological
49Note that, in Norwegian, ‘weak’ could be characterized by definiteness. However, data from strong/weak
adjectival inflection in German suggest that the picture is in fact more complex.
80 3. Morphology
phenomena. For example, there is contextual allomorphy, i.e. the case that morphemes can
have various context-dependent realizations. Furthermore, morphemes can be realized by
the null exponent, i.e. these morphemes are silent. In addition to such irregularities, there are
also cases (i) where one surface exponent corresponds to two (or more) abstract morphemes,
or (ii) where one abstract morpheme corresponds to two (or more) surface exponents. These
types of mismatches between structure and surface motivate the morphological operations
Fusion and Fission, respectively. Take a look at Embick’s (2015) considerations in (134).
(134) Two Types of Mismatches
a. Case 1: The morphosyntactic analysis motivates two distinct morphemes, X
and Y. In some particular combination(s) of feature values for X and Y, though,
there are no two distinct exponents realizing X and Y on the surface. Rather,
there appears to be a “portmanteau” realization instead of the expected indi-
vidual realizations of X and Y.⇒ This case motivates Fusion.
b. Case 2: The morphosyntactic analysis motivates a single morpheme X, with
features [±α] and [±β]. In particular combinations of feature values, though,
there are two (or more) distinct exponents on the surface, corresponding to the
different features [±α] and [±β].⇒ This case motivates Fission
(Embick 2015: 213)
Both the operation Fusion and the operation Fission apply prior to Vocabulary Insertion.
Fusion
In some situations, two abstract morphemes independently motivated are realized by one
morphologically non-decomposable exponent. In DM, this type of morphological mismatch
is typically accounted for with the operation Fusion, which creates – at PF – one morpheme
out of two. In general, the operation Fusion can be defined as given in (135), where two
abstract morphemes X[α] and Y[β] fuse to one complex morpheme X/Y[α, β].
(135) Fusion:
X[α] Y[β] → X/Y[α, β]
Let us look at a textbook example of the PF-operation Fusion: Latin indicative present
tense conjugation (Embick and Halle 2005b, Embick 2015) of the verb lauda¯re (‘praise’) given
in (136).
3.4. Operations on nodes 81
(136) Present indicative active and passive of Latin lauda¯re (‘praise’):
active passive
singular first person laud-o¯ laud-o-r
second person laud-a¯-s laud-a¯-ri-s
third person laud-a-t laud-a¯-t-ur
plural first person laud-a¯-mus laud-a¯-mu-r
second person laud-a¯-tis laud-a¯-minı¯
third person laud-a-nt laud-a-nt-ur
(Embick 2015: 214)
The verb forms in (136) comprise the verbal root laud-, in most cases the theme vowel -a¯
or -a, an agreement suffix indicating person and number, and an r-suffix indicating passive
voice. A reasonable verb structure in terms of a complex head analysis is given in (137). It
involves (i) the Root
√
laud, (ii) the verb morpheme V that is morphologically extended by
the dissociated node AGR for finite verb agreement, and (iii) the voice morpheme Voice. Note
that the structure in (137) differs in several respects from the comparable structure in (118).
However, with regard to the argument to be made here, this difference does not matter.
(137) Voice
VoiceV
AGRV
V
√
laud
In all verb forms, the Root is realized by the exponent laud-. The theme vowel -a¯/-a is assumed
to be realization of V (Embick 2015: 215).50 In the case of the first person singular, the theme
vowel is deleted phonologically.51 We can observe that the verb forms in the passive voice
are, in most cases, morphologically marked with a so-called r-exponent. It has the allomorphs
-r for the first person, -ri for the second person singular, and -ur for the third person. We
can further observe that most verb forms in the active and passive voice share a common
person/number agreement suffix, i.e. -o¯/-o for the first person singular, -s for the second
person singular, -t for the third person singular, -mus/-mu for the first person plural, and -nt
for the third person plural. Crucially, only the agreement suffix of the second person plural in
the active -tis is not preserved in the passive. Furthermore, the second person plural passive
form does not involve an r-exponent. In the second person plural, the suffix -minı¯ expresses
50This is, for instance, different in the analysis above. However, this difference is not crucial here.
51Meyer (1992: 27–28) assumes that the first person singular forms of verbs belonging to the First Conjugation
(a), e.g. laud-o¯ and laud-o¯-r, derive from forms involving a theme vowel, i.e. laud-a-o and laud-a-o-r, respectively.
82 3. Morphology
both agreement and voice.52 With respect to the feature structure of the second person plural
passive, we can assume that it looks as given in (138), viz. AGR is valued as [−1,+2,+PL] for
second person plural, and Voice is valued as [+PASS] for passive.
(138)
Voice[+PASS]
AGR[−1,+2,+PL]...
In all cases, except for the second person plural passive, the two morphemes, i.e. the AGR-
morpheme and the passive voice morpheme, are realized separately. Instead of a hypothetical
ending *-ri-tis for the second person plural passive, the respective exponent is minı¯. This
suffix contains neither a residue of the AGR-exponent -tis for the second person plural nor a
residue of the passive Voice exponent, viz. some form of the r-exponent. In DM, this kind
of morphological mismatch can be modeled with the operation Fusion. In particular, it is
assumed that the AGR-morpheme and the Voice morpheme undergo Fusion in the context
of second person plural passive. This yields a complex AGR/Voice-morpheme. Fusion for
the second person plural passive in Latin can be formalized as given in (139). Note that the
feature specifications of the AGR-morpheme and Voice morpheme suffice to trigger Fusion
here, that is, we do not need to assume an ‘external’ context.
(139) Latin passive Fusion:
AGR[−1,+2,+PL] Voice[+PASS] → AGR/Voice[−1,+2,+PL,+PASS]
(adapted from Embick 2015: 215)
We can now state a VI for the fused AGR/Voice-morpheme, as given in (140). This VI applies
to fused AGR/Voice-morphemes in the second person plural passive and realizes them with
the suffix -minı¯. In particular, the VI in (140) is more specific than both the VI for AGR (141)
and the VI for Voice in (143). As a result, VI in (140) takes precedence over the VIs in (141)
and (143), and thus the exponents -tis and -r are blocked for insertion in the second person
plural passive.
(140) VI for fused AGR/Voice-morpheme:
AGR/Voice ↔ -minı¯ / [+2,+PL,+PASS]
52Note that there is a further complication in the second person concerning the Linearization of the exponents.
While the dissociated AGR-morpheme and the Voice morpheme (r-exponent in the passive) are linearized as
AGR–Voice in the first and third person, they are linearized in the reverse order as Voice–AGR in the second
person singular. In line with Embick (2015: 214), I will put this aside, since it does not affect any point about the
motivation of Fusion.
3.4. Operations on nodes 83
In the non-fused cases, the AGR-morpheme is straightforwardly realized by the exponents
listed in the VI in (141). Subsequently, the exponents of the first person are subject to the
morphophonological Readjustment rule (cf. Section 3.6) stated in (142). These rules yield the
respective agreement suffixes in the plural.
(141) Exponents of Latin AGR:
a. AGR ↔ -tis / [+2,+PL]
b. ↔ -mus / [+1,+PL]
c. ↔ -s / [+2]
d. ↔ -o¯ / [+1]
e. ↔ -nt / [+PL]
f. ↔ -t elsewhere
(142) Latin AGR-Readjustment:
a. -o¯ → -o / [+PASS]
b. -mus → -mu / [+PASS]
For the realizations of the Voice-morpheme we can assume the VI in (143), yielding the
r-exponent in the passive voice. Note that I refrain from specifying all potential realizations of
the Voice-morpheme because this is not crucial here. Subsequently, the r-exponent is subject
to a morphophonological Readjustment rule, which can be formulated as given in (144). This
yields the respective suffixes.
(143) Exponents of Latin Voice:
a. Voice ↔ -r / [+PASS]
b. ↔ ...
(144) Latin passive voice Readjustment:
a. -r → -ur / [−1,−2]
b. -r → -ri / [+2]
Fission
Normally, one abstract morpheme is realized by one exponent. There are, however, situations
where features that are normally part of one morpheme are realized by two distinct exponents.
In DM, this kind of morphological mismatch, is accounted for with the morphological
operation Fission, which splits – at PF – one morpheme into two (or more). In general,
the operation Fission, which can be considered to be the opposite operation of Fusion, can
84 3. Morphology
be defined as given in (145), where one abstract morpheme, say, X[α, β] split into the two
morphemes Xi[α] and Xj[β].
(145) Fission:
X[α, β] → Xi[α] Xj[β]
Let us look at a textbook example of the PF operation Fission. Consider verbal conjugation
in San Mateo Huave, a Mexican isolate language (Stairs and Hollenbach 1981). (146) illustrates
the present (atemporal) tense agreement pattern containing the verbal root -rang (‘make, do’).
The example is taken from Embick and Noyer (2007: 315).
(146) Huave verbal conjugation: present (atemporal) tense of -rang (‘make, do’)
non-plural plural
first person exclusive s-a-rang s-a-rang-an
first person inclusive a-rang-ar a-rang-acc
second person i-rang i-rang-an
third person a-rang a-rang-aw’
(Embick and Noyer 2007: 315)
The conjugation pattern of the present (atemporal) tense of the verb -rang (‘make, do’) involves
eight distinct verb forms. There are four singular (i.e. non-plural) forms and four plural
forms. This cuts across four person specifications. The first person comes in two varieties: (i)
in an exclusive version (i.e. speaker only) and (ii) in an inclusive version (i.e. speaker and
addressee). Furthermore, there is the second person and the third person. All four persons
have a singular form and a plural form. The verb forms comprise a verbal kernel which is
-rang here. The verbal kernel is prefixed with a theme vowel that usually is a-, except for the
second person, where it is i-. The first person exclusive is marked with the prefix s-. The
suffix -an appears to be the default plural marker, while the suffixes -acc and -aw’ are more
specific plural markers for the first person inclusive and for the third person, respectively.
Embick and Noyer (2007) straightforwardly assume a complex head structure for the
Huave verb forms illustrated in (147). The structure contains (i) a Root position, (ii) the verb
morpheme V, (iii) the tense morpheme T, and (iv) the dissociated node AGR.
(147) T
AGRT
TV
V
√
Root
(Embick and Noyer 2007: 316)
3.4. Operations on nodes 85
Embick and Noyer assume that V hosts the theme vowel and is linearized to the left of
the Root, i.e. the inverse image of (147); with regard to Linearization, I refer the reader to
Section 3.2. T does not have an overt realization in this example, so we can ignore it here. The
dissociated AGR-morpheme, which is inserted at PF, comprises person and number features
and can have the φ-specification depicted in (148).
(148) Possible φ-specifications of Huave AGR:
non-plural plural
first person exclusive AGR[+1,−2,−PL] AGR[+1,−2,+PL]
first person inclusive AGR[+1,+2,−PL] AGR[+1,+2,+PL]
second person AGR[−1,+2,−PL] AGR[−1,+2,+PL]
third person AGR[−1,−2,−PL] AGR[−1,−2,+PL]
With regard to the verb forms presented in (146), we see that, in some cases, AGR is realized
by one exponent, while in other cases AGR is realized by two distinct exponents. The forms
with one exponent realizing AGR are (I.i) first person inclusive singular AGR[+1,+2,−PL]
realized by the exponent -ar, (I.ii) first person inclusive plural AGR[+1,+2,+PL] realized by
the exponent acc, (I.iii) third person singular AGR[−1,−2,−PL] realized by the null exponent∅, and (I.iv) third person plural AGR[−1,−2,+PL] realized by the exponent -aw’. The forms
with two exponents realizing AGR are (II.i) first person exclusive singular AGR[+1,−2,−PL],
where person features are realized by the prefixed exponent s- and number features by the
null exponent ∅; (II.ii) first person exclusive plural AGR[+1,−2,+PL], where person features
are again realized by the prefixed exponent s- and number features by the suffixed exponent
-an; (II.iii) second person singular AGR[−1,+2,−PL], where person features are realized by
ablauting the prefixed theme vowel and number features by the null exponent ∅; and (II.iv)
second person plural AGR[−1,+2,+PL], where person features are again realized by ablauting
the prefixed theme vowel and number features by the suffixed exponent -an. That is, in the
case of the first person exclusive and in the case of the second person, the person features
are expressed at a different position than the number features. In particular, person features
are realized to the left of the verbal kernel (the prefixed exponent s- realizes the first person
exclusive and ablauting the theme vowel preceding the verbal kernel realizes the second
person), while number features are realized to the right of the verbal kernel (the suffixed
exponent -an realizes plural and the null exponent realizes singular). In fact, we can assume
that the AGR-morpheme is split in the first person exclusive and in the second person. In DM,
this can be accounted for by the morphological operation Fission. A potential formulation of
Huave AGR-Fission is given in (149).
(149) Huave AGR-Fission:
a. AGR[+1,−2,αnumber] → AGRi[+1,−2] AGRj[αnumber]
b. AGR[−1,+2,αnumber] → AGRi[−1,+2] AGRj[αnumber]
86 3. Morphology
These Fission rules split AGR into two morphemes iff the person features have distinct values.
The result of these Fission rules are two AGR-morphemes: AGRi containing person features
and AGRj containing number features. These two AGR-morphemes are then subject to a
Linearization rule to the effect that AGRi precedes the verbal kernel, while AGRj follows it.
Taking these considerations into account, we can formulate the VI of Huave AGR as given
in (150). Note that the ‘exponent’ [−BACK] is supposed to be a floating phonological feature
triggering the ablaut of the theme vowel (Embick and Noyer 2007: 315).53
(150) VI of Huave verbal AGR:
a. AGR ↔ -aw’ / [−1,−2,+PL]
b. ↔ -acc / [+1,+2,+PL]
c. ↔ -ar / [+1,+2]
d. ↔ s- / [+1]
e. ↔ [−BACK] / [+2]
f. ↔ -an / [+PL]
g. ↔ ∅ elsewhere
(adapted from Embick and Noyer 2007: 317)
The non-fissioned overt realizations of AGR are specified in (150a)–(150c). The exponents
that apply in the fissioned forms are less specific and specified as given in (150d)–(150f). The
null exponent ∅ can then be assumed to be the elsewhere form.
3.5 Morphological Merger
In some cases, the ultimate morphological structure seems to be derived from syntactic
structure via movement operations at PF. Marantz (1984, 1988) provides a general formulation
for such displacement processes in terms of Morphological Merger (151).
(151) Morphological Merger:
At any level of syntactic analysis (D-Structure, S-Structure, phonological structure),
a relation between X and Y may be replaced by (expressed by) the affixation of the
lexical head of X to the lexical head of Y.
(Marantz 1988: 261)
In DM, it is typically assumed that Vocabulary Insertion and concomitant Linearization takes
place late at PF. With regard to movement at PF, Embick and Noyer (2001, 2007) propose
that there are at least two varieties of Morphological Merger: (i) one taking place before
Vocabulary Insertion and Linearization (152a) and (ii) one taking place after, or concomitant
with, Vocabulary Insertion and Linearization (152b).
53Considering the assumptions concerning Linearization made above, the feature [−BACK] triggering ablaut
is adjacent to the position hosting the theme vowel. This yields the shift from a- to i-.
3.5. Morphological Merger 87
(152) Two movement operations at PF:
a. Before Linearization: The derivation operates in terms of hierarchical struc-
tures. Consequently, a movement operation that applies at this stage is defined
hierarchically. This movement is Lowering; it lowers a head to the head of its
complement.
b. After Linearization: The derivation operates in terms of linear order. The
movement operation that occurs at this stage, Local Dislocation, operates in
terms of linear adjacency, not hierarchical structure.
(Embick and Noyer 2007: 319)
In the following, I briefly discuss these two morphological movement operations.
The motivation of Lowering, i.e. the morphological movement operation taking place
prior to Vocabulary Insertion, is that syntactic terminals can unite and be spelled out together,
even if they do not join in narrow syntax. Lowering has the form depicted in (153). Here, the
head X○ lowers to Y○, the head of its complement. The docking of X○ at its landing site Y○
takes the form of adjunction.
(153) Lowering of X○ to Y○:
[XP ... X○ [YP ... Y○ ... ] ] → [XP ... [YP ... [Y○ Y○ X○ ] ... ] ]
(Embick and Noyer 2001: 561)
A paradigmatic example of Lowering is the realization of the English past tense morpheme.
Based on observations of adverb placement, it is assumed that in English, unlike in several
other languages, verbs do not move to the tense head in the narrow syntax. Nonetheless,
tense morphology is typically realized on the verb when it is not prevented by negation, for
instance. Embick and Noyer (2001: 562) thus propose that English T undergoes Lowering to
the head of its complement, which is the verb. Consider the respective examples (154).
(154) a. Mary [TP ti [VP loudly play-ed1 the trumpet ] ]
b. *Mary did loudly play the trumpet.
(Embick and Noyer 2001: 562)
The respective English Lowering rule can be formulated as in (155).
(155) English T Lowering:
T lowers to V
(Embick and Noyer 2007: 319)
Lowering has a non-local (non-adjacent) character. As can be seen in (154a), an intervening
adverb such as loudly does not prevent Lowering of T to V.
The morphological movement operation Local Dislocation applies after Vocabulary In-
sertion and Linearization. Thus, it does not make reference to hierarchical order but to linear
88 3. Morphology
order, which I represent with ⌢ in this thesis. A general formalization is given in (156), where
the morphemes X and Y, which are assumed to contain morphophonological material already,
are linearized such that X precedes Y. Local Dislocation re-orders them to the effect that
ultimately Y precedes X.
(156) Local Dislocation:
X ⌢ Y → Y–X
(Embick and Noyer 2007: 319)
Local Dislocation can, for instance, target affixation. As an example, consider the verbal
suffixes in Huave (Stairs and Hollenbach 1981) in (157).54 As a general rule, the reflexive (refl)
suffix -ay appears directly before the final inflectional suffix of a verb – if any is present
(Embick and Noyer 2007: 319). Person is expressed as a prefix, while plural number can be
expressed as a suffix
(157) a. s-a-kohcˇ-ay
1-TH-cut-REFL
‘I cut myself’
b. s-a-kohcˇ-ay-on
1-TH-cut-REFL-PL
‘we cut ourselves’
(Embick and Noyer 2007: 320)
The examples in (158) and (159) are in the past tense, which is expressed by means of the
prefix t-. Number and person is expressed as suffixes following the verb stem. In the singular
(158), the reflexive suffix -ay precedes the person suffix. In the plural (159), however, the
reflexive suffix -ay follows the person suffix and precedes the number suffix. Crucially, it
does not precede the person suffix and thus is adjacent to the verb stem.
(158) a. t-e-kohcˇ-ay-os
PAST-TH-cut-REFL-1
‘I cut (past) myself’
b. *t-e-kohcˇ-as-ay
PAST-TH-cut-1-REFL
(Embick and Noyer 2007: 320)
(159) a. t-e-kohcˇ-as-ay-on
PAST-TH-cut-1-REFL-PL
‘we cut (past) ourselves’
b. *t-e-kohcˇ-ay-os-on
PAST-TH-cut-REFL-1-PL
(Embick and Noyer 2007: 320)
54The affixes -a- in (157) and -e- in (158) and (159) are considered to be theme vowels (glossed with TH). They,
however, are of no interest here.
3.6. Readjustment Rules 89
These data can be explained if we assume that -ay is linearized peripheral to the verb+inflection
complex. Embick and Noyer (2007) assume that the exponent -ay in the respective linearized
structures undergoes Local Dislocation to the effect that it occurs in the penultimate position.
The verb forms in (158a) and (159a) are derived in (160a) and (160b), respectively.
(160) a. ((( t-e-kohcˇ ) ⌢ os ) ⌢ ay ) → (( t-e-kohcˇ ) ⌢ ay-os )
b. (((( t-e-kohcˇ ) ⌢ as ) ⌢ on ) ⌢ ay ) → ((( t-e-kohcˇ ) ⌢ as ) ⌢ ay-on )
3.6 Readjustment Rules
Distributed Morphology (DM) is a piece-based morphological framework. However, there
are situations in which the syntactic structure is morphologically not only reflected by (the
concatenation of) individual pieces, i.e. exponents, but by non-concatenative morphological
processes, e.g. stem alternation. In DM, such non-concatenative morphological processes can
be accounted for with so-called Readjustment rules that operate on certain morphophono-
logical exponents in specified contexts to the effect that the respective exponent is changed
into a morphophonologically-cognate exponent. The general form of a morphophonological
Readjustment rule is given in (161), where the exponent ℘ is morphophonologically changed
into the cognate exponent ℘′ in the context C.
(161) Readjustment Rule:℘ → ℘′ / C
By hypothesis, morphophonological Readjustment rules operate on morphophonological
exponents in specified contexts. Thus, these rules are assumed to apply after Vocabulary
Insertion.
Let us look at a paradigmatic example of a morphophonological Readjustment rule.
Consider the irregular past tense formation of English verbs like sing, which is sang and not
*sing-ed (Embick and Halle 2005a, Embick 2015). The morphophonological Readjustment rule
in (162) changes the vowel /I/ in the phonological exponent /sIN/ to the vowel /æ/ in the
context of the past tense feature [+PAST], which results in the exponent /sæN/.
(162) /sIN/ → /sæN/ / [+PAST]
The phonologically regular pattern underlying this kind of Readjustment rule is ablauting.55
Consider the following verbs, which are subject to the same phonological Readjustment:
begin, give, ring, sink, sit, spring, stink, swim, etc. What is crucial here is the assumption that
Readjustment rules and Vocabulary Insertion are distinct morphophonological operations
(Embick 2015: 204). In particular, it is not assumed that Readjustment blocks Vocabulary
55For a potential modeling of the phonological Readjustment rule changing the stem vowel in the past tense
of verbs like sing, I refer the reader to Halle and Mohanan (1985: 107–108).
90 3. Morphology
Insertion in any way. That is, Readjustment of /sIN/ to /sæN/ does not block the realization
of the past tense morpheme T[+PAST] as -ed. The reason for this assumption is that both
morphological processes can apparently co-occur. In past tense forms like tol-d (from tell)
or froz-en (from freeze), for example, the respective suffixes are arguably a realization of the
past tense morpheme T[+PAST], even though the exponent of the verbal kernel is subject to
Readjustment.
3.7 Summary
This chapter explored the morphological branch of the Y-model of grammar, that is Phono-
logical Form (PF). In this thesis, I adopted the tenets of Distributed Morphology (DM) (Halle
and Marantz 1994, Embick 2015).
Section 3.1 presented the operation Vocabulary Insertion. In DM, morphophonological
exponents are inserted late, i.e. after the syntactic derivation, into the terminal nodes of
syntax, which are considered to be abstract morphemes. Vocabulary Insertion is controlled
by the Subset Principle (Halle 1997: 128); according to the Subset Principle, the phonological
exponent of a Vocabulary Item (VI) is inserted into a morpheme if the item matches all or a
subset of the grammatical features specified in the terminal node. Insertion does not take
place if the VI contains features that are not present in the morpheme. Where several VIs
meet the conditions for insertion, the item matching the greatest number of features specified
in the terminal node is chosen. Then, Section 3.2 discussed the Late Linearization Hypothesis
according to which the elements of a phrase marker are linearized at Vocabulary Insertion
(Embick and Noyer 2001: 562). In the Minimalist Program (MP), it is typically assumed
that syntax does not commit to a inherent serialization of the terminal nodes (Chomsky
1995, Embick and Noyer 2001, 2007, Hornstein et al. 2005, Bobaljik 2015). At PF, the two-
dimensional, hierarchical structure generated by syntax is flattened to a one-dimensional
string by the morphological operation Lin (linearization) (Embick and Noyer 2007: 294).
Section 3.3 discussed two instances of ornamental morphology (Embick and Noyer
2007: 305): (i) dissociated nodes, i.e. nodes that are added to a structure under specified
conditions at PF; and (ii) dissociated features, i.e. features that are added to a node under
specified conditions at PF.
Section 3.4 presented morphological operations on nodes. Section 3.4.1 presented the
operation Impoverishment, where certain features are deleted from a node under specified
conditions (Bonet 1991, Embick 2015). Section 3.4.2 presented two morphological operations
with which one can account for syntax/morphology mismatches: (i) Fusion, where two
abstract morphemes fuse to one abstract morpheme, under specified conditions; and (ii)
Fission, where one abstract morpheme splits into two abstract morphemes, under specified
conditions.
Section 3.5 addressed morphological displacement operations generally referred to as
Morphological Merger (Marantz 1988: 261). Two such movement operations at PF, were
3.7. Summary 91
briefly presented: (i) Lowering, which takes place before Linearization (Embick and Noyer
2001: 561); and (ii) Local Dislocation, which takes place after Linearization (Embick and Noyer
2007: 319).
Section 3.6 presented Readjustment Rules with which one can account for (minor) changes
of morphophonological exponents in certain contexts (Embick 2015: 204).
92 3. Morphology
Chapter 4
Semantics
This chapter explores the branch from Spell-Out to the Conceptual-Intentional (C-I) system
in the Y-model of grammar (Semantics) depicted in Figure 6.
Numeration
Spell-Out
Phonological
Form (PF)
A-P
system
Morphology
Logical
Form (LF)
C-I
system
Semantics
Syntax
Lexicon:
The generative items
of a language
Content:
The non-generative,
contentful items
of a language
(List 2)
Vocabulary:
Instructions for
pronouncing
terminal nodes
in context
(List 3)
Encyclopedia:
Instructions for
interpreting
terminal nodes
in context
. . . . .(List. . .1)
Figure 6: Semantics in the Y-model of grammar
At Spell-Out, syntactic structures generated by Syntax (cf. Chapter 2) are sent off to be
interpreted at the interfaces. Logical Form (LF) is the interface representation of the C-I
systems. At LF, each terminal node of a syntactic structure receives a context-sensitive seman-
tic interpretation. As for the LF-representation formalism, I use Discourse Representation
93
94 4. Semantics
Theory (DRT) (Kamp and Reyle 1993, 2011, Kamp 2010, 2015, Kamp et al. 2011, a.o.). In par-
ticular, I assume that each terminal node receives a semantic representation in the form of a
Discourse Representation Structure (DRS), the choice of which depends on its context. The
DRSs of the terminal nodes are composed bottom-up along the syntactic structure, leading to
semantic representations of larger linguistic units, viz. phrases, clauses, etc. (see Section 4.1
for the semantic construction algorithm).
One of the motives for using DRT is that it separates the semantic representation from its
model-theoretic interpretation. DRT offers a controlled way to ask and answer the question
of what an expressive, and yet parsimonious, formalism has to be like in order to adequately
represent natural language. In particular, it allows a language-driven representation of the
cognitively relevant relations that are expressed by sentences containing spatial prepositions.
4.1 Semantic construction algorithm
At LF, each terminal node of a syntactic structure receives a context-dependent semantic
interpretation (Encyclopedia Item, EI), which takes the form of a (fragmental) DRS. Compo-
sitionally, these DRSs are combined by means of unification-based composition rules. This
happens bottom-up along the syntactic structure. The following section presents the semantic
construction algorithm.
4.1.1 Context-sensitive interpretation
At LF, terminal nodes are semantically interpreted depending on their context. In particular, I
assume that a terminal node X can be assigned different Encyclopedia Items (EIs) depending
on X’s local environment (context). That is, terminal nodes may not only have a set of
PF-instructions for their phonological realizations, but also a set of LF-instructions for their
semantic interpretations. This operationalizes contextual allosemy (Marantz 2013), namely
that the choice of the meaning of X depends on its local environment (cf. Anagnostopoulou
2014: 305).
(163) Generalized LF-instruction:
Terminal node Encyclopedia Items Context
a. X ↔ `1 / Ca
b. ↔ `2 / Cb
c. ↔ ... / ...
d. ↔ `n elsewhere
The generalized LF-instructions in (163) are to be read as follows. X receives the EI `1 if it
occurs in the context Ca. If X occurs in the context Cb, it receives the EI `2, and so on. If
X occurs in none of the specified contexts, then there is normally an EI that serves as the
4.1. Semantic construction algorithm 95
elsewhere interpretation of X (here `n). The relevant contexts triggering different EIs are
normally ordered according to specificity, starting with Ca as being the most specific context.
In particular, the respective EIs compete for being the assigned to X at LF. More specific
contexts win over less specific contexts.
In line with Harley (2014), I assume that not only functional material, but also contentful
features can receive various EIs. In the framework advocated here, these are (bundles of)
Content features occurring in Root positions – Roots, in Harley’s terms. In order to illustrate
this, I adopt Harley’s (2014) example for what she labels as
√
77 underlying the verb throw.56
The PF-instructions for
√
77 are given in (164a). As /TroU/ is the only possible Vocabulary
Item (VI) (pronunciation) for
√
77, no contextual specification is needed; note that this is
under the assumption that the past tense form threw /Tru:/ is formed by the application
of a morphophonological Readjustment Rule (cf. Section 3.6). The VI /TroU/ is thus the
phonological ‘elsewhere’ pronunciation that applies everywhere for
√
77. In contrast, the LF-
instructions for
√
77 in (164b) comprise different EIs (interpretations) depending on different
contexts. Here, the most specific context is the construction with the particle up, resulting in
the interpretation »vomit« (164b-i).57 The next context in which
√
77 can appear is a nominal
context. Here,
√
77 receives the EI »a light blanket«. As given in (164b-iii), other EIs could be
assigned to
√
77 in other contexts. Ultimately, the ‘literal’ or ‘transparent’ interpretation of√
77 as »throw« is assumed to be the elsewhere EI, as given in (164b-iv).
(164) Interface instructions for Harley’s (2014: 244) Root
√
77
a. PF-instructions√
77 ↔ /TroU/
b. LF-instructions
(i)
√
77 ↔ »vomit« / [ v [ [__]√ [up]P ] ]vP
(ii) ↔ »a light blanket« / [ n [__]√ ]
(iii) ↔ {...other meanings in other contexts...}
(iv) ↔ »throw« elsewhere
(Harley 2014: 244)
Indeed, we find more possible interpretations for the verb throw, as we can see in (165), where
the choice of the complement leads to different interpretations of the verb throw. In fact,
Marantz (1984: 25) notes that “every simple transitive English verb expresses a wide range of
predicates depending on the choice of direct object.”
(165) a. throw a baseball→ ‘throw a baseball’ (literal meaning)
56Note at this point that I do not commit to all the details of Harley’s syntactic analyses, in particular to the
claim that Roots are supposed to take complements.
57For the sake of illustration, I reproduce Harley’s informal semantic notation here. Ultimately, I represent
EIs as (fragmental) DRSs.
96 4. Semantics
b. throw support behind a candidate→ ‘support a candidate’
c. throw a boxing match (i.e., take a dive)→ ‘surrender in a boxing match’
d. throw a party→ ‘arrange a party’
e. throw a fit→ ‘go crazy’
(cf. Marantz 1984: 25; glosses are mine)
It seems tempting to model this variety of idiomatic interpretations that depend on the
complement of the verb in terms of LF-instructions as described above. However, we have to
be careful here. LF-instructions model a decision process for semantic interpretation, based
on competition between several possible EIs. If we identify a particular context, the die is
cast for the respective EI. Focusing on PF-instructions of functional material (Vocabulary
Insertion), Embick and Marantz (2008: 7) describe this competition-based process as one in
which the various possible interpretations “are [...] competing with one another, and when
one wins this competition, it prevents others from doing so.” This means that if the verb
throw takes the DP party as its complement, it receives the interpretation ‘arrange’. All other
interpretations are then blocked. At first glance, this seems reasonable. Nevertheless, consider
the idiomatic expression kill an audience (meaning ‘to wow them’, cf. Marantz 1984: 25) in
(166), or the German idiomatic expressions jdm. den Kopf waschen (‘to give sb. a telling-off’, lit.
‘to wash sb.’s head’) in (167) and jdm. einen Korb geben (‘to turn sb. down’, lit.: ‘to give sb. a
basket’) in (168).
(166) Hans killed an audience.
(167) Maria
Maria
wusch
washed
Hans
Hans
den
the
Kopf.
head
a. ‘Maria gave Hans a telling-off.’
b. ‘Maria washed Hans’ head.’
(168) Hans
Hans
gab
gave
Maria
Maria
einen
a
Korb.
basket
a. ‘Hans turned Maria down.’
b. ‘Hans gave Maria a basket.’
The important observation in all these idiomatic examples is that the verbs combined with
the respective direct objects can be interpreted idiomatically (a) or, crucially, also literally
(b). This is, however, not expected if these idiomatic expressions are modeled in terms of
LF-instructions because the special idiomatic interpretation would block the elsewhere inter-
pretation, i.e. the so-called literal interpretation. In order to obtain the literal interpretations,
4.1. Semantic construction algorithm 97
we would need to assume some semantic coercion process from the special idiomatic to the
regular elsewhere interpretation – which is obviously counterintuitive. I thus assume that
idiomatic meaning of the examples in (165)–(168) is not achieved by means of LF-instructions
as presented above, but by some other semantic (re)interpretation process. This is in line with
Anagnostopoulou and Samioti (2014) who also claim that contextual allosemy (i.e. sets of
LF-instructions for terminal nodes) must be separated from idiom formation. Note that I fol-
low Marantz (1997), Harley and Schildmier Stone (2013), Anagnostopoulou (2014), a.o., and
assume that the external-argument-introducing head, i.e. Voice (Kratzer 1996), constitutes a
domain for idiom formation.
Let us now look at the locality domain of LF-instructions. I adopt the locality condition in
(169) (Bobaljik 2012, Alexiadou 2014). It states that the feature [β] may condition the feature[α] only if the two features are not separated by a phrase boundary.
(169) Locality:[β] may condition [α] in (a), not in (b):
a. [β] ... [X○ ... [α] ... ]
b. *[β] ... [XP ... [α] ... ]
(adopted from Bobaljik 2012: 12–13)
With regard to the LF-instructions of P, this means that features within a PP, e.g. P’s synsem
features or features within the complement of P, can influence the interpretation of P. Features
outside a PP cannot influence the interpretation of P.
Let us now look at the locality domain of the contextual allosemy of Content features in
Root positions, i.e. Roots. For that, we have to determine the notions of inner derivation
(Root attaching) and outer derivation (lexically typed/categorized stem-attaching) (Marantz
1997, Embick and Marantz 2008, Embick 2010, Marantz 2013). Inner derivation (or inner
cycle) refers to the first categorization step of a Root, i.e. to the domain of Primary Merge in
the sense of De Belder and Van Craenenbroeck (2015). Consider (170a) as an instance of inner
derivation with X. Outer derivation (or outer cycle) refers to successive derivational steps.
Consider (170b) as an instance of outer derivation with X.
(170) a. Inner derivation: [
√
X ]
b. Outer derivation: [ [
√
Y ] X ]
Anagnostopoulou and Samioti (2013, 2014), Anagnostopoulou (2014) investigate what they
dub the Marantz/Arad Hypothesis (Marantz 2001, 2007, Arad 2003, 2005), given in (171).
It basically states that inner derivation constitutes the interpretative domain for Roots, i.e.
Content features in Root positions.
98 4. Semantics
(171) The Marantz/Arad Hypothesis:
Roots are assigned an interpretation in the context of the first category assigning
head/phase head merged with them, which is then fixed throughout the derivation.
(Anagnostopoulou and Samioti 2014: 81)
In particular, Anagnostopoulou and Samioti (2013, 2014), Anagnostopoulou (2014) examine
Greek participle morphology involving two adjectival suffixes: (i) -tos that is assumed to
serve, a.o., as the phonological realization of a Root adjectivizer, i.e. inner derivation and
thus local to a Root; and (ii) -menos that is assumed to derive deverbal adjectives, i.e. outer
derivation, and thus not local to a Root. Consider the Greek Root
√
SPAS with the conceptual
content “break”. Inner derivation with -tos yields the special interpretation “folding” of√
SPAS, as given in (172a). Deverbal outer derivation with adjectival -menos preserves the
verbal interpretation “break”, yielding the the interpretation “broken” for the participles in
(172b).
(172) a. spas-ti
break-tos.FEM
ombrella
umbrella
/
/
spas-to
break-tos.NEUT
trapezi
table
‘folding umbrella’ ‘folding table’
b. spas-meni
break-menos.FEM
ombrella
umbrella
/
/
spas-meno
break-menos.NEUT
trapezi
table
‘broken umbrella’ ‘broken table’
(Anagnostopoulou 2014: 305)
While the data in (172) are in line with the Marantz/Arad Hypothesis, the data in (173) pose
a potential problem. Consider the Root
√
KOKIN with the conceptual content “red” and inner
derivation with the verbalizer -iz in both (173a) and (173b). While outer derivation with
-menos in (173b) preserves the verbal meaning (‘make red’) in the participle (‘made red’),
outer derivation with -tos in (173a) yields the special interpretation ‘cooked with a red sauce’.
This is unexpected considering the Marantz/Arad Hypothesis. Outer derivation with the
adjectivizer -tos triggers special meaning of the Root through the verbalizer. It seems as if the
verbalizer is ‘ignored’ with respect to interpretation in (173a).
(173) a. kokin-is-to
red-V-tos.NEUT
kreas
meat
/
/
kotopoulo
chicken
/
/
*magoulo
*cheek
‘meat/chicken with a red sauce’
b. kokin-iz-meno
red-V-menos.NEUT
derma
skin
/
/
magulo
cheek
/
/
mati
eye
/
/
xroma
color
‘skin/cheek/eye/color that has turned red as a result of an event’
(Anagnostopoulou 2014: 308)
In order to account for this observation, Anagnostopoulou and Samioti (2013) propose that
the verbalizing head (i.e. -iz) in -tos participles is a semantically-empty head. Following
Embick (2010), who proposes that phonologically-empty heads are ignored for contextual
4.1. Semantic construction algorithm 99
allomorphy (i.e. the morphological parallel for contextual allosemy), Anagnostopoulou and
Samioti (2013) assume that semantically-empty heads are respectively ignored for contextual
allosemy; see also Marantz (2013).
Finally, a word on the representation of the EIs is in order. In (164b), Harley (2014)
uses an informal representation with quotes, which I have adapted here for the sake of
illustration. Harley (2014: 243) notes that her “informal representations [are] model-theoretic
interpretations along the lines proposed by Doron (2003).” For example, »vomit« in (164b-i)
“stands for whatever function will produce the correct predicate of [events] in [the respective
verbal] syntactic environment”. In this thesis, I do not apply Doron’s formalism as proposed
by Harley. Instead, I apply DRT, where “interpretation involves a two stage process: first, the
construction of semantic representations, referred to as Discourse Representation Structures,
[...] and, second, a model-theoretic interpretation of those DRSs” (Kamp et al. 2011: 9). For
the approach advocated here, this means that Harley’s »vomit« in (164b-i) stands for an EI
represented as a (fragmental) DRS, which is then interpreted model-theoretically. DRT is
addressed in Section 4.1.2 below.
4.1.2 Discourse Representation Theory
This thesis uses Discourse Representation Theory (DRT) (Kamp and Reyle 1993, 2011, Kamp
et al. 2011) for the representation of the LF-interface. A key feature of DRT is that it is repre-
sentational. It promotes a language-driven representation of the cognitively relevant relations
that can be verified model-theoretically. DRT includes a level of abstract mental represen-
tations, so-called Discourse Representation Structures (DRSs). This section introduces the
DRS-language that serves as the representation language at LF. The DRS-language can be
defined as given in (174).
(174) The DRS-language:
a. A DRS K is a pair
UK
ConK
where
(i) UK is a (possibly empty) set discourse referents, the universe, and
(ii) ConK is a set of DRS-conditions.
b. A DRS-condition is an expression of one of the following forms:
(i) If P in an n-place predicate and x1, ..., xn are discourse referents, then
P(x1, ..., xn) is a DRS-condition.
(ii) If x1, x2 are discourse referents, then x1 = x2 is a DRS-condition.
(iii) If K is a DRS, then ¬K is a DRS-condition.
(iv) If K1 and K2 are DRSs, then K1 ⇒ K2 is a DRS-condition.
(v) If K1 and K2 are DRSs, then K1 ∨K2 is a DRS-condition.
100 4. Semantics
(vi) If K1 and K2 are DRSs, and x is a discourse referent, then K1
∀
x K2 is a
DRS-condition.
UK is referred to as the universe of K and ConK is referred to as the condition set of K. In this
thesis, I adopt the usual graphical representation for DRSs as box diagrams. The universe is
displayed at the top of the diagram, while the set of DRS-conditions is typically displayed
below the universe (Kamp and Reyle 1993: 63). The DRS-conditions described in (174b-i) and
(174b-ii) are atomic DRS-conditions, while those described in (174b-iii) (negation), (174b-iv)
(implication), (174b-v) (disjunction), and (174b-vi) (universal quantification) are complex (or
non-atomix) DRS-conditions. In an implicational DRS-condition K1 ⇒ K2, the DRS K1 is
referred to as the antecedent DRS and the DRS K2 as the consequent DRS. In a disjunctive
DRS-condition K1 ∨K2, the DRSs K1 and K2 are referred to as disjunct DRSs. In a quantifi-
cational complex DRS-condition K1
∀
x K2 (for some discourse referent x), the DRS K1 is
referred to as the restrictor DRS and the DRS K2 as the nuclear scope DRS.
In order to define what is a proper DRS, we need to look at relations that can hold between
DRSs in complex DRS-structures. Two such relations are important: (i) subordination and (ii)
accessibility. They are defined in the following.
Let us first look at subordination of DRSs in (175). The basic relation is the one of
immediate subordination as defined in (175a). Based on this, we can recursively define the
relation of subordination in (175b) and, based on that, we can define the relation of weak
subordination in (175c).
(175) Subordination of DRSs:
a. K1 is immediately subordinate to K2 if and only if either
(i) ConK2 contains the condition ¬K1; or
(ii) ConK2 contains a condition of the form K1 ⇒ K3 or
one of the form K3 ⇒ K1 for some K3; or
(iii) ConK2 contains a condition of the form K
′
1 ∨ ...∨K′n and
for some i ≤ n K1 = K′i ; or
(iv) ConK2 contains a condition of the form K1
∀
x K3 or
one of the form K3
∀
x K1
for some K3 and some discourse referent x.
b. K1 is subordinate to K2 if and only if either
(i) K1 is immediately subordinate to K2 or
(ii) there is a K3 such that K3 is subordinate to K2 and
K1 is immediately subordinate to K3.
c. K1 is weakly subordinate to K2 (i.e. K1 ≤ K2) if and only if either
4.1. Semantic construction algorithm 101
(i) K1 = K2 or
(ii) K1 is subordinate to K2.
(Kamp and Reyle 1993: 230;
(a-iv) adapted from Kamp 2010: 48)
Sometimes a DRS K1 that is weakly subordinate to a DRS K2 is referred to as a sub-DRS of K2.
It is often convenient to distinguish a DRS K from various subordinate DRSs. Commonly this
is done by referring to K itself as the main or principal DRS (Kamp and Reyle 1993: 110–111).
Let us now look at accessibility of DRSs in (176). Accessibility is basically a three-place
relation between two sub-DRSs K1 and K2 in a given DRS K, with K itself also counting as
an (improper) sub-DRS of K. The basic relation is immediate accessibility as defined in (176a).
With this, we can define the relation of accessibility as the transitive closure of the relation
of immediate accessibility in (176b). Sometimes, the fact that K1 is (immediately) accessible
from K2 in K is simply stated as “K1 is (immediately) accessible from K2.”
(176) Accessibility or DRSs:
a. K1 is immediately accessible from K2 in K if and only if
K1 and K2 are sub-DRSs of K and
(i) ConK1 contains the condition ¬K2; or
(ii) ConK contains the condition K1 ⇒ K2, or
ConK1 contains the condition K2 ⇒ K3 for some DRS K3; or
(iii) K1 is immediately subordinate to K and
ConK1 contains the condition K2 ∨K3 or K3 ∨K2 for some K3; or
(iv) CondK contains the condition K1
∀
x′ K2
for some discourse referent x′, or
ConK1 contains the condition K2
∀
x′′ K3
for some DRS K3 and for some discourse referent x′′.
b. K1 is accessible from K2 if and only if
(i) K1 = K′1 and K2 = K′n and
(ii) K′i is immediately accessible from K′i+1 for 1 ≤ i ≤ n − 1.
(adapted from Kamp 2010: 48–49)
We can state the following example accessibility relations (Kamp and Reyle 2011: 888). The
DRS K1 of a DRS-condition ¬K1 belonging to ConK2 is not accessible from another DRS-
condition belonging also to ConK2 . The antecedent DRS K1 is accessible from the consequent
DRS K2 in an implicational DRScondition K1 ⇒ K2, but not conversely. The two disjunct
DRSs K1 and K2 of a disjunctive DRS-condition K1 ∨K2 are not accessible from one another.
The restrictor DRS K1 is accessible from the nuclear scope DRS K2 in an quantificational
DRS-condition K1
∀
x K2 (for some discourse referent x), but not conversely.
102 4. Semantics
With the subordination and accessibility relations, we can state under which conditions
an occurrence of a discourse referent is bound or free in a given DRS; see the definitions in
(177) for this.
(177) Bound and free occurrences of discourse referents in a DRS:
a. Let α be an occurrence of the discourse referent x within the atomic DRS-
condition γ occurring somewhere in the DRS K. Then α is bound in K if and
only if there are sub-DRSs K1 and K2 of K such that
(i) x belongs to UK1 (x is existentially bound),
(ii) γ belongs to ConK2 , and
(iii) K1 is accessible from K2 in K.
(iv) A discourse referent occurrence α in K is free in K if and only if it is not
bound in K.
(adapted from Kamp 2010: 49)
With that, we can now define proper and improper DRSs in (178).
(178) Properness of a DRS:
A DRS K is proper if and only if all occurrences of discourse referents in K are bound
in K; otherwise K is improper.
(Kamp 2010: 49)
At various levels of a derivation, two proper DRSs can merge into one DRS. For this, we
can define the operation of (symmetric) DRS-Merge in (179).58
(179) DRS-Merge:
UK1
ConK1
⊎ UK2ConK2 = UK1 ∪UK2ConK1 ∪ConK2
(Kamp et al. 2011: 140)
Assuming a bottom-up construction algorithm, I take the view that DRS-Merge can take
place along syntactic structure, as illustrated in the sample structure in (180).
58For discussion on various strategies of merging DRSs, I refer the reader to Fernando (1994), Vermeulen
(1995), Van Eijck and Kamp (1997, 2011).
4.1. Semantic construction algorithm 103
(180) Sample DRS-Merge along syntactic structure:
K1 ⊎K2 ⊎K3 ⊎K4
K4K1 ⊎K2 ⊎K3
K1 ⊎K2
K2K1
K3
It is crucial to note here that compositionality in a DRT-based syntax-semantics interface
cannot be boiled down to DRS-Merge only. In fact, more operations need to be assumed
for an exhaustive modeling of the syntax-semantics interface. For instance, at some points
of a derivation, the introduction of additional predicates could be required, which extends
beyond simple DRS-Merge.
Take, as a case in point, Roßdeutscher and Kamp’s (2010) analysis of German ung-
nominalizations. Roßdeutscher and Kamp argue that a bi-eventive structure is a licensing
condition for verbs forming ung-nominalizations in German. Consider, as an illustrative
example, the contrast in (181), where the ung-nominalization Säuberung (‘cleaning’) in (181a)
is grammatical, while the ung-nominalization *Wischung (intended: ‘wiping’) in (181b) is not.
(181) a. die
the
Säuberung
cleaning
eines
a.GEN
Tischs
table.GEN
‘the cleaning of a table’
b. *die
the
Wischung
wiping
a
a.GEN
Tischs
table.GEN
intended: ‘the wiping of a table’
Roßdeutscher and Kamp claim that this contrast corresponds to the underlying verbal
constructions, which are given in (182).
(182) a. einen
a.ACC
Tisch
table
säubern
clean
‘to clean a table’
b. einen
a.ACC
Tisch
table
wischen
wipe
‘to wipe a table’
The VP given in (182b) is argued to instantiate a mono-eventive, transitive structure involving
the inherently atelic manner verb wischen (‘wipe’) without a result state entailment as depicted
in (183). The verb contributes the eventive manner predicate wipe with an open argument
104 4. Semantics
slot for a nominal argument (cf. the anticipated discourse referent x), which is saturated by
the referential argument of the DP-complement (cf. the discourse referent x′).
(183) VP
e′ x′
wipe(e′, x′)
table(x′)
V○
e′
wipe(e′, x)
DP
x′
table(x′)
In contrast, the VP given in (182a) is argued to instantiate a bi-eventive structure where the
verbal kernel is morphophonologically and semantically empty to begin with – semantically, it
only contributes the discourse referent e′ for the event –, while the complement AP contributes
the stative predication that the table is clean. Morphophonologically, the underlying adjectival
head sauber (‘clean’) can be considered to conflate with the morphophonologically empty
verb leading to the surface verb säubern (‘[to] clean’); for the notion of ‘conflation’ I refer
the reader to Hale and Keyser (2002). With regard to semantics, Roßdeutscher and Kamp
(2010: 191) argue that both AP and V○ have representations with referential arguments. For
the AP this is s′, and for V○ it is the event discourse referent e′. In order to combine these two
representations, a relation must be introduced between these two arguments. In this case, it
is the relation that Kamp and Roßdeutscher refer to as cause. It relates e′ to s′ as the causing
event and the result state, i.e. e′ causes s′, and s′ is the result state of e′. This is illustrated in
(184).
(184) VP
e′ s′
e′ cause s′
s′ ∶ clean(x′)
table(x′)
V○
e′APs′ x′
s′ ∶ clean(x′)
table(x′)
Roßdeutscher and Kamp (2010: 187) assume that the input structure to the operator forming
ung-nominalizations must contain a condition of the form e′ cause s′. In this way, they account
predict the grammaticality of (181a) and the ungrammaticality of (181b).
4.1. Semantic construction algorithm 105
For a generalized account to ung-nominalizations, Roßdeutscher and Kamp (2010: 183)
propose the LF-interface rule depicted in (185). Crucially, the DRS-condition e′ cause s′ does
not stem from the DRSs of the daughters of the VP, but it is introduced at the level of VP – an
operation that extends beyond the plain DRS-Merge as depicted in (179).
(185) VP
e′ s′
e′ cause s′
s′ ∶ φ
V○
e′XPs′
s′ ∶ φ
(Roßdeutscher and Kamp 2010: 183)
However, plain DRS-Merge along the syntactic structure suffices for deriving most of the
German spatial prepositions at the LF-interface. Nevertheless, in Section 5.5.3, which focuses
on the aspectual structure of spatial prepositions, I will also propose an LF-instruction that
goes beyond plain DRS-Merge. In order to account for the idea that the unbounded goal
circumposition auf ... zu (‘towards’) is derived from the bounded goal preposition zu (‘to’), I
assume that the functional head Q – a light preposition in the extended projection of prepo-
sitions that contributes goal semantics – can be reinterpreted in certain syntacticosemantic
contexts. In particular, see the reinterpretation rules in (476) on page 275. In addition, I will
assume an LF-operation that adjusts the semantic contribution of the terminal node Dx○
(functional category for for deixis) in order to account for postpositional deictic elements of
route prepositions, e.g. hin-durch (‘thither-through’); cf. the so-called Dx-Adjustment at LF
formulated (465) on page 271.
I assume unification-based semantic construction rules (Kamp 2015). In particular, I
assume that semantic structure can be anticipated in the course of derivation such that it
awaits instantiation through unification under DRS-Merge. Anticipated semantic structure
is indicated by both over- and underlining it; semantic structure of various size can be
anticipated. Furthermore, only free discourse referents can be anticipated. Consider the
example in (186). In the DRS K1, the predicate pi and the discourse referent x are anticipated,
while the discourse referent y′ is existentially bound. The two-place predicate pi establishes a
relation between the discourse referents x and y′. In the DRS K2, the discourse referent y is
anticipated, while the discourse referent x′ is existentially bound. The predicate two-place
predicate φ establishes a relation between the discourse referents x′ and y. Under DRS-Merge
of K1 and K2 to the DRS K3, the anticipated predicate pi from K1 unifies with the predicate φ
from K2 and the anticipated discourse referent x from K1 unifies with the discourse referent x′
106 4. Semantics
from K2. Furthermore, the anticipated discourse referent y from K2 unifies with the discourse
referent y′ from K1.
(186) Instantiation through unification:
K3 ∶ x′ y′φ(x′, y′)
K2 ∶ x′φ(x′, y)K1 ∶ y′pi(x, y′)
With regard to semantic arguments, I distinguish between referential and non-referential
arguments (Williams 1977, Kamp and Reyle 2011, a.o.). The referential argument of some
linguistic unit is the semantic argument that this linguistic unit refers to. In the case of verbs,
the referential argument is normally the event or the state the verb describes. In the case of
nouns, the referential argument is normally the individual the noun describes. In addition, a
linguistic unit can also have non-referential arguments which are those semantic arguments
that are not the referential argument. In the case of an active transitive verb, for instance, the
semantic argument denoted by subject of this verb and the semantic argument denoted by
the direct object of this verb are non-referential arguments, while the referential argument of
the verb is the event it describes. Note that I indicate referential arguments in the universe of
a DRS with bold typeface.
4.1.3 Reproducing a textbook example
This section illustrates the construction algorithm described above, by reproducing a textbook
example. The proper treatment of tense and aspect information, not only within a sentence
but also across sentences in discourse, is one of the strengths of DRS. Consider the French
sentence in (187) and potential subsequent sentences in (188a) and (188b). If the sentence
following (187) is in passé simple (ps), which is comparable to simple past in English, the event
denoted by (188a) is understood as a reaction to the event denoted by (187), i.e. the event
where Alain opened his eyes. However, if the sentence following (187) is in imparfait (imp),
which is comparable to past progressive in English, the event denoted by (188b) is understood
as a ‘background’ state holding temporally around the event denoted by (187). The same
difference is observed in its English equivalents with simple past and past progressive.
(187) Quand
when
Alain
Alain
ouvrit
open.PS
les
the
yeux,
eyes
il
he
vit
see.PS
sa
his
famme
wife
qui
who
était
be.IMP
debout
standing
près
next to
de
of
son
his
lit.
bed
‘When Alain opened his eyes he saw his wife who was standing by his bed.’
4.1. Semantic construction algorithm 107
(188) a. Elle
she
lui
him
sourit.
smile.PS
‘She smiled at him.’
b. Elle
she
lui
him
souriait.
smile.IMP
‘She was smiling at him.’
(Kamp and Reyle 2011: 873)
In order to illustrate the DRS-construction algorithm, consider the simplified sentences in
(189) and (190), which show the same phenomenon as the French sentences above.
(189) Alain woke up.
(190) a. His wife smiled.
b. His wife was smiling.
Some syntactic remarks on these examples are in order. The verbs in both (189) and (190)
are intransitive, i.e. they have one non-referential argument. However, the verb wake up in
(189) is assumed to give rise to an unaccusative structure as depicted in (191), while the verb
smile in (190) is assumed to give rise to an unergative structure as depicted in (192). That is,
the DP Alain is base-generated as an internal argument of the verb wake up and then moves to
the subject position, i.e. the specifier of TP. In contrast, the DP his wife is not base-generated
within the VP of the verb smile, but as an external in the specifier of VoiceP (Kratzer 1996)
and then moves to the subject position.
(191) CP
TP
T′
AspP
VP
tiV○
woke up
Asp○[−PROG]∅
T○[+PAST]∅
DPi
Alain
C○∅
108 4. Semantics
(192) CP
TP
T′
AspP
VoiceP
Voice′
V○/VP
{ smilingsmile }
Voice○∅
ti
Asp○[±PROG]
{ was∅ }
T○[+PAST]
{ ∅-d }
DPi
His wife
C○∅
All clauses in (189) and (190) are in the past, thus we can assume T[+PAST]. Furthermore,
the clause in (190b) is marked with progressive (prog) aspect. For this, we can assume
Asp[+PROG]. In contrast, the clauses in (189) and (190a) are non-progressive, that is, they have
Asp[−PROG]. The structure in (192) gives both potential pronunciations for the respective
nodes. The upper line in the curly brackets represents the case of [+PROG], while the top line
represents the case of [−PROG]. Note that I illustrate the DRS-construction algorithm with
the DP-arguments in their base positions and only up to TP.
Let us first look at (189), i.e. Alain woke up. The respective structure is semantically fleshed
out in (193). The referential argument x′ of the DP Alain fills the open argument slot of the
two-place predicate wake-up contributed by the verb wake up.59 The DRS of V○ and the DRS
of DP merge to the DRS of VP. As the verb projects, the referential argument of V○, which
is e′, becomes the referential argument of VP. The clause has non-progressive aspect and
hence we can assume that the event e′ is temporally included in the time point or interval t′.
Accordingly, Asp[−PROG] is interpreted to the effect that an anticipated event is temporally
included in an anticipated time point e ⊆ t. By merging Asp○ with VP, the anticipated event e
unifies with e′. As the clause is in the past, the time point t′, which is the referential argument
of T○, precedes the utterance time n (now) (Kamp et al. 2011: 201). When merging T○ and
AspP to TP, the anticipated time t unifies with t′.
59For the sake of illustration, I leave the morphologically complex predicate wake up unanalyzed; it consists
of a base verb and a particle.
4.1. Semantic construction algorithm 109
(193) TP
t′ e′ x′
Alain(x′)
wake-up(e′, x′)
t′ ≺ n e′ ⊆ t′
AspP
e′ x′
Alain(x′)
wake-up(e′, x′)
e′ ⊆ t
VP
e′ x′
Alain(x′)
wake-up(e′, x′)
DP
x′
Alain(x′)
V○
e′
wake-up(e′, x)
Asp○[−PROG]
e ⊆ t
T○[+PAST]
t′
t′ ≺ n
Ultimately, this leads to the DRS K1 in (194b) for the clause in (189); this clause is repeated in
(194a).
(194) a. Alain woke up.
b. K1 ∶ t′ e′ x′
Alain(x′)
wake-up(e′, x′)
t′ ≺ n e′ ⊆ t′
(Kamp and Reyle 2011: 875)
Let us now look at the clause in (190a), i.e. his wife smiled, and its semantically fleshed-out-
structure in (195). Unlike the verb wake up, the verb smile gives rise to an unergative structure,
as sketched in (192). That is, the subject is base-generated as an external argument of the verb
by means of a Voice projection (Kratzer 1996). V○/VP contributes the verbal predicate smile,
with e′′ being the referential argument. Voice○ licenses an agent x of an anticipated event
e. In particular, the agent DP, his wife, is base-generated in the specifier position of VoiceP.
Kinship-terms typically denote relations between individuals. Thus, I assume that the noun
wife contributes the two-place predicate wife. It establishes a relation between the referential
argument of the DP x′′, i.e. the wife, and an anticipated individual u. The possessive pronoun
110 4. Semantics
his contributes the information that the anticipated individual is male, i.e. male(u).60 When
Voice○ and V○/VP merge to Voice′, the anticipated event e unifies with e′′, the referential
argument of V○/VP. When Voice′ and the DP merge into VoiceP, the referential argument of
DP x′′ fills in the argument slot of the predicate agent. With regard to the functional structure
above VoiceP, the derivation is parallel to (193). The clause has non-progressive aspect and,
therefore, the event e′′ is temporally included in the time point t′′. Asp[−PROG] contributes
the condition e ⊆ t. Anticipated e unifies with the referential argument of VoiceP e′′, while
anticipated t unifies with the referential argument contributed by T○, namely t′′. As the clause
is in the past, T[+PAST] contributes the condition t′′ ≺ n, i.e. that the time point/interval t′′
precedes the utterance time n.
60Note that a common way of treating anaphoric elements, such as his, is in terms of presupposition (Van der
Sandt 1992, Geurts 1999, Kamp 2001, a.o.). To a certain extent, the mechanism of instantiation through unification
(anticipation) is in fact similar to presupposition justification. One difference is, however, that presupposition
justification can take the form of accommodation, while anticipated structure must be justified by contextual
material that is typically available below the sentence level.
4.1. Semantic construction algorithm 111
(195) TP
t′′ e′′ x′′
wife(x′′, u) male(u)
smile(e′′)
agent(x′′, e′′)
t′′ ≺ n e′′ ⊆ t′′
AspP
e′′ x′′
wife(x′′, u) male(u)
smile(e′′)
agent(x′′, e′′)
e′′ ⊆ t
VoiceP
e′′ x′′
wife(x′′, u) male(u)
smile(e′′)
agent(x′′, e′′)
Voice′
e′′
smile(e′′)
agent(x, e′′)
V○/VP
e′′
smile(e′′)
Voice○
agent(x, e)
DP
x′′
wife(x′′, u)
male(u)
Asp○[−PROG]
e ⊆ t
T○[+PAST]
t′′
t′′ ≺ n
Ultimately, this leads to the DRS K2a in (196b) for the clause in (190a); this clause is
repeated in (196a).
(196) a. His wife smiled.
b. K2a ∶ e′′ t′′ x′′
wife(x′′, u) male(u)
smile(e′′)
agent(x′′, e′′)
t′′ ≺ n e′′ ⊆ t′′
(deduced from Kamp and Reyle 2011: 883)
112 4. Semantics
Let us now look at the clause in (190b), i.e. his wife was smiling, and its semantically-
fleshed-out structure in (198). For the sake of parallelism, we can straightforwardly assume
that the derivations of (190a) and (190b) are parallel up to VoiceP. Further, both (190a) and
(190b) are in the past tense. Therefore, we can assume that T[+PAST] is again interpreted as
contributing the relation t′′ ≺ n with t′′ as the referential argument. However, the clauses in
(190a) and (190b) differ with respect to aspect. The former has non-progressive aspect, while
the latter has progressive aspect. This is morphologically marked with the auxiliary was and
the ing-suffix on the verb. For (190b), we can assume Asp[+PROG]. That means that we have
now two contrasting feature bundles for Asp○, Asp[−PROG] for non-progressive aspect and
Asp[+PROG] for progressive aspect. With that said, we can formulate a context-sensitive
interpretation rule for the interpretation of the feature Asp at the LF-interface. Asp[−PROG]
is interpreted as in (193) and (195), viz. that an anticipated event e is simply included in an
anticipated time t; that is e ⊆ t. In contrast, Asp[+PROG] receives a progressive interpretation.
For the progressive, Kamp et al. (2011: 205) propose a progressive operator prog that turns
an event type into a state type. In particular, it characterizes a state s′ to the effect that it
holds during the run time of some anticipated event e. Note that ∧ denotes an intensional
abstraction operator of Intensional Logic (Kamp et al. 2011: 162–163). In this example, it
abstracts over an anticipated event. Further, an anticipated time point/interval t is included
in or equal to the described state s′, that is t ⊆ s′ (Kamp et al. 2011: 200). I thus propose the
LF-instructions for Asp in (197).
(197) a. Asp ↔ s′
s′ ∶ prog(∧e
ψ(e) )
t ⊆ s′
/ [+PROG]
b. ↔
e ⊆ t / [−PROG]
The interpretation of Asp gives rise to the semantically-fleshed-out structure in (198) for
the past progressive clause in (190b), i.e. his wife was smiling.
4.1. Semantic construction algorithm 113
(198) TP
t′′ s′ x′′
wife(x′′, u) male(u)
s′ ∶ prog(∧e smile(e)
agent(x′′, e) )
t′′ ≺ n t′′ ⊆ s′
AspP
s′ x′′
wife(x′′, u) male(u)
s′ ∶ prog(∧e smile(e)
agent(x′′, e) )
t ⊆ s′
VoiceP
e′′ x′′
wife(x′′, u) male(u)
smile(e′′)
agent(x′′, e′′)
Voice′
e′′
smile(e′′)
agent(x, e′′)
V○/VP
e′′
smile(e′′)
Voice○
agent(x, e)
DP
x′′
wife(x′′, u)
male(u)
Asp○[+PROG]
s′
s′ ∶ prog(∧e
ψ(e) )
t ⊆ s′
T○[+PAST]
t′′
t′′ ≺ n
This leads to the DRS K2b in (199b) for the clause in (190b), repeated in (199a).
(199) a. His wife was smiling.
b. K2b ∶ s′ t′′ x′′
wife(x′′, u) male(u)
s′ ∶ prog(∧e smile(e)
agent(x′′, e) )
t′′ ≺ n t′′ ⊆ s′
114 4. Semantics
Let us now go back to the discourses in (189)/(190a) and (189)/(190b). On the one hand,
the non-progressive clause in (190a) could be the follow-up sentence to (189), or, on the other
hand, the follow-up sentence could be the progressive clause in (190b). Let us first consider
the case where (189) is followed by (190a). This discourse is repeated in (200a). As illustrated
in (200b), the DRSs K1 and K2a undergo DRS-Merge into K3a. This means that the universe of
K3a is the union of the universe of K1 and the universe of K2a. Likewise, the condition set of
K3a is the union of the condition set of K1 and the condition set of K2a. Further, the anticipated
discourse referent u for the pronoun his from K2a unifies with the discourse referent x′ for
Alain from K1 (u = x′). Furthermore, we can assume that the rhetorical relation Narration
holds between the two sentences in (200a) (Mann and Thompson 1988, Zeevat 2011). This
gives rise to a temporal ordering where t′ from K1 precedes t′′ from K2a; cf. the precedence
condition t′ ≺ t′′ in K3a.
(200) a. Alain woke up. His wife smiled.
b. K1 ∶ ⊎ K2a ∶
e′ t′ x′
Alain(x′)
wake-up(e′, x′)
t′ ≺ n e′ ⊆ t′
e′′ t′′ x′′
wife(x′′, u) male(u)
smile(e′′)
agent(x′′, e′′)
t′′ ≺ n e′′ ⊆ t′′= K3a ∶
e′ e′′ t′ t′′ x′ x′′
Alain(x′)
wake-up(e′, x′)
t′ ≺ n e′ ⊆ t′
wife(x′′, x′) male(x′)
smile(e′′)
agent(x′′, e′′)
t′′ ≺ n e′′ ⊆ t′′
t′ ≺ t′′
Let us now consider the case when (190b) follows (189). This discourse is repeated in
(201a). Here, the DRSs K1 and K2b merge into K3b. Again, the anticipated discourse referent u
for the pronoun his from K2b unifies with the discourse referent x′ for Alain from K1 (u = x′).
Progressive in English typically provides some stative background information for some
particular time. Hence, we can unify the time t′′ from K2b with the time t′ from K1, cf. t′ = t′′
in K3b (Kamp and Reyle 2011: 881–882).
4.2. Figure and Ground 115
(201) a. Alain woke up. His wife was smiling.
b. K1 ∶ ⊎ K2b ∶
e′ t′ x′
Alain(x′)
wake-up(e′, x′)
t′ ≺ n e′ ⊆ t′
s′ t′′ x′′
wife(x′′, u) male(u)
s′ ∶ prog(∧e smile(e)
agent(x′′, e) )
t′′ ≺ n t′′ ⊆ s′= K3b ∶
e′ s′ t′ t′′ x′ x′′
Alain(x′)
wake-up(e′, x′)
t′ ≺ n e′ ⊆ t′
wife(x′′, x′) male(x′)
s′ ∶ prog(∧e smile(e)
agent(x′′, e) )
t′′ ≺ n t′′ ⊆ s′
t′ = t′′
For the sake of completeness, let me close this section with a note on the interpretation of
T. The examples here are all in the past tense, which is expressed with the condition t ≺ n, i.e.
that the respective time point or interval precedes the utterance time n (now) (Kamp et al.
2011: 201). It should be clear that this correlates to T[+PAST]. For future tense, we can equally
assume that T[+FUTURE] is interpreted to the effect that the respective time point/interval
succeeds the utterance time, i.e. n ≺ t. For convenience, let us assume that present tense
corresponds to the absence of the features [+PAST] and [+FUTURE]. That means that present
tense is the elsewhere tense. These considerations give rise to the LF-instruction for T in (202).
(202) a. T ↔ t′
t′ ≺ n / [+PAST]
b. ↔ t′
n ≺ t′ / [+FUTURE]
c. ↔ t′
t′ = n elsewhere
(cf. Kamp et al. 2011: 201)
4.2 Figure and Ground
This thesis focuses on prepositions that typically express spatial relations between two entities.
Conceptually, these two entities play asymmetrical roles. Adopting the terms from Gestalt
psychology, Talmy (1975, 1978, 2000: 311) posits
116 4. Semantics
[...] two fundamental cognitive functions, that of the Figure, performed by the
concept that needs anchoring, and that of the Ground, performed by the concept
that does the anchoring. This pair of concepts can be of two objects relating to each
other in space in an event of motion or location—and represented by nominals in
a single clause. [...]
That is, the stationary or dynamic position of the Figure is described relative to the Ground.61
Consider the examples in (203), where in both sentences the position of the pen (Figure) is
expressed relative to the table (Ground), either in a stationary situation (203a) or in a dynamic
one (203b).
(203) a. [Figure The pen ] lay on [Ground the table ].
b. [Figure The pen ] fell off [Ground the table ].
(Talmy 2000: 311)
Talmy characterizes Figure and Ground as given in (204).
(204) The general conceptualization of Figure and Ground in language
a. The Figure is a moving or conceptually movable entity whose path, site, or
orientation is conceived as a variable, the particular value of which is the
relevant issue.
b. The Ground is a reference entity, one that has a stationary setting relative to a
reference frame, with respect to which the Figure’s path, site, or orientation is
characterized.
(Talmy 2000: 312)
It is important to emphasize that Grounds are typically conceptualized as stationary
relative to a reference frame, even if they are in motion. Consider, for instance, the sentences
in (205).
(205) a. Throughout the entire race, [Figure Häkkinen ] was driving in front of[Ground Schumacher’s car ].
(Kracht 2002: 194)
b. [Figure The bird ] is flying around [Ground the rising balloon ].
(adopted from Zwarts 2005b: 743)
In (205a), Häkkinen’s position is understood as a constant position (expressed by the stative
preposition in front of ) in terms of the reference frame set by Schumacher’s car. The same
reasoning applies to (205b), where the bird’s movement along a spatial path (expressed by
the directional preposition around) is understood in terms of the relative frame set by the
balloon, and not in terms of an absolute frame. I follow Zwarts (2005b: 743) in assuming that
61Note that Figures are sometimes referred to as Trajectors, and Grounds as Landmarks.
4.3. Space as seen through the eyes of natural language 117
“this idealization is somehow part of the relativistic way in which we conceptualize position
and motion in space.”
With regard to the structure of spatial prepositions, Svenonius (2003) proposes that
the Figure/Ground relation is reflected syntactically in much the same way as it has been
proposed for the Agent/Patient relation. In particular, he formulates the so-called Split P
Hypothesis, stating that the light preposition “little p” introduces the Figure as the external
argument of the preposition; little p is above PP, which has the Ground as the internal
argument. This is parallel to the Voice Hypothesis formulated by (Kratzer 1996), which states
that the light verb Voice introduces the Agent as the external argument of the verb; Voice is
above VP, which has the Patient as the internal argument. For further discussion, I refer the
reader to Section 2.1.2; see page 26.
Let me close this section with a comment on the relation between spatial prepositions and
the Figure/Ground relation. Arguably, spatial prepositions are often the linguistic means of
choice for expressing a Figure/Ground relation. However, it should be clear that this is not
the only way. Consider the clause (206), where a Figure/Ground relation is established solely
with the verb climb.
(206) [Figure The monkey ] climbed [Ground the tree ].
On the other hand, if we assume that the complement of a spatial preposition is always a
Ground, following Svenonius (2003), then we cannot help but assume also that there is a
Figure corresponding to that Ground.62 Otherwise the notion of Ground by itself would not
be adequate. We can conclude that a spatial preposition is a sufficient, but not a necessary
condition for establishing a Figure/Ground relation.
4.3 Space as seen through the eyes of natural language
This thesis models the interface representation Logical Form (LF) in terms of Discourse
Representation Theory (DRT) (Kamp and Reyle 1993, 2011), cf. Section 4.1.2. One key feature
of DRT is that it distinguishes between representation and model-theoretic interpretation.
DRT thereby offers a controlled way to ask and answer the question of what an expressive,
and yet parsimonious, formalism requires, in order to be able to adequately represent natural
language. However, Discourse Representation Structures (DRSs) are the formulas of a formal
language that comes with a model-theoretic semantics. The models for this language must
permit the correct semantic evaluations. For the DRS-language used in this thesis, this means
that the spatial representations on which this thesis focuses are represented in the models by
the right spatial relations. The natural way to satisfy this desideratum is to assume that the
62Note that the Figure does not need to be an entity. Consider, as a case in point, PPs that serve as frame-
setting modifiers in the sense of Maienborn (2001). For instance, in the sentence “In [Ground Argentina ], [Figure
Eva is still very popular ]”, it is reasonable to assume that the entire proposition Eva is still very popular serves as
the Figure.
118 4. Semantics
models contain three-dimensional geometric space as part of their ontologies. However, this
still leaves room for variation. Two conceptions of such spaces are of particular relevance
for the present investigation: (i) the traditional concept of three-dimensional Euclidean
space – I will refer to this model as a vector space model – and (ii) a perception-driven
model that more naturally reflects the expressive constraints that can be observed for a
substantial part of the space-related (prepositional) repertoire of German and many other
human languages. There are various ways in which three-dimensional Euclidean space can
be defined and represented. One is a real-based three-dimensional vector space with an inner
product operation. It is an essential feature of vector spaces that they are closed under certain
operations, in particular under the operation of vector sum. This is an essential difference
with a perception-based model of space I referred to above as the alternative option. Primary
Perceptual Space (as defined by Kamp and Roßdeutscher 2005) also is three-dimensional in
that is starts from the assumption of three orthogonal axes – an ‘absolute’ axis, the vertical,
which is given by gravity, and two orthogonal, horizontal axes whose orientation varies
with context. Vectors along these axes can be of arbitrary sizes. But – this is the crucial
point – there is no closure under vector sums. For instance, while there is a unit vector in
the direction of the vertical and two unit vectors in the direction of the horizontal axes, there
is no diagonal vector that is to be found as the vector sum of the first vector and one of the
latter two. Non-closure is a central feature of cognitively-relevant subsystems of our spatial
cognition.
A vector space model of three-dimensional space
Zwarts (1997, 2003b, 2005b), and Zwarts and Winter (2000) advocate a model of three-di-
mensional space based on a vector space that is closed under vector addition. The principles
of such a vector space model are formally grounded in Euclidean geometry and motivated
independently from natural language, which leads to an immense expressiveness of the
formalism.
Take the modeling of spatial paths (SPs) as a case in point. Zwarts (2005b: 743) assumes
that SPs are “directed stretches of space” that geometrically correspond to a curve with an
arrow at one end. In particular, he (2005b: 748) defines SPs as “continuous functions from
the real unit interval [0, 1] to positions in some model of space.63 The relation between SPs
and positions is straightforward: the starting point of a spatial path p is p(0), the end point is
p(1); and for any i ∈ [0, 1], p(i) is the corresponding point of the spatial path.” He (2005a: 748)
further argues that such “positions and other spatial properties are best understood as relative
positions, modeled by vectors (Zwarts 1997, 2003b, Zwarts and Winter 2000).” Equipped with
this, Zwarts can model SPs as directed curves that can have virtually any shape. Consider,
for instance, the SP p depicted in Figure 7 below. Zwarts (2005b: 748) further argues that this
63For further discussion of spatial paths, I refer the reader to Section 4.5.
4.3. Space as seen through the eyes of natural language 119
way of constructing SPs “has the advantage of making the relation between [spatial] paths
and places maximally explicit and of being closer to our geometric intuitions.”
p(0)
p(i) p(1)
Figure 7: Spatial path p as a directed curve (cf. Zwarts 2005b: 744)
In fact, adopting a Euclidean vector space as a model of three-dimensional space leads to
an immense expressiveness of the formalism, because, for instance, every point in R3 can
be identified by a unique coordinate on the three axes x, y, and z. Take, e.g., the point Q in
the Cartesian coordinate system in Figure 8, which can be identified with the position vector
v⃗Q = (−6, 7,−5).
x
y
z
-5
-5-5
5
5
5Q(−6 ∣ 7 ∣ −5)
v⃗Q
Figure 8: Euclidean vector space
However, the question is whether this kind of expressiveness is required – or even
adequate – for a formalism representing the semantics of (spatial prepositions in) natural
language. I believe that such models of three-dimensional space are generally too explicit
and thus too liberal, as they allow natural language descriptions to express SPs with shapes
of any kind. SPs, as referred to by basic prepositional expressions, can apparently not have
any kind of shape. Consider the examples of the route preposition over in (207).64
64Note that I discuss route prepositions in Section 5.4.3 in more detail.
120 4. Semantics
(207) a. John jumped over the fence.
b. John hit the ball over the net.
c. John ran over the bridge.
Zwarts (2005b: 763) proposes that the denotation of the PP in (207a) is as in (208). This means
that the set of SPs denoted by over the fence is such that the starting points p(0) and the end
points p(1) of the SPs are ‘not on/above the fence’, while the points p(i) in-between the
starting and the end points are ‘on/above the fence’.
(208) J over the fence K = {p ∶ there is an interval I ⊂ [0, 1] that includes neither
0 nor 1 and that consists of all the i ∈ [0, 1] for which p(i) is on/above the
fence}
(Zwarts 2005b: 763)
This can be schematized as in (209), where the line of pluses and minuses represents the
points of the interval [0, 1] where the SP is ‘on/above the fence’ (+) or not (−).
(209) − − − − + + + + − − − −
0 1
(Zwarts 2005b: 760)
However, without further geometric rectilinearity constraints on SPs, the semantic rep-
resentation of (207a) in (208) does not exclude the interpretation where John does not cross
the fence.65 Consider (207b). This clause would be an infelicitous description of a situation
where the ball does not reach the other side of the net. Imagine a solo table tennis training
where John plays on a table with one half folded up. Here, the net is taut along the side of
the table in an upright position. On such a tennis table, the ball bounces back when it is
right above the net. That is, the SPs, along which a ball in this configuration typically moves,
fall under the denotation in (208) (though with ‘net’, instead of ‘fence’); the starting and
end points are not above the net, while there is a subpart of the SP in between that is above
the net. Nevertheless, such a scenario cannot felicitously be described with (207b). From
that observation, I conclude that the SPs denoted by over (and German über, which behaves
identically in this respect) come with a certain rectilinearity constraint – a fact that Zwarts’
(2005b) approach to SPs, although geometrically explicit, does not inherently account for.
A further prediction that straightforwardly follows from Zwarts’ (2005b) geometrically
explicit approach to SPs is that SPs cannot but have an inherent direction. Recall that Zwarts
(2005b: 748) defines SPs as continuous functions from the real unit interval [0, 1] to locations
in some model of space. The starting point of a SP p is then p(0), while the end point is
p(1). That is, the real unit interval [0, 1] imposes a direction on SPs. However, not all path
prepositions apparently commit to directed SPs. Consider again route prepositions as a case
65Note that this entailment is not related to the achievement predicate jump. In fact, (207c) with the manner
of motion predicate run has the same entailment, viz. namely that John has crossed the street.
4.3. Space as seen through the eyes of natural language 121
in point. Compare the German route prepositions durch (‘through’) and um (‘around’) in
(210) with the goal prepositions in (‘into’) and an (‘onto’) in (211). The route prepositions in
(210) can serve as felicitous modifiers of underived nominals not conceptualized as having
an inherent direction, such as wall or fence, while the goal prepositions in (211) are odd as
modifiers of these nouns.
(210) a. [ Die
the
Mauer
wall
durch
through
die
the.ACC
Stadt
city
] wurde
was
niedergerissen.
torn down
b. [ Der
the
Zaun
fence
um
around
das
the.ACC
Gebäude
building
] war
was
blutverschmiert.
blood-smeared
(211) a. [ Die
the
Mauer
wall
??in
into
die
the.ACC
Stadt
city
] wurde
was
niedergerissen.
torn down
b. [ Der
the
Zaun
fence
??an
onto
das
the.ACC
Gebäude
building
] war
was
blutverschmiert.
blood-smeared
Compare the data in (210) and (211) with the data in (212) and (213), both containing the same
prepositions. The difference is, however, that the nouns being modified in the latter examples
can be conceptualized as having an inherent direction: creeks have flow direction, and roads
typically have one (or two) driving direction(s). The examples containing route prepositions
in (212) are felicitous, and, crucially, so are the examples containing goal prepositions in (213).
(212) a. [ Der
the
Bach
creek
durch
through
den
the.ACC
Wald
forest
] wurde
was
begradigt.
rectified
b. [ Die
the
Straße
road
um
around
den
the.ACC
See
lake
] wurde
was
erneuert.
renewed
(213) a. [ Der
the
Bach
creek
in
into
den
the.ACC
Wald
forest
] wurde
was
begradigt.
rectified
b. [ Die
the
Straße
road
an
to
den
the.ACC
See
lake
] wurde
was
erneuert.
renewed
This different behavior of route and goal prepositions points to a difference with regard to
their conceptualizations. I take this to mean that goal (and source) prepositions commit to
SPs that relate to direction (cf. Section 5.4.2), while route prepositions commit to SPs that do
not necessarily relate to direction (cf. Section 5.4.3). This means that SPs denoted by route
prepositions can do just fine without direction. Taking this into account, I take the view that
direction built into the representation of SPs as it is in Zwarts’ approach, is appropriate for
directed prepositions such as goal (and source) prepositions, but that it does not appear to be
appropriate for undirected prepositions, viz. route prepositions.
Summarizing, we can say that, by adopting a vector space model (Zwarts 1997, 2003b,
Zwarts and Winter 2000), Zwarts (2005b) barters the restrictiveness and the underspecifica-
tion that seem to be appropriate in the semantic representation of spatial prepositions for
maximal geometric expressiveness. Instead of adopting a vector space model for modeling
122 4. Semantics
three-dimensional space, I adopt a geometrically more sparse, yet adequately expressive,
perception-driven model of space (Kamp and Roßdeutscher 2005). I will address this in the
following.
A perception-driven model of space
Basing their account on cognitive principles, Kamp and Roßdeutscher (2005) develop a
perception-driven model of three-dimensional space that is tailored to natural language.
Their approach is in the spirit of Lang (1990), who studies the conceptualization of spatial
objects. A fundamental principle on which Kamp and Roßdeutscher build their approach is
the idea that the semantic representation should formalize what natural language expressions
minimally commit to. That is, the model of three-dimensional space should account for
the minimal commitments of spatial expressions. Kamp and Roßdeutscher’s perception-
driven model of three-dimensional space is more restrictive and sparse, as compared to the
vector space model advocated by Zwarts (1997, 2003b, 2005a), Zwarts and Winter (2000). I
take the view that a more restrictive and sparse model of three-dimensional space is more
appropriate for the modeling of spatial prepositions. Take again spatial paths (SPs) as a case
in point. What should a minimal model of SPs look like? To begin with, a minimal model of
a spatial path (SP) arguably corresponds to a rectilinear and undirected line segment. Note
that Section 4.5 addresses SPs in more detail. Consider again the route preposition over as
used in the examples in (207). For convenience, (207a) is repeated in (214).
(214) John jumped over the fence.
Zwarts’ (2005b: 763) semantic representation of (214) does not exclude the interpretation
where John did not land on the other side of the fence. This is because Zwarts’ model of
SPs does not exclude non-rectilinear SPs. However, if we assume a minimal model that
takes SPs as being rectilinear line segments, this problem will no longer arise. Consider also
the examples in (210), which show that route prepositions typically can serve as felicitous
modifiers of underived nominals that are not conceptualized with an inherent direction. The
respective example in (210a) is repeated here in (215).
(215) [ Die
the
Mauer
wall
durch
through
die
the.ACC
Stadt
city
] wurde
was
niedergerissen.
torn down
Zwarts (2005b)’ defines SPs as continuous functions from the real unit interval [0, 1] to the
locations in some model of space.66 Hence, SPs inevitably impose, in one way or another,
a direction on undirected entities in examples like (215). Although this does not affect the
validity of the semantic representation of the clause as a whole, it is nevertheless unintuitive.
I think that a more intuitive semantic representation of the PPs in (215) should be based on
SPs that are undirected in the first place. These considerations lead to the conviction that a
66For further discussion of spatial paths, I refer the reader to Section 4.5.
4.3. Space as seen through the eyes of natural language 123
perception-driven and parsimonious model of three-dimensional space is more adequate,
while being equally sufficient, for modeling the spatial prepositions in focus here.
A fundamental assumption of the perception-driven model of three-dimensional space
by Kamp and Roßdeutscher is that orthogonality (and parallelism) are primary geometric
relations “constitut[ing] a cognitively and lexically important subsystem of a fuller concep-
tualization of space in which there is full range of orientations” (Kamp and Roßdeutscher
2005: 7). A further assumption they make is that the three axes (i) orthogonal to one another
and (ii) determined on the basis of perceptual input (Lang 1990) span a three-dimensional
space, referred to as Primary Perceptual Space (PPS). The first axis of PPS is the vertical
axis determined by equilibrioception, i.e. the perception of gravity that manifests itself in
the sense of balance. The second axis of PPS is the observer axis determined by the visual
perception of an observer, the viewing direction to be precise; it is orthogonal to the vertical
axis. The third axis of PPS is the transversal (or horizontal) axis identified as that axis that
is orthogonal to both the vertical and the observer axis. As stated above, orthogonality is
considered to be a primary geometric relation. In particular, Kamp and Roßdeutscher (2005: 7)
state the principle of POSC as formulated in (216).
(216) Primacy of Orthogonality in Spatial Conceptualization (POSC):
Spatial orientations are perceived as much as possible in such a way that all relevant
directions are parallel to one of the axes of PPS.
(Kamp and Roßdeutscher 2005: 7)
This limits the total number of orientations in the PPS to six, i.e. two on each axis. Note that
this is unlike how it is commonly assumed by those who model space as Euclidean space,
where, in principle, infinitely many different orientations are available. These six orientations
are ‘up’ and ‘down’ on the vertical axis, ‘fore’ and ‘back’ on the observer axis, and ‘left’ and
‘right’ on the transversal axis.67 Consider Figure 9 as an illustration of a PPS. Section 4.3.3
addresses the PPS in more detail.
4.3.1 Material objects
Material objects correspond to the real world entities with respect to which we compute
spatial relations. Strictly speaking, material objects are not part of the spatial ontology, but
they are mapped to spatial regions that are part of PPS. In order to achieve this mapping,
we first have to assume that material objects can be conceived as being either one-, two-, or
three-dimensional. The different dimensionalities in the conceptualization of material objects
are mutually exclusive.68
67I use the label ‘fore’ for forward orientation.
68Note that the axioms for material objects, as given in (217), show some redundancy. In general, a more
economic formulation is possible.
124 4. Semantics
vertical
axis
↑ up
↓ down
↙ back
observer
axis
fore↗
← left
transversal
axis
right →
Figure 9: Primary Perceptual Space (PPS)
(217) Axioms for material objects (obj):
a. ∀x[obj(x)→ 1D(x)∨ 2D(x)∨ 3D(x)]
b. ∀x[obj(x)∧ 1D(x)→ ¬[2D(x)∨ 3D(x)]]
c. ∀x[obj(x)∧ 2D(x)→ ¬[1D(x)∨ 3D(x)]]
d. ∀x[obj(x)∧ 3D(x)→ ¬[1D(x)∨ 2D(x)]]
The distinction between one-, two-, or three-dimensionality is a matter of conceptualization
within a certain type of context. For instance, a house is a material object that is typically
conceptualized as three-dimensional, which fits the fact that houses are three-dimensional
material objects in the real world. In contrast, take a tile or a whiteboard. Such material objects
are canonically conceptualized as two-dimensional (i.e. as the surface of the tile or as the
white plane to write on), even though in the real world they are basically three-dimensional
material objects, too. Nevertheless, all material objects allow for conceptualization as three-
dimensional, in addition to their typical conceptualization. For example, in some situations
it might be relevant to conceptualize a tile as three-dimensional, e.g. when measuring the
thickness of tiles in order to decide whether they are suitable for laying them on a certain
floor. An example of a material object that is typically conceptualized as one-dimensional is a
rod. Again, a rod can be conceptualized both as one-dimensional (in its typical usage) or as
three-dimensional.
4.3. Space as seen through the eyes of natural language 125
Of course, material objects come in a multitude of shapes and sizes. While this issue
might be crucial for other domains of natural language semantics, it plays a minor role in the
analysis of spatial prepositions. Thus, I presume to abstract over shapes and sizes of material
objects in this thesis.
4.3.2 Spatial ontology
This section addresses the primes of the spatial ontology that are relevant with respect to the
spatial configurations expressed by the prepositions in focus here.
Regions
Spatial regions, or henceforth simply regions, are primitives of the model of space that I
adopt here. In particular, I take regions as locations that can come in several categories:
zero-dimensional, one-dimensional, two-dimensional, or three-dimensional (Kamp and
Roßdeutscher 2005: 19–20). The mereological structure of space that I assume is given in (218).
In fact, it is similar to Krifka’s (1998: 199) part structure, but without the adjacency relation,
the proper part relation, and the remainder principle.
(218) S = ⟨US,⊕S,≤S,⊗S⟩ is a space structure iff
a. US is the set of spatial regions
b. ⊕S, the spatial sum operation, is a function from US ×US to US that is
(i) idempotent, i.e. ∀x ∈ US[x⊕S x = x]
(ii) commutative, i.e. ∀x, y ∈ US[x⊕S y = y⊕S x]
(iii) associative, i.e. ∀x, y, z ∈ US[x⊕S (y⊕S z) = (x⊕S y)⊕S z]
c. ≤S, the spatial part relation, defined as:∀x, y ∈ US[x ≤S y↔ x⊕S y = y]
d. ⊗S, the spatial overlap relation, defined as:∀x, y ∈ US[x⊗S y↔ ∃z ∈ US[z ≤S x ∧ z ≤S y]]
Conveniently, I refer to the spatial part relation ≤S as (spatial) inclusion, for which I use
the symbol ⊆. We can formulate the axioms pertaining to regions, given in (219). Regions are
identified with the predicate reg.
(219) Axioms for regions (reg):
a. ∀x[reg(x)→ 0D(x)∨ 1D(x)∨ 2D(x)∨ 3D(x)]
“every region is either zero-dimensional (i.e. points), one-dimensional, two-
dimensional, or three-dimensional”
b. ∀x[obj(x)→ ∃!y[reg(y)∧ occ(x, y)]]
“for every material object x there is exactly one region y such that y is the region
that is occupied by x”
126 4. Semantics
c. ∀x, y[occ(x, y)→ [1D(x)↔ 1D(y)∧ 2D(x)↔ 2D(y)∧ 3D(x)↔ 3D(y)]]
“the dimensionality of a material object and the dimensionality of the region
occupied by the material object are the same”
(cf. Kamp and Roßdeutscher 2005: 19)
For every material object, there is one particular region that the material object occupies. I
refer to this region as the ‘occupied region’ or as the ‘region occupied by the (material) object.’
Depending on the conceptualization of a material object, the region occupied by it can be the
exact physical eigenspace (or eigenplace) of the object (Wunderlich 1991, Zwarts and Winter
2000, Svenonius 2010) or its convex hull. In this regard, I refer the reader to Herskovits’s
(1986) discussion concerning the geometric conceptualizations of material objects. A case in
point here is the geometric conceptualization of a vase. Compare the two usages of the PP in
the vase in (220).
(220) a. the water in the vase
b. the crack in the vase
(Herskovits 1986: 41)
In (220a), the water is within the volume of containment defined by the concavity of the
vase – a volume delimited by the interior of the vase. Here, the region occupied by the
vase is understood as the three-dimensional convex hull of the vase, including its volume
of containment; while the physical vase is understood, I suppose, as the two-dimensional
skin that defines this volume of containment. In (220b), in contrast, the crack is within what
Herskovits calls the normal volume of the vase; that is, within the part of space the vase
would occupy if it had no crack, seeing the crack as a negative part. In this case, the region
occupied by the vase is understood as being the eigenspace of the vase. In this thesis, however,
I have nothing more to say about such variable conceptualizations of material objects.
Lines, directions, and points
Let us first look at one-dimensional spatial entities. They come in several varieties. An
important type of one-dimensional spatial entity is characterized by rectilinearity. Two types
of rectilinear one-dimensional spatial entities primarily figure in the geometric model pursued
here: (i) undirected rectilinear one-dimensional spatial entities, which I refer to as lines, and
(ii) directed rectilinear one-dimensional spatial entities, which I refer to as directions.
Orthogonality (⊥) and parallelism (∥) are primary relations between rectilinear one-
dimensional spatial entities. Therefore, let us first look at the orthogonality and parallelism
axioms pertaining to lines in (221).
(221) Axioms for lines (lin):
a. ∀x[lin(x)→ x ∥ x]
“every line is parallel to itself”
4.3. Space as seen through the eyes of natural language 127
b. ∀x, y[lin(x)∧ lin(y)∧ x ∥ y → y ∥ x]
“if line x is parallel to line y, then line y is also parallel to line x”
c. ∀x, y, z[lin(x)∧ lin(y)∧ lin(z)∧ x ∥ y ∧ y ∥ z → x ∥ z]
“if line x is parallel to line y and line y is parallel to line z, then line x is also
parallel to line z”
d. ∀x[lin(x)→ ¬x ⊥ x]
“every line is not orthogonal to itself”
e. ∀x, y[lin(x)∧ lin(y)∧ x ⊥ y → y ⊥ x]
“if line x is orthogonal to line y, then line y is also orthogonal to line x”
f. ∀x, y, z[lin(x)∧ lin(y)∧ lin(z)∧ x ∥ y ∧ y ⊥ z → x ⊥ z]
“if line x is parallel to line y and line y is orthogonal to line z, then line x is
orthogonal to line z”
g. ∀x, y[lin(x)∧ lin(y)∧ x ∥ y → ¬x ⊥ y]
“if two lines are parallel to one another, then they are not orthogonal to one
another”
(cf. Kamp and Roßdeutscher 2005: 8)
In addition to lines (undirected one-dimensional spatial entities), I assume directed one-
dimensional spatial entities. I refer to them as directions. Directions are one-dimensional
and rectilinear, and thus the axioms for lines in (221) also hold for directions. Directions
come with an inherent orientation. I use the two-place predicate align, in order to express the
fact that two directions share the same orientation. We can formulate axioms pertaining to
directions as in (222).
(222) Axioms for directions (dir):
a. ∀x, y[align(x, y)→ dir(x)∧ dir(y)]
“only two directions can be aligned”
b. ∀x[dir(x)→ align(x, x)]
“every direction is aligned with itself”
c. ∀x, y[dir(x)∧ dir(y)∧ align(x, y)→ align(y, x)]
“if direction x is aligned with direction y, then direction y is also aligned with
direction x”
d. ∀x, y[dir(x)∧ dir(y)∧ align(x, y)→ x ∥ y]
“if direction x is aligned with direction y, then direction x is also parallel to y”
(cf. Kamp and Roßdeutscher 2005: 9)
It is convenient to have a predicate for opposed directions, i.e. directions that are parallel but
do not share the same orientation. For this, I use the two-place predicate opp, as defined in
(223).
128 4. Semantics
(223) Opposed directions (opp):
a. ∀x, y[opp(x, y)→ dir(x)∧ dir(y)]
“if opp holds between x and y, then x and y are directions”
b. ∀x, y[dir(x)∧ dir(y)→ [opp(x, y)→ x ∥ y ∧¬ align(x, y)]]
“direction x is opposed to direction y if x and y are parallel to one another but
not aligned with one another”
c. ∀x, y[dir(x)∧ dir(y)∧ opp(x, y)→ opp(y, x)]
“if direction x is opposed to direction y, then direction y is also opposed to
direction x”
Let us now look at zero-dimensional spatial entities, viz. at points. A points can lie on
a line or direction. Then, the point is incident with the line or direction. For the incidence
relation, I use the two-place predicate inc, as axiomatized in (224).
(224) Axioms for points (poi):
a. ∀x, y[inc(x, y)→ poi(x)∧ [lin(y)∨ dir(y)]]
“points can be incident with lines or with directions”
b. ∀x, y, z[poi(x)∧ lin(y)∧ lin(z)∧ inc(x, y)∧ inc(x, z)∧ y ∥ z → y = z]
“if point x is incident with line y and with line z and line y is parallel to line z,
then line y is identical with line z”
c. ∀x, y, z[poi(x)∧ dir(y)∧ dir(z)∧ inc(x, y)∧ inc(x, z)∧ align(y, z)→ y = z]
“if point x is incident with direction y and with direction z and direction y is
aligned with direction z, then direction y is identical with direction z”
d. ∀x, y[[lin(x)∨ dir(x)]∧ [lin(y)∨ dir(y)]∧ x ∥ y →¬∃z[poi(z)∧ inc(z, x)∧ inc(z, y)]]
“for every two lines or directions x, y that are parallel to one another, there is no
point z that is incident with both x and y”
(cf. Kamp and Roßdeutscher 2005: 9)
Line segments
Up to now, I have more or less implicitly assumed that lines (and directions) are unbounded
one-dimensional spatial entities. However, for SPs it is necessary to have the notion of a
finite line segment (lis), that is, a one-dimensional spatial entity (line) that is delimited by two
zero-dimensional spatial entities (points). Line segments are determined by (i) a line and
(ii) a pair of points that are each incident with that line. These two points are referred to as
endpoints of the line segment. Furthermore, line segments should be closed, which means
that they should include their endpoints. In order to make these considerations explicit,
Kamp and Roßdeutscher (2005: 13) introduce a four-place predicate that cuts out a finite line
segment from a line between two distinct points on that line. While Kamp and Roßdeutscher
4.3. Space as seen through the eyes of natural language 129
refer to this four-place predicate as LS, I refer to it as cutout. We can axiomatize line segments
as given in (225).
(225) Axioms for line segments (lis):
a. ∀x, y, z, u[cutout(x, y, z, u)→ lin(x)∧ poi(y)∧ poi(z)∧ y /= z ∧ lis(u)]
“if u is cut out from x between y and z, then x is a line, y and z are distinct points,
and u is a line segment”
b. ∀x, y, z, u[cutout(x, y, z, u)→ endpoi(y, u)∧ endpoi(z, u)]
“if u is cut out from x between y and z, then y, z are the endpoints of the line
segment u”
c. ∀x, y, z, u[cutout(x, y, z, u)→ inc(x, u)∧ inc(z, u)]
“if u is cut out from x between point y and point z, then both y and z are incident
with u”
d. ∀x, y, z[lin(x)∧ poi(y)∧ poi(z)∧ inc(y, x)∧ inc(z, x)∧ y /= z →∃u[lis(u)∧ cutout(x, y, z, u)∧∀v[lis(v)∧ cutout(x, y, z, v)→ v = u]]]
“for every line x and every two distinct points y, z on the line x, there is a
line segment u such that u is cut out from x between y and z, and for all line
segments v that are cut out from x between y and z it is the case that v and u
are identical”
(cf. Kamp and Roßdeutscher 2005: 13)
Directed line segments
Just as we can cut out line segments from lines, we can also cut out directed line segments
(dls) from directions. Unlike (plain) line segments that are delimited by two tantamount end
points, directed line segments are delimited by two points x, y that are in an ordered relation,
say Ð→xy, to the effect that x is the initial point of the directed line segment, and y the terminal
point of the directed line segment.69 In order to account for directed line segments, we can
extend the axiom for line segments (225a) to directed line segments (226a).
(226) Axioms for directed line segments (dls):
a. ∀x, y, z, u[cutout(x, y, z, u)→[lin(x)∧ poi(y)∧ poi(z)∧ y /= z ∧ lis(u)]∨ [dir(x)∧ poi(y)∧ poi(z)∧ dls(u)]]
“if u is cut out from x between y and z, then x is a line, y and z are distinct points,
and u is a line segment, or x is a direction, y and z are points, and u is a directed
line segment”
b. ∀x, y, z, u[cutout(x, y, z, u)∧ dir(x)→ dls(u)∧[inipoi(y, u)∧ termpoi(z, u)]∨ [inipoi(z, u)∧ termpoi(y, u)]]
“if u is cut out from x between y and z and x is a direction, then u is a directed
69Note at this point that this conception of a directed line segment comes quite close to the concept of a
Euclidean vector in the narrow sense.
130 4. Semantics
line segment such that y is the initial point of the directed line segment u and z
is the terminal point of the directed line segment u or that z is the initial point
of the directed line segment u and y is the terminal point of the directed line
segment u”
c. ∀x, y, z, u[cutout(x, y, z, u)∧ dir(x)∧ dls(u)→ align(x, u)]
“if u is cut out from x between y and z and x is a direction and u a directed line
segment, then the directed line segment u is aligned with the direction x”
d. ∀x[dls(x)→ ∃y[dir(y)∧ align(x, y)]]
“if x is a directed line segment, then there is a direction y with which the directed
line segment x is aligned”
e. ∀x[dls(x)→ ∃!y, z[poi(y)∧ poi(z)∧ inipoi(y, x)∧ termpoi(z, x)]]
“if x is a directed line segment, then there is exactly one point y and exactly one
point z, such that y is the initial point of the directed line segment x and z is the
terminal point of the directed line segment x”
f. ∀x, y[inipoi(x, y)→ poi(x)∧ dls(y)∧ inc(x, y)∧∃!z[poi(z)∧ inc(z, y)∧ termpoi(z, y)∧Ð→xz]]
“if x is the initial point of y, then x is a point, y is a directed line segment, and
x is incident with y, and there is exactly one point z that is also incident with
the directed line segment y and that is the terminal point of the directed line
segment y”
g. ∀x, y[termpoi(x, y)→ poi(x)∧ dls(y)∧ inc(x, y)∧∃!z[poi(z)∧ inc(z, y)∧ inipoi(z, y)∧Ð→zx]]
“if x is the terminal point of y, then x is a point, y is a directed line segment,
and x is incident with y, and there is exactly one point z that is also incident
with the directed line segment y and that is the initial point of the directed line
segment y”
h. ∀x, y, z, u, a, b, c, d[cutout(x, y, z, u)∧ cutout(a, b, c, d)∧
dir(x)∧ dir(a)∧ align(x, a)→ align(u, d)]
“if u is cut out from direction x between y and z, and if d is cut out from
direction a between a and b, and if directions x, a are aligned, then the directed
line segments u, d are also aligned”
Note at this point that the axioms for lines (221) also hold for (directed) line segments. In
addition, the axioms for directions (222) also hold for directed line segments. Moreover, the
axioms for (239) also hold for (directed) line segments. Furthermore, the predicate opp for
opposed directions extends to directed lines segments.
Planes
Let us now look at two-dimensional spatial entities. An important type of two-dimensional
spatial entities are flat planes. In the same way as we can say that zero-dimensional spatial
4.3. Space as seen through the eyes of natural language 131
entities (points) can lie on one-dimensional spatial entities (lines and directions), we can
also say that one-dimensional spatial entities lie on two-dimensional spatial entities (e.g.
planes). In that case, the two-dimensional spatial entity contains the one-dimensional spatial
entity, or, the other way round, the one-dimensional spatial entity is contained within the
two-dimensional spatial entity. For the containment relation, I use the two-place predicate
con. Planes, as defined below, are flat two-dimensional spatial entities – a property that can
be derived from the assumptions that planes contain at least two lines that are orthogonal to
one another and that lines are, by definition, rectilinear. To a certain extent we can transfer
the relations of orthogonality (⊥) and parallelism (∥) to planes. In particular, lines can be
orthogonal to planes, and vice versa. Furthermore, planes can be parallel to one another.
Moreover, points can be incident with planes. However, there is a problem when it comes to
parallelism between planes and lines. A plane can be parallel to two lines without entailing
that the two lines are parallel to one another. In order to retain the structural properties of the
‘default’ relation of parallelism, Kamp and Roßdeutscher (2005: 11) introduce the predicate∥PL for parallelism between lines and planes. These considerations are axiomatized in (227).
(227) Axioms for planes (pla):
a. ∀x[pla(x)→ ∃y, z[lin(y)∧ con(x, y)∧ lin(z)∧ con(x, z)∧ z ⊥ y]]
“if x is a plane, then there are two lines y, z that are both contained in plane x
and that are orthogonal to one another”
b. ∀x, y, z[pla(x)∧ lin(y)∧ lin(z)∧ x ⊥ y ∧ x ⊥ z → y ∥ z]
“if x is a plane and y, z are lines that are both orthogonal to plane x, then the
lines y, z are parallel to one another”
c. ∀x, y, z[lin(x)∧ pla(y)∧ pla(z)∧ x ⊥ y ∧ x ⊥ z ∧ y /= z →¬∃w[lin(w)∧ con(y, w)∧ con(z, w)]]
“if x is a line and y, z are planes that are both orthogonal to line x and that are
not identical, then there is no line w that is contained in both planes y and z”
d. ∀x, y[pla(x)∧ pla(y)∧ x ∥ y ∧ x /= y → ¬∃z[poi(z)∧ inc(z, x)∧ inc(z, y)]]
“if x, y are planes that are parallel to one another and that are not identical, then
there is no point z that is incident with both planes x and y”
e. ∀x, y[pla(x)∧ lin(y)∧ x ∥PL y → ∃!z[pla(z)∧ con(z, y)∧ z ∥ x]]
“if x is a plane and y is a line and x and y are parallel to one another, then there
is exactly one plane z that contains line y and that is parallel to plane x”
f. ∀x, y, z[pla(x)∧ poi(y)∧ lin(z)∧ con(x, z)∧ inc(y, z)→ inc(y, x)]
“if x is a plane and y is a point and z is a line and plane x contains line z and
point y is incident with line z, then point y is incident with plane x”
g. ∀x, y[pla(x)∧ pla(y)∧¬x ∥ y → ¬∃z[lin(z)∧ con(x, z)∧ con(y, z)]]
“if x, y are planes that are not parallel to one another, then there is no line z that
is contained in both planes x and y”
(cf. Kamp and Roßdeutscher 2005: 11–12)
132 4. Semantics
4.3.3 Primary Perceptual Space
A core device of the spatial model advocated by Kamp and Roßdeutscher (2005) is the Primary
Perceptual Space (PPS), which spans a three-dimensional space on the basis of “categorized
sensory input delivered by our biological equipment” (Lang 1990: 135). In particular, “PPS
draws on perceptual input available from the organ of equilibrium, from upright walk, from
vision, and from eye level, each of which contributes a specific interpretation of external
physical space” (Lang 1990: 135). Like a Cartesian coordinate system, PPS consists of three
axes that are orthogonal to one another. However, PPS differs from a Cartesian coordinate
system in at least two respects: (i) PPS is not closed under vector addition, while vector
spaces in a Cartesian space are typically closed under vector addition; and (ii) the axes of
PPS have an unequal status and are motivated perceptually. The three axes of PPS are the
vertical axis, the observer axis, and transversal (or horizontal) axis. Consider Lang’s (1990)
definition of these three axes in (228).
(228) a. Vertical axis:
Due to its origin in gravitation as perceived by the organ of equilibrium, the
vertical axis is constant and ubiquitous; upright walk assigns it a foot and a
fixed (geofugal) direction. These properties make the vertical axis superior to
the other axes, which in a way are defined in relation to it.
b. Observer axis:
Originating in the visual organ, the observer axis has an anatomically deter-
mined pivot allowing for a 180○ turn; the position of the eyes determine its
direction (away from the observer) and its orthogonality to the vertical axis.
c. Transversal (or horizontal) axis:
This third axis has no endpoints and no direction; it is not an axis we are
equipped to identify by primary perceptual information, but is derived from
the two others just to fill the gap determined by the properties of the latter.
(Lang 1990: 135–136)
Note that Lang conceives the vertical and the observer axes as inherently directed. I assume
that these axes are inherently undirected, but that they have a primary orientation, which
ultimately amounts to the same thing.
Axes are one-dimensional, rectilinear lines constitutive of equivalence classes in PPS.
Using the predicate axi for axes, we can identify the three axes described by Lang (1990) in
(228) as the equivalence classes that axes in PPS can instantiate. For the three possible axes in
PPS, I use the predicate VERT for the vertical axis, OBS for the observer axis, and TRANS for
the transversal axis.
(229) ∀x[axi(x)→ VERT(x)∨OBS(x)∨TRANS(x)]
“every x that is an axis is either a vertical axis, an observer axis, or a transversal axis”
4.3. Space as seen through the eyes of natural language 133
As axes are essentially lines, the axioms for lines in (221) also pertain to axes. In addition, we
can formulate the axioms pertaining to axes, as in (230). These axioms guarantee that there
are exactly three orthogonal axes in PPS.
(230) Axioms for axes (axi):
a. ∃x, y[axi(x)∧ axi(y)∧¬x ∥ y]
“there are at least two axes that are orthogonal to one another”
b. ∀x, y[axi(x)∧ axi(y)∧ x ⊥ y → ∃!z[axi(z)∧ z ⊥ x ∧ z ⊥ y]]
“for every two axes x, y that are orthogonal to one another, there is exactly one
third axis z that is orthogonal to both axes x, y”
c. ∀x, y[axi(x)∧ axi(y)→ x ∥ y ∨ x ⊥ y]
“for every two axes x, y are parallel or orthogonal to one another”
d. ∀x, y, z, u[axi(x)∧ axi(y)∧ axi(z)∧ axi(u)∧
x ⊥ y ∧ x ⊥ z ∧ y ⊥ z ∧ u ⊥ x ∧ u ⊥ y → u ∥ z]
“for all axes x, y, z, u, if axis x is orthogonal to axes y, z, and u, and if axis y is
orthogonal to axes z and u, then axis u parallel to axis z”
e. ∀x, y[axi(x)∧ axi(y)∧ x ∥ y → x = y]
“all axes that are parallel are identical”
(cf. Kamp and Roßdeutscher 2005: 8,10)
The three equivalence classes of axes described above extend to lines in PPS. That is, lines
can also instantiate these three equivalence classes.
(231) a. ∀x, y[axi(x)∧ lin(y)∧ x ∥ y ∧VERT(x)→ VERT(y)]
“every line y that is parallel to a vertical axis x is a vertical line”
b. ∀x, y[axi(x)∧ lin(y)∧ x ∥ y ∧OBS(x)→ OBS(y)]
“every line y that is parallel to an observer axis x is an observer line”
c. ∀x, y[axi(x)∧ lin(y)∧ x ∥ y ∧TRANS(x)→ TRANS(y)]
“every line y that is parallel to a transversal axis x is a transversal line”
What directions are to lines, orientations are to axes; namely they are constitutive of
equivalence classes. With regard to the perceptually grounded system established here, we
can identify six distinct orientations: upward, downward, forward, backward, rightward,
and leftward. These orientations are identified with the predicates UP for upward, DOWN
for downward, FORE for forward, BACK for backward, RIGHT for rightward, and LEFT for
leftward.
(232) ∀x[ori(x)→ UP(x)∨DOWN(x)∨ FORE(x)∨BACK(x)∨RIGHT(x)∨ LEFT(x)]
“every x that is an orientation is either upward, downward, forward, backward,
rightward, or leftward”
134 4. Semantics
Orientations are basically directions. Thus, we can assume that the axioms pertaining to
directions in (222), and also those pertaining to lines, also pertain to orientations. In addition,
we can formulate the axioms in (233) that guarantee exactly six orientations in PPS.
(233) Axioms for orientations (ori):
a. ∀x, y, z[ori(x)∧ ori(y)∧ ori(z)∧
x ∥ y ∧ x ∥ z ∧¬ align(x, y)∧¬ align(x, z)→ align(y, z)]
“for all orientations x, y, z, if x is parallel to both y and z, and if x is neither
aligned with y nor with z, then y and z are aligned”
b. ∀x[ori(x)→ ∃!y[axi(y)∧ y ∥ x]]
“for every orientation x, there is exactly one axis y such that x and y are parallel”
c. ∀x[axi(x)→ ∃y, z[ori(y)∧ ori(z)∧ y ∥ x ∧ z ∥ x ∧¬ align(y, z)∧∀w[ori(w)∧w ∥ x → w = y ∨w = z]]]
“for every axis x, there are two orientations y, z such that they are both parallel
to x but not aligned with one another, and for all other orientations w that are
parallel to axis x it is such that w is either identical with y or with z”
d. ∀x, y[ori(x)∧ ori(y)∧ align(x, y)→ x = y]
“all orientations that are aligned with one another are identical”
(Kamp and Roßdeutscher 2005: 9,10)
The six equivalence classes of orientations extend to directions in PPS. That is, directions can
also instantiate the six equivalence classes.
(234) a. ∀x, y[ori(x)∧ dir(y)∧ align(x, y)∧UP(x)→ UP(y)]
“every direction y that is aligned with an upward orientation x is an upward
direction”
b. ∀x, y[ori(x)∧ dir(y)∧ align(x, y)∧DOWN(x)→ DOWN(y)]
“every direction y that is aligned with a downward orientation x is a downward
direction”
c. ∀x, y[ori(x)∧ dir(y)∧ align(x, y)∧ FORE(x)→ FORE(y)]
“every direction y that is aligned with a forward orientation x is a forward
direction”
d. ∀x, y[ori(x)∧ dir(y)∧ align(x, y)∧BACK(x)→ BACK(y)]
“every direction y that is aligned with a backward orientation x is a backward
direction”
e. ∀x, y[ori(x)∧ dir(y)∧ align(x, y)∧RIGHT(x)→ RIGHT(y)]
“every direction y that is aligned with a rightward orientation x is a rightward
direction”
f. ∀x, y[ori(x)∧ dir(y)∧ align(x, y)∧ LEFT(x)→ LEFT(y)]
“every direction y that is aligned with a leftward orientation x is a leftward
direction”
4.3. Space as seen through the eyes of natural language 135
Let us now link the six orientations with the three axes. The vertical axis is determined by
gravity, and it is linked to the orientations upward and downward. Upward orientation is
opposed to downward orientation.
(235) a. ∀x[ori(x)∧UP(x)→ ∃!y[axi(y)∧ x ∥ y ∧VERT(y)]]
“for every upward orientation x, there is exactly one axis y that is parallel to x
and that is vertical”
b. ∀x[ori(x)∧DOWN(x)→ ∀y[axi(y)∧ x ∥ y → VERT(y)]]
“for every downward orientation x, there is exactly one axis y that is parallel to
x and that is vertical”
c. ∀x[ori(x)∧UP(x)→ ∃!y[ori(y)∧ opp(x, y)∧DOWN(y)]]
“for every upward orientation x, there is exactly one orientation y that is opposed
to x and that is downward”
d. ∀x[ori(x)∧DOWN(x)→ ∀y[ori(y)∧ opp(x, y)→ UP(y)]]
“for every downward orientation x, there is exactly one orientation y that is
opposed to x and that is upward”
The observer axis is determined by the viewing direction of the observer, and it is linked
to the orientations forward and backward. Forward orientation is opposed to backward
orientation.
(236) a. ∀x[ori(x)∧ FORE(x)→ ∃!y[axi(y)∧ x ∥ y ∧OBS(y)]]
“for every forward orientation x, there is exactly one axis y that is parallel to x
and that is the observer axis”
b. ∀x[ori(x)∧BACK(x)→ ∃!y[axi(y)∧ x ∥ y ∧OBS(y)]]
“for every forward orientation x, there is exactly one axis y that is parallel to x
and that is the observer axis”
c. ∀x[ori(x)∧ FORE(x)→ ∃!y[ori(y)∧ opp(x, y)∧BACK(y)]]
“for every forward orientation x, there is exactly one orientation y that is op-
posed to x and that is backward”
d. ∀x[ori(x)∧BACK(x)→ ∃!y[ori(y)∧ opp(x, y)∧ FORE(y)]]
“for every backward orientation x, there is exactly one orientation y that is
opposed to x and that is forward”
The transversal axis is orthogonal to both the vertical axis and the observer axis. We can
identify the two orientations on the transversal axis as rightward and leftward. Rightward
orientation is opposed to leftward orientation.
(237) a. ∀x[ori(x)∧RIGHT(x)→ ∃!y[axi(y)∧ x ∥ y ∧TRANS(y)]]
“for every rightward orientation x, there is exactly one axis y that is parallel to x
and that is transversal”
136 4. Semantics
b. ∀x[ori(x)∧ LEFT(x)→ ∃!y[axi(y)∧ x ∥ y ∧TRANS(y)]]
“for every leftward orientation x, there is exactly one axis y that is parallel to x
and that is transversal”
c. ∀x[ori(x)∧RIGHT(x)→ ∃!y[ori(y)∧ opp(x, y)∧ LEFT(y)]]
“for every rightward orientation x, there is exactly one orientation y that is
opposed to x and that is leftward”
d. ∀x[ori(x)∧ LEFT(x)→ ∃!y[ori(y)∧ opp(x, y)∧RIGHT(y)]]
“for every leftward orientation x, there is exactly one orientation y that is op-
posed to x and that is rightward”
At least for the vertical and the observer axis, it makes sense to assume a primary orienta-
tion; I identify this orientation with the two-place predicate priori. This models Lang’s (1990)
idea that axes have an inherent direction. For the vertical axis, the upward orientation is
primary; and for the observer axis, the forward orientation is primary. For the transversal axis
the rightward orientation is primary, which can, at worst, be considered to be a convention.
(238) a. ∀x[axi(x)∧VERT(x)→ ∃!y[ori(y)∧ priori(y, x)∧UP(y)]]
“for every vertical axis x, there is exactly one orientation y that is primary to x
and that is upward”
b. ∀x[axi(x)∧OBS(x)→ ∃!y[ori(y)∧ priori(y, x)∧ FORE(y)]]
“for every observer axis x, there is exactly one orientation y that is primary to x
and that is forward”
c. ∀x[axi(x)∧TRANS(x)→ ∃!y[ori(y)∧ priori(y, x)∧RIGHT(y)]]
“for every transversal axis x, there is exactly one orientation y that is primary to
x and that is rightward”
As axes are instances of lines and orientations are instances of directions, we can assume
the axioms for points in (224). In addition, we can formulate the axioms (239) for points in
PPS, and the axioms in (240) for lines and directions in PPS.
(239) Axioms for points (poi) in a PPS:
a. ∀x, y[axi(x)∧ poi(y)→ ∃z[lin(z)∧ inc(y, z)∧ z ∥ x]]
“for every axis x and every point y, there is a line z such that y is incident with z
and z is parallel to x”
b. ∀x, y[ori(x)∧ poi(y)→ ∃z[dir(z)∧ inc(y, z)∧ align(z, x)]]
“for every orientation x and every point y, there is a direction z such that y
incident with z and z is aligned with x”
c. ∀x[poi(x)→ ∃y, z[pla(y)∧ axi(z)∧ inc(x, y)∧ y ⊥ VERT(z)]]
“for every point x, there is a plane y and an axis z in a PPS such that point x is
incident with plane y and plane y is orthogonal to z, which is the vertical axis”
(cf. Kamp and Roßdeutscher 2005: 9,11)
4.3. Space as seen through the eyes of natural language 137
Figure 10: Left-handed coordinate system
(240) Axioms for lines (lin) and directions (dir) in a PPS:
a. ∀x[lin(x)→ ∃y[axi(y)∧ x ∥ y]]
“for every line x, there is an axis y in a PPS and line x is parallel to axis y”
b. ∀x[dir(x)→ ∃y[ori(y)∧ align(y, x)]]
“for every direction x, there is an orientation y in a PPS and direction x is aligned
with orientation y”
(cf. Kamp and Roßdeutscher 2005: 9)
We can now formally define the PPS. This definition of PPS includes the notion of a point
where all orientations, and thus all axes, intersect. This point is typically referred to as the
origin o. The location of the origin depends on the perspective-taking strategy of the speaker
(cf. Levelt 1996). With a deictic perspective-taking strategy, speakers locate themselves at the
origin. That is, the speaker and the observer physically coincide. In contrast, with an intrinsic
perspective-taking strategy, speakers locate the reference object at the origin.70 In that case,
the reference object is understood as an ‘observer’; that is the speaker takes the perspective
as if she were at the position of the reference object.71
(241) Primary Perceptual Space (PPS):∃!x, y, z[ori(x)∧ ori(y)∧ ori(z)∧UP(y)∧ FORE(y)∧RIGHT(z)
x ⊥ y ∧ x ⊥ z ∧ y ⊥ z ∧∃!o[poi(o)∧ inc(o, x)∧ inc(o, y)∧ inc(o, z)]]
(cf. Kamp and Roßdeutscher 2005: 10)
The PPS defined (241) can be visualized as a left-handed coordinate system. To do this,
take your left hand and form a three-dimensional axial system with your thumb, index finger,
and middle finger. Let the thumb point upward, the index finger in your viewing direction,
and the middle finger rightward. That gives you a PPS with the center of your left hand as
the origin; this is depicted in Figure 10.
70Note that an intrinsic perspective-taking strategy is felicitous only if the reference object has an intrinsic
front by which one can determine (i) the observer axis and (ii) its orientation.
71Note that perspective taking plays a minor part with respect to topological prepositions. With projective
prepositions and expressions, however, perspective taking is of major importance in order to be able to
determine, e.g., left and right.
138 4. Semantics
4.3.4 Boundaries of material objects and regions
In general, material objects can be conceived as being delimited or bounded, i.e. as having
boundaries in space; or as being undelimited or unbounded, i.e. as having no boundaries in
space. In what follows, I focus on material objects that are understood to have boundaries in
space.
I follow Kamp and Roßdeutscher (2005: 20) and distinguish between the notion of a skin
and the notion of a surface. The skin of a two- or three-dimensional material object is that
two-dimensional part of the material object that literally delimits the object, while the surface of
a material object is the two-dimensional region that its skin occupies. Both skins and surfaces
are two-dimensional. Nevertheless, we should distinguish between skins and surfaces of
three-dimensional material objects, and between skins and surfaces of two-dimensional
material objects.
Skins and surfaces of three-dimensional material objects have the topology of a sphere,
i.e. they can be obtained from a sphere under topological transformation (homeomorphism).
For any three-dimensional material object, this has the consequence that we can determine
its inside and its outside on the basis of its surface. For this, I use the predicates inside and
outside, respectively. Furthermore, any line (segment) that extends from the outside of a
material object to its inside (or conversely), passes through the surface of the material object.
That is, a line (segment) that goes through one point belonging to the inside of a material
object and through one point belonging to its outside will have at least one point in common
with the surface of the material object. Note also that the material object occupies its inside
region and its surface region. I use the predicate ball-like for surfaces (two-dimensional)
of three-dimensional material objects. In contrast, skins and surfaces of two-dimensional
material objects have the topology of a disc; i.e. they can be obtained from a disc under
topological transformation. In particular, two-dimensional material objects do not have an
inside or an outside. They coincide with their skin, ergo they only occupy their surface. I
use the predicate disc-like for surfaces (two-dimensional) of two-dimensional material objects.
Skins and surfaces can be axiomatized as in (242).
(242) Axioms for skins (skin) and surfaces (surf):
a. ∀x[obj(x)∧ [2D(x)∨ 3D(x)]→ ∃!y[obj(y)∧ skin(y, x)]]
b. ∀x, y[skin(x, y)→ obj(x)∧ obj(y)∧ 2D(x)]
c. ∀x, y[skin(x, y)∧ 2D(y)→ x = y]
d. ∀x, y[surf(x, y)↔ reg(x)∧∃!z[skin(z, y)∧ occ(z, x)]]
e. ∀x, y[surf(x, y)∧ 3D(y)→ ball-like(x)]
f. ∀x, y[surf(x, y)∧ 2D(y)→ disc-like(x)]
g. ∀x[ball-like(x)→∃!y, z[inside(y, x)∧ outside(z, x)∧¬y⊗ z ∧¬x⊗ y ∧¬x⊗ z ∧∀u, v[reg(u)∧ reg(v)∧ y⊆u ∧ z⊆u ∧ x ⊆u → v⊆u]]]
4.3. Space as seen through the eyes of natural language 139
h. ∀x[disc-like(x)→ ¬∃y, z[inside(y, x)∧ outside(z, x)]]
(cf. Kamp and Roßdeutscher 2005: 21)
We can further state that the region occupied by a three-dimensional material object is the
mereological sum of its ball-like surface region and inside region. In the case of a two-
dimensional material object, the occupied region is identical to the surface.
(243) a. ∀x[ball-like(x)→ ∃!y, z, w[obj(y)∧ reg(z)∧occ(y, z)∧ surf(x, y)∧ inside(w, x)∧ z =
x⊕S w]]
b. ∀x[disc-like(x)→ ∃!y, z[obj(y)∧ reg(z)∧ occ(y, z)∧ surf(x, y)∧ z = x]]
Let me close this section with a note on rims and contours. Bounded two-dimensional
material objects have a disc-like surface, and they do not have an inside and outside re-
gion. Nevertheless, they have what I call an inner surface. An inner surface is the two-
dimensional counterpart to a three-dimensional inside region. The one-dimensional part
of a two-dimensional material object that delimits the material object is the rim. The one-
dimensional region that the rim occupies is the contour. In this sense, the relation between
rim and contour is similar to the relation between skin and surface. I refer to the part of a disc-
like surface that is delimited by the contour as the inner surface. Hence, a disc-like surface
(two-dimensional) is partitioned into a two-dimensional inner surface and a one-dimensional
circle-like, i.e. circular, contour.
4.3.5 Spatial contact
This section addresses the notion of spatial contact, a relation holding between two regions.
Two regions have spatial contact with one another iff they touch one another. Intuitively,
spatial contact is tantamount to adjacency defined in terms of adjacency structures in (255)
below. However, the adjacency relation typically defined in terms of adjacency structures
would not straightforwardly cover cases where the regions at issue are curved in such
ways that they touch one another at several points. Instead of adjacency, I thus propose
a conception of spatial contact that incorporates the idea where two regions have spatial
contact with one another in (at least) one point. One way of defining spatial contact is by
using the notion of a line segment. In particular, two regions are in contact with one another
iff the two regions do not spatially overlap, and there is at least one line segment that has one
endpoint in one region and the other endpoint in the other region and all (other) points on
the line segment are either in the one region or the other region. That is, no point on the line
segment is outside the two regions, or put differently, is not in one of the two regions. Note
that points qua zero-dimensional regions can be included in regions. The relation of spatial
contact ⊃⊂ holding between two regions x, y is formalized in (244). Figure 11 diagrams this
configuration.
140 4. Semantics
(244) Spatial contact:∀x, y[x ⊃⊂ y↔ reg(x)∧ reg(y)∧¬x⊗ y ∧∃z, v, w[lis(z)∧ endpoi(v, z)∧ endpoi(w, z)∧¬v⊗w ∧ v⊆ x ∧w⊆ y ∧∀u[poi(u)∧ inc(u, z)→ u⊆ x ∨ u⊆ y]]]
“the regions x, y are in contact with one another iff they do not overlap and there is
(at least) one line segment z with the distinct endpoints v, w such that v is included
in the region x, and w in the region y, and for every point u that is incident with the
line segment z, then u is either included in the region x or in the region y”
x
y
v wz
Figure 11: Spatial contact between regions
4.3.6 Conditions on line segments
This section discusses several spatial configurations of line segments that figure in semantic
modeling of route prepositions (see Section 5.4.3). In general, I assume that line segments
are constitutive of spatial paths (SPs). With regard to SPs denoted by route prepositions,
I assume that line segments can ‘directly relate’ to material objects. Thus, I define several
spatial relations between line segments and material objects below. Note that I further assume
that SPs are line segments that are elements of an (undirected) path structure H in the sense
of Krifka (1998: 203) (see Section 4.4.1). Thus, line segments can be subject to the part relation≤ in the definitions below.
In general, we can identify two types of predicates over line segments. On the one hand,
there are predicates according to which all subparts of the line segment must obey what I call
a boundary condition. These predicates impose an exhaustive condition on a line segment
such that one must be able to drop a perpedicular from the boundary of a material object
onto every point of the line segment. As for boundary conditions, I define two predicates.
The first one relates to the situation where a line segment is completely inside a material
object (internal line segment), while the second one relates to the situation where a line
segment is completely outside of a material object (external line segment). On the other
hand, there are predicates where at least one subpart of the line segment must obey what
I call a configurational condition. That is, these predicates impose a minimal condition on
4.3. Space as seen through the eyes of natural language 141
line segments such that only a subpart of the line segment must obey this condition. As for
configurational conditions, I define three predicates. The first one relates to the configuration
where at least one subpart of a line segment has a change of direction (L-shaped line segment);
the second one relates to the configuration where at least one subpart of a line segment is in a
horizontal position above a material object (plumb-square line segment); and the third one
relates to the configuration where at least one subpart of a line segment pierces through a
material object (spear-like line segment). In the following, I first define internal and external
line segments; the type of line segment which must wholly obey the exhaustive boundary
condition. Then, I define L-shaped line segments, plump-square line segments, and spear-like
line segments; the type of line segment which must only partially obey a configurational
condition.
Internal and external line segments
As for boundary conditions, line segments related to material objects must obey two condi-
tions. First, the line segment has to be either completely inside or completely outside the
material object. I refer to the former as internal line segments of material objects and to the
latter as external line segments of material objects. Second, for both internal and external line
segments of material objects, it must be possible to drop a perpendicular from the boundary
of the material object onto every point of the line segment; i.e. from the skin if the material
object is three-dimensional, or from the rim if the material object is two-dimensional. That is,
every point on the line segment must be such that there is a point on the boundary (surface
or contour) of the material object from which one can drop a perpendicular onto this point
of the line segment.72 These considerations are formalized in (245) in terms of the predicate
intlis for internal line segments of material objects, and in (246) in terms of the predicate extlis
for external line segments of material objects. In fact, the two definitions are identical, except
for the question of whether all points z that are incident with the line segment are included
in the inside or inner surface v of the material object (245c) or not (246c). An internal line
segment x of a material object y is diagrammed in Figure 12, and an external line segment x
of a material object y is diagrammed in Figure 13.
(245) ∀x, y[intlis(x, y)↔
“x is an internal line segment of y iff”
a. lis(x)∧ obj(y)∧∀x′[x′ ≤ x
“x is a line segment and y a material object and for all x′ ≤ x ”
b. → ∃u, v[[3D(y)→ surf(u, y)∧ inside(v, y)]∧ [2D(y)→ cont(u, y)∧ insurf(v, y)]
“there are u, v such that u is the surface of y and v the inside of y if y is three-
72Note that this conception of ‘dropping a perpendicular’ onto line segments is, in some sense, close to the
notion of internally and externally closest boundary vectors discussed by Zwarts (1997), Zwarts and Winter
(2000). However, they use these notions for different purposes than I do.
142 4. Semantics
dimensional, or such that u is the contour of y and v the inner surface of y if y
is two-dimensional”
c. ∧ ∀z[poi(z)∧ inc(z, x′)→ z⊆ v
“and for all points z that are incident with x′, z is included in v”
d. ∧ ∃w, p[poi(w)∧ lin(p)∧w⊆u ∧ inc(w, p)∧ inc(z, p)∧ p ⊥ x′]]]]]
“and there is a point w and a line p such that w is included in u and w is incident
with p and z is incident with p and p is orthogonal to x′ ”
v
z
w
u
y
∀x′ ≤ x
p
Figure 12: Internal line segment
(246) ∀x, y[extlis(x, y)↔
“x is an external line segment of y iff”
a. lis(x)∧ obj(y)∧∀x′[x′ ≤ x
“x is a line segment and y a material object and for all x′ ≤ x ”
b. → ∃u, v[[3D(y)→ surf(u, y)∧ inside(v, y)]∧ [2D(y)→ cont(u, y)∧ insurf(v, y)]
“there are u, v such that u is the surface of y and v the inside of y, if y is three-
dimensional, or such that u is the contour of y and v the inner surface of y, if y
is three-dimensional”
c. ∧ ∀z[poi(z)∧ inc(z, x′)→ ¬z⊆ v
“and for all points z that are incident with x′, z is not included in v”
d. ∧ ∃w, p[poi(w)∧ lin(p)∧w⊆u ∧ inc(w, p)∧ inc(z, p)∧ p ⊥ x′]]]]]
“and there is a point w and a line p such that w is included in u and w is incident
with p and z is incident with p and p is orthogonal to x′ ”
4.3. Space as seen through the eyes of natural language 143
v
z
w u
y
∀x′ ≤ x
p
Figure 13: External line segment
L-shaped line segments
A line segment can involve one or more changes of direction. In particular, they can involve
dramatic changes in which there is an angle of 90○. Such dramatic changes can be modeled by
a succession of two sub-line-segments that are orthogonal to one another and that touch one
another at endpoints. I call line segments consisting of two such successive sub-line-segments
L-shaped line segments. L-shaped line segments figure in the modeling of the German route
preposition um (‘around’). The definition of the predicate L-shaped is given in (247), and a
minimal model of an L-shaped line segment is depicted in Figure 14. I consider this to be a
configurational condition on line segments.
(247) ∀x[L-shaped(x)↔ lis(x)∧∃x′[x′ ≤ x∧∃!y, z[lis(y)∧ lis(z)∧ y ⊥ z∧∃u, v, w[poi(u)∧ poi(v)∧ poi(w)∧ u /= v ∧ v /= w ∧w /= u ∧ inc(w, x′)∧ endpoi(u, x′)∧ endpoi(u, y)∧ endpoi(v, x′)∧ endpoi(v, z)∧ endpoi(w, y)∧ endpoi(w, z)]]]]
“x is an L-shaped line segment iff there is a x′ ≤ x and there are two line segments
y, z that are orthogonal to one another, and y, z each share one endpoint with x′ and
one with one another, and the endpoint that y, z share is incident with x′ ”
u
w
v
y
z
∃x′ ≤ x
Figure 14: L-shaped line segment
144 4. Semantics
Plumb-square line segments
Line segments can have at least one subpart that is in a horizontal position above a material
object, which I consider to be a configurational condition on line segments. This is reminiscent
of a plumb square, as depicted in Figure 15 below. We can picture such a plumb-square line
segment as the horizontal top edge of a plumb square that has a plumb line attached to it.
The plumb line is orthogonal to the top edge and has a plumb bob attached to it. The plumb
bob represents the material object above which the plumb-square line segment is situated.
Figure 15: A plumb square from the book Cassells’ Carpentry and Joinery
Plumb-square line segments above material objects figure in the modeling of the German
route preposition über (‘over, across’). The definition of the predicate plumb-square is given in
(248), and a minimal model of a plumb-square line segment is depicted in Figure 16 below.
(248) ∀x, y[plumb-square(x, y)↔ lis(x)∧ obj(y)∧∃x′[x′ ≤ x∧∃z, u, v[dls(z)∧ z ⊥ x′ ∧ inipoi(u, z)∧ termpoi(v, z)∧ inc(u, x′)∧∃w[[3D(y)→ surf(w, y)]∧ [2D(y)→ cont(w, y)]∧ v⊆w]∧∃a[ori(a)∧DOWN(a)∧ align(z, a)]]]]
“x is an plumb-square line segment above material object y iff there is a x′ ≤ x, and
there is a directed line segment z such that it is orthogonal to x′ and that its initial
point u is incident with x′ and its terminal point v is included in the surface w of a
three-dimensional y or with the contour w of a two-dimensional y, and the directed
line segment z is aligned with the downward orientation a”
Spear-like line segments
Line segments can have at least one subpart that pierces directly through a material object.
I consider this to be a configurational condition on line segments. Such a spear-like line
segment is reminiscent of a cocktail stick with an olive (the material object) on it, as depicted
in Figure 17. Typically, a spear-like line segment is orthogonal to a plane that is a cross section
of the material object.
4.3. Space as seen through the eyes of natural language 145
∃x′ ≤ x u
v
w
y
z
DOWN(a)
Figure 16: Plumb-square line segment
Figure 17: Cocktail stick through olive
Spear-like line segments of material objects figure in the modeling of the German route
preposition durch (‘through’). The definition of the predicate spear-like is given in (249), and a
minimal model of a spear-like line segment is depicted in Figure 18 below.
(249) ∀x, y[spear-like(x, y)↔ lis(x)∧ obj(y)∧∃x′[x′ ≤ x∧∃z[[3D(y)→ cross-section(z, y)]∧ [2D(y)→ insurf(z, y)]∧ x′ ⊥ z]]]
“x is a spear-like line segment of material object y iff there is a x′ ≤ x, and there is a
z, which is y’s cross-section if y is three-dimensional and which is y’s inner surface
if y is two-dimensional and x′ is orthogonal to z”
I assume that the cross section of a three-dimensional material object can be defined,
for instance, as the intersection of the region that the material object occupies with a two-
dimensional plane. This plane is typically orthogonal (or parallel) to a certain axis of the
material object.73 At this point, however, I refrain from defining cross sections of three-
dimensional material objects.
73For a discussion of axes of material objects, e.g., in terms of Inherent Proportion Schema, I refer the reader
to Lang (1990).
146 4. Semantics
∃x′ ≤ x
y
z
Figure 18: Spear-like line segment
4.4 Algebra
4.4.1 Mereological structures
With regard to mereological structures, I adopt Krifka’s (1998) algebra, which I outline in the
following. The basic algebraic structure is a part structure P, defined in (250).
(250) P = ⟨UP,⊕P,≤P,<P,⊗P⟩ is a part structure iff
a. UP is a set of entities
b. ⊕P, the sum operation, is a function from UP ×UP to UP that is
idempotent, commutative, and associative, that is:∀x, y, z ∈ UP[[x⊕P x = x]∧ [x⊕P y = y⊕P x]∧[x⊕P (y⊕P z) = (x⊕P y)⊕P z]]
c. ≤P, the part relation, defined as: ∀x, y ∈ UP[x ≤p y↔ x⊕P y = y]
d. <P, the proper part relation, defined as:∀x, y ∈ UP[x <P y↔ x ≤P y ∧ x /= y]
e. ⊗P, the overlap relation, defined as:∀x, y ∈ UP[x⊗P y↔ ∃z ∈ UP[z ≤P x ∧ z ≤P y]]
f. Remainder principle:∀x, y ∈ UP[x <P y → ∃!z[¬z⊗P x ∧ x⊕P z = y]]
(Krifka 1998: 199)
Follwing Krifka (1998, 2007), Champollion and Krifka (2016), we can define the three types of
predicates in (251). A predicate Φ on a part structure P can be cumulative (CUMP), divisive
(DIVP), or quantized (QUAP). Typically, cumulativity is called an “upward-looking property”
because it looks upward from the part to the sum, while divisivity is called a “downward-
looking property” because it looks downward from the sum to the parts (Champollion and
Krifka 2016: 525).
4.4. Algebra 147
(251) a. ∀Φ ⊆ UP[CUMP(Φ)↔ ∀x, y ∈ UP[Φ(x)∧Φ(y)→ Φ(x⊕P y)]]
“a predicate Φ is cumulative if and only if whenever it holds of two things, it
also holds of their sum”
(Champollion and Krifka 2016: 524)
b. ∀Φ ⊆ UP[DIVP(Φ)↔ ∀x ∈ UP[Φ(x)→ ∀y ∈ UP[y <P x → Φ(y)]]]
“a predicate Φ is divisive if and only if whenever it holds of something, it also
holds of each of its proper parts”
(Champollion and Krifka 2016: 525)
c. ∀Φ ⊆ UP[QUAP(Φ)↔ ∀x ∈ UP[Φ(x)→ ∀y ∈ UP[y <P x → ¬Φ(y)]]
“a predicate Φ is quantized if and only if whenever it holds of something, it
does not hold of any of its proper parts”
(Champollion and Krifka 2016: 526)
For example, a predicate like water is cumulative because, if both parts x and y each qualify
for the predicate water, then also their sum x⊕P y qualifies for the predicate water. In contrast,
a predicate like three liters of water is non-cumulative because if both parts x and y each qualify
for the predicate three liters of water, then their sum x⊕P y qualifies for the predicate three liters
of water.
At this point, we should draw attention to extensive measure functions. In general,
measure functions relate an empirical relation like be cooler than, for physical bodies, to
a numerical relation, like be smaller than, for numbers (Krifka 1998: 200–201). In addition,
extensive measure functions are based on the operation of concatenation, which is related
to arithmetical addition. I assume that the operation of concatenation is an operation in a
static sense, i.e. it does not transform the elements that serve as its input. I further assume
that ‘concatenation’ is a partial binary operation that associates to the pair (x, y) consisting of
non-overlapping elements, the unique element x? y – if it exists. The partial binary operation
of concatenation can be considered to be a ternary relation, i.e. the set of triples (x, y, x? y).
Thus, the extension of the concatenation ? is a subset of the extension of the mereological
sum ⊕. Take two rods x, y. The extensive measure function for centimeter cm yield the length
in centimeter for each rod, viz. cm(x) and cm(y). The concatenation of the two rods is x? y.
The measure of the concatenation should, of course, be the numerical sum of the measures
of both rods, i.e. cm(x? y) = cm(x)+ cm(y). That is, extensive measure functions have the
property of additivity, as defined in (252b). Furthermore, extensive measure functions have
the property of commensurability, as defined in (252c). This means that the measure of a
concatenation is commensurate with the measure of its concatenants.
(252) m is an extensive measure function for a set U
with respect to concatenation ? iff:
a. m is a function from U to the set of positive real numbers.
b. ∀x, y ∈ U[m(x? y) = m(x)+m(y)] (additivity)
148 4. Semantics
c. ∀x, y ∈ U[m(x) > 0∧∃z ∈ U[x = y? z]→ m(y) > 0] (commensurability)
(Krifka 1998: 201)
The concatenation operation over extensive measure functions is commutative (x? y =
y? x) and associative (x?(y? z) = (x? y)? z), but it is not idempotent (x? x /= x). The
concatenation operation over extensive measure functions is typically restricted to non-
overlapping elements, as stated in (253). As a result, the concatenation operation equals the
mereological sum operation for non-overlapping elements.
(253) If P = ⟨UP,⊕P,≤P,<P,⊗P⟩ is a part structure, and m is an extensive measure function
for (subsets of) U with concatenation ?, then m is an extensive measure function for
P iff the following holds:∀x, y ∈ UP, x? y is defined only if ¬x⊗P y, and if defined, x? y = x⊕P y
(Krifka 1998: 201)
Further, Krifka (1998: 201) defines a part relation <m for an extensive measure function m
as given in (254). If m is an extensive measure function for a part structure P, then x <m y
implies x <P y.
(254) If m is an extensive measure function with concatenation?, then <m, the part relation
for m, is defined as follows:∀x, y ∈ U[x <m y↔ ∃z ∈ U[y = x? z]]
(cf. Krifka 1998: 201)
Based on a part structure P, we can define an adjacency structure A as given in (255).
Adjacent elements do not overlap, and if two elements x and y are adjacent and y is part of
a third element z, then is z either also adjacent to x or overlaps with x. The conditions for
convex elements states that all convex parts that do not overlap or are adjacent are connected
by a convex element.
(255) A = ⟨UA,⊕A,≤A,<A,⊗A,∞A, CA⟩ is an adjacency structure iff
a. ⟨UA,⊕A,≤A,<A,⊗A⟩ is a part structure
b. ∞A, adjacency, is a two-place relation in UA such that
(i) ∀x, y ∈ UA[x∞A y → ¬x⊗A y]
(ii) ∀x, y, z ∈ UA[x∞A y ∧ y ≤A z → x∞A z ∨ x⊗A z]
c. CA ⊆ UA, the set of convex elements, is the maximal set such that∀x, y, z ∈ CA[y, z ≤A x ∧¬y⊗A z ∧¬y∞A z →∃u ∈ CA[u ≤A x ∧ u∞A y ∧ u∞A z]]
(Krifka 1998: 203)
4.4. Algebra 149
Building on an adjacency structure A, we can define a path structure H as defined in
(256).74 The elements of a path structure (the paths) are convex and linear. Condition (256b)
ensures uniqueness of subpaths. It says that two disjoint, non-adjacent parts of a path
are connected by exactly one subpath, excluding circular and branching paths. Condition
(256c) ensures that there is a path between any two locations. It says that each two disjoint,
non-adjacent elements are connected by a path.
(256) H = ⟨UH,⊕H,≤H,<H,⊗H,∞H, CH, PH⟩ is a path structure iff
a. ⟨UH,⊕H,≤H,<H,⊗H,∞H, CH⟩ is an adjacency structure
b. Uniqueness of subpaths: PH ⊆ CH is the maximal set such that∀x, y, z ∈ PH[y, z ≤H x ∧¬y⊗H z ∧¬y∞H z →∃!u ∈ PH[u ≤H x ∧ y∞H u∞H z]]
c. ∀x, y ∈ UH[¬x⊗H y ∧¬x∞H y → ∃z[x∞H z∞H y]]
(Krifka 1998: 203)
Following Krifka (1998: 204), I illustrate a path structure with the toy model in Figure 19.
For instance, the sum a ⊕ b ⊕ c is a path, while the sum a ⊕ b ⊕ d is not a path, because it
contains two parts, b and d, that are not connected, which violates uniqueness of subpaths.
The sum a⊕ b⊕ c⊕ j also violates uniqueness of subpaths because, both the subpaths b and
b⊕ j connect a and c. Note at this point that I model SPs as elements of path structures, as
defined in (256). For this, I refer to Section 4.5.
a b c d e f g
j i
Figure 19: Toy model of (im)possible paths
For some applications of path structures, it is useful to have a concept of tangentiality
at an endpoint. Tangentiality is defined as the union of external tangentiality (257a) and
internal tangentiality (257b). In the model in Figure 19, the paths a⊕ b and c⊕ d are externally
tangential, and the paths a⊕ b⊕ c and b⊕ c are internally tangential. However, the paths b⊕ c
and j are not tangential.
(257) a. External tangentiality:∀x, y ∈ PH[ETANGH(x, y)↔ [[x⊕H y] ∈ PH ∧ [x∞H y]]]
b. Internal tangentiality:∀x, y ∈ PH[ITANGH(x, y)↔ ∃z ∈ PH[¬x⊗H z ∧ y = x⊕H z]]
74In order to distinguish path structures H, as defined in (256), from directed path structures D, as will be
defined in (259), I sometimes refer to path structures H as undirected path structures.
150 4. Semantics
c. Tangentiality:
TANGH = ETANGH ∪ ITANGH
(Krifka 1998: 204)
Furthermore, we can identify one-dimensional part structures as those for which it holds
that any two paths are part of a path. This is given in (258).
(258) A path structure H is called one-dimensional iff∀x, y ∈ PH∃z ∈ PH[x ≤H z ∧ y ≤H z]
(Krifka 1998: 205)
Unlike a(n) (undirected or plain) path structure H, as defined in (256), a directed path
structure D, as defined in (259), has a direction induced by the two-place ordering relation of
precedence “≺”.75
(259) D = ⟨UD,⊕D,≤D,<D,⊗D,∞D, PD, CD,≺D, DD⟩ is a directed path structure iff
a. ⟨UD,⊕D,≤D,<D,⊗D,∞D, PD, CD⟩ is a path structure
b. DD ⊆ PD, the set of directed paths, is the maximal set, and ≺D, precedence, is a
two-place relation in DD with the following properties:
(i) ∀x, y, z ∈ DD[[¬x ≺D x]∧ [x ≺D y → ¬y ≺D x]∧[x ≺D y ∧ y ≺D z → x ≺D z]]
(ii) ∀x, y ∈ DD[x ≺D y → ¬x⊗D y]
(iii) ∀x, y, z ∈ DD[x, y ≤D z ∧¬x⊗D y → x ≺D y ∨ y ≺D x]
(iv) ∀x, y ∈ DD[x ≺D y → ∃z ∈ DD[x, y ≤D z]]
(Krifka 1998: 205)
The precedence relation is irreflexive, asymmetric, and transitive (259b-i), and it holds for non-
overlapping elements (259b-ii). Whenever two subpaths of a directed path do not overlap,
one must precede the other (259b-iii). And only parts of a directed path can stand in the
precedence relation to one another (259b-iv). With (260), we can identify one-dimensional
directed path structures as those directed path structures with a total ordering. That is, for
each two convex, non-overlapping directed paths x and y, it holds that either x precedes y, or
y precedes x.
(260) A directed path structure D is called one-dimensional iff∀x, y ∈ DD[¬x⊗D y → x ≺D y ∨ y ≺D x]
(Krifka 1998: 205)
I follow Krifka (1998) and assume a one-dimensional directed path structure D for time.
That is, a time structure T is defined as given in (261). The precedence relation is interpreted
as temporal precedence.
75Krifka (1998) uses the symbol “≪” for the precedence relation; I use the symbol “≺” for it.
4.4. Algebra 151
(261) A time structure T is a one-dimensional directed path structure⟨UT,⊕T,≤T,<T,⊗T,∞T, PT, CT,≺T, DT⟩
(Krifka 1998: 205)
Based on a time structure T, we can now define an event structure E as given in (262).
It is a directed path structure that additionally involves a time structure. It also involves a
temporal trace function τE, mapping event to times. We can say that it maps events to their
run time, i.e. the time at which an event is happening.76 Adjacent events are defined as events
that are temporally adjacent, as in (262c-ii); and precedence of events is defined in terms
of temporal precedence, as in (262c-iii). An event structure contains the set of temporally
contiguous events, which shows a homomorphism with respect to the sum operations for
events and times (262c-i): the run time of the sum of two events e and e′ is the sum of the run
time of e and the run time of e′. Temporally contiguous events are events with a contiguous
run time (262c-iv), and the set of all events is the closure of the contiguous events under sum
formation.
(262) E = ⟨UE,⊕E,≤E,<E,⊗E, TE, τE,∞E,≺E, CE⟩ is an event structure iff
a. ⟨UE,⊕E,≤E,<E,⊗E⟩ is a part structure
b. TE is a time structure ⟨UT,⊕T,≤T,<T,⊗T,∞T, PT, DT,≺T⟩
c. τE, the temporal trace function, is a function from UE to UT;∞E, temporal adjacency, is a two-place relation in UE;≺E, temporal precedence, is a two-place relation in UE;
CE, the set of temporally contiguous events, is a subset of UE, with the follow-
ing properties:
(i) ∀e, e′ ∈ UE[τE(e⊕E e′) = τE(e)⊕T τE(e′)]
(ii) ∀e, e′ ∈ UE[e∞E e′↔ τE(e)∞T τE(e′)]
(iii) ∀e, e′ ∈ UE[e ≺E e′↔ τE(e) ≺T τE(e′)]
(iv) ∀e ∈ CE[τE(e) ∈ PT]
(v) UE is the smallest set such that CE ⊆ UE, and ∀e, e′ ∈ UE[[e⊕E e′] ∈ UE].
(Krifka 1998: 206)
As an event structure includes a time structure, which is a one-dimensional directed path
structure (i.e. temporal order), we can define the predicate INIE for initial parts of events
in (263a), and the predicate FINE for final parts of events in (263b). In particular, an event e′
is an initial part of an event e if it is a part of e that is not preceded by any other subevent
of e. Similarly, an event e′ is a final part of an event e if no other subevent of e follows e′.
Graphically, this can be illustrated as in Figure 20, where e′1 is an initial part of e1, that is
INIE(e′1, e1), and where e′2 is a final part of e2, that is FINE(e′2, e2).
76Note that I use, in the tradition of DRT, the short form “e ⊆ t” for “τE(e) ≤T t”, meaning that event e is
temporally included within time t (Kamp and Reyle 1993: 511).
152 4. Semantics
(263) a. Initial parts of an event:∀e, e′ ∈ UE[INIE(e′, e)↔ e′ ≤E e ∧¬∃e′′ ∈ UE[e′′ ≤E e ∧ e′′ ≺E e′]]
b. Final parts of an event:∀e, e′ ∈ UE[FINE(e′, e)↔ e′ ≤E e ∧¬∃e′′ ∈ UE[e′′ ≤E e ∧ e′ ≺E e′′]]
(Krifka 1998: 207)
e1
e′1
20.a: Event e′1 is an initial part of event e1
e2
e′2
20.b: Event e′2 is a final part of event e2
Figure 20: Initial and final parts of events
Note that the notions of initial and final parts of events figure in the definition of sources
and goals of (spatial) paths. The notions of initial and final parts of an event also play a
crucial role in Krifka’s account of telicity, because he uses them to define telicity as a property
of event predicates; see his definition of telic event predicates in (264).77 In particular, Krifka
(1998: 207) characterizes “telicity as the property of the extension of an event predicate X that
applies to events e such that every part of e that falls under X is both an initial and a final
part of e.”
(264) Telicity:∀X ⊆ UE[TELE(X)↔ ∀e, e′ ∈ UE[X(e)∧X(e′)∧ e′ ≤E e → INIE(e′, e)∧ FINE(e′, e)]]
(Krifka 1998: 207)
Take a quantized predicate such as eat two apples. This predicate is telic because if it applies to
an event e then it does not apply to any proper part of e. That is, the only e′, such that e′ ≤ e,
to which the predicate applies is e itself. And thus it is both an initial and final part of e. On
the other hand, take a cumulative predicate such as sleep. This predicate is atelic because it
applies to at least two events e, e′ that are not contemporaneous, that is, for which there is an
e′′ with e′′ ≤E e and e′ ≺E e′′ (Krifka 1998: 208). Note that this is all that this thesis has to say
about telicity in the event domain.
4.4.2 Incremental relations
A basic observation concerning verbs and their arguments is that certain arguments can
measure out an event (Dowty 1979, 1991, Tenny 1992, Jackendoff 1996, Krifka 1998, Beavers
2012). Dowty (1991) terms arguments measuring out events incremental themes. Several
types of arguments can serve as incremental themes. For example, in the case of consumption
77Note that Beavers (2012: 34–35) proposes a weaker definition of telic event predicates by omitting the INIE
condition, an issue that should not matter here.
4.4. Algebra 153
verbs such as eat (cf. Levin 1993: 213–214), the entities denoted by direct objects serve as
incremental themes. Furthermore, in the case of manner of motion verbs such as run (cf. Levin
1993: 265–267), the spatial paths (SPs) (see Section 4.5) denoted by PPs serve as incremental
themes (Dowty 1991, Tenny 1995, Jackendoff 1996, Krifka 1998, Beavers 2012).
Temporal adverbials of the form in an hour and for an hour typically serve as a standard test
for telicity (Vendler 1957, Verkuyl 1972, Filip 2012). While telic predicates are felicitous with
temporal in-PP adverbials, atelic predicates are felicitous with temporal for-PP adverbials.
Consider the examples in (265) containing the consumption verb eat. When used intransitively,
as in (265a), the predicate is atelic. Without the temporal adverbial, we would not have any
information about the boundaries of the eating event. The for-PP can provide the temporal
boundaries. In contrast, when used transitively with the directed object the apple, as in (265b),
the predicate is telic. Even without the temporal adverbial, we know the boundaries of the
eating event. In particular, we know that the eating event described in (265b) takes place
right up to the moment the apple is completely eaten. That is, the apple measures out the eating
event. The in-PP provides a temporal measure of the bounded event.
(265) a. John ate for/??in an hour.
b. John ate the apple in/?for an hour.
It is crucial to note here that telicity of the event description (265b) depends on the bounded-
ness of the incremental theme. If the incremental theme is unbounded, that is, if it does not
have quantized reference, it cannot provide the boundaries for measuring out the event.78
Bare plurals typically do not have quantized reference. Hence, a clause with a bare plural
direct object as in (266) is atelic.
(266) John ate apples for/??in an hour.
A parallel story can be told for the manner of motion verb run in (267). The difference
is, however, that the incremental theme is not an entity like the apple but a SP expressed by
the two PPs from the university and to the capitol. When used without a path description as
in (267a), the predicate is atelic. Without the temporal adverbial, we would not have any
information about the boundaries of the running event. Again, the for-PP can provide the
temporal boundaries. Opposed to that, when used with a bounded path description as in
(267b), the predicate is telic. Even without the temporal adverbial we know the boundaries
of the running event. In particular, we know that the running event described in (267b) starts
at the university and ends at the capitol. That is, from the university to the capitol measures out
the running event. Again, the in-PP provides a temporal measure of the bounded event.
(267) a. John ran for/??in an hour.
b. John ran from the university to the capitol in/?for an hour.
78See Krifka’s (1998: 200) definition of quantized predicates in (251c) above.
154 4. Semantics
The boundedness of the path description is relevant for the telicity of the event description.
For instance, PPs headed by towards are unbounded. That is, the predicate in (268) is atelic.
(268) John ran towards the sea for/??in an hour.
There are also verbs with two incremental themes. In the literature, they are referred to as
cases of multidimensional measuring-out (Jackendoff 1996) or double incremental themes
(Beavers 2012). Consider the examples in (269), involving the verb flow. Here, the subject
DP describes the entity undergoing movement, i.e. the Figure (cf. Section 4.2), while the PP
describes the SP. The observation is that the boundedness of both the Figure and the SP
determines the telicity of the predicate. Note that boundedness is indicated by underlining
in (269). The Figure can be unbounded like oil in (269a)–(269c) or bounded like a gallon of
oil in (269d)–(269f). In the former case, the Figure-DP has cumulative reference, while it has
quantized reference in the latter case. Likewise, the SP can be unbounded like towards the
island in (269c) and (269e), or bounded like to the island in (269c) and (269f). Alternatively,
the SP can also be implicit and thus be unbounded, as in (269a) and (269d). Only in the case
where both the Figure and the SP are bounded, i.e. (269f), is the predicate telic. In all other
cases, i.e. (269a)–(269e), are the predicates atelic.
(269) a. Oil flowed for/??in an hour.
b. Oil flowed towards the island for/??in an hour.
c. Oil flowed to the island for/??in an hour.
d. A gallon of oil flowed for/??in an hour.
e. A gallon of oil flowed towards the island for/??in an hour.
f. A gallon of oil flowed to the island in/?for an hour.
In order to capture the phenomena of incrementality or measuring out discussed above,
we can define isomorphic relations based on the part structures defined above. Following
Krifka (1998) and Beavers (2012), I assume that these isomorphic relations establish a mapping
between events and their arguments. These relations are typically termed thematic relations
or θ-relations (Krifka 1998: 210). The following sections address some θ-relations: (i) Strictly
Incremental Relations (SINCs) relations account for incrementality, as seen in the context of
verbs such as eat in (265)/(266); (ii) Movement Relations (MRs) account for incrementality,
as seen in the contexts of verbs such as run in (267)/(268); (iii) Figure/Path Relations (FPRs)
(Beavers 2009, 2012) account for predicates with double incremental themes, as seen in the
context of verbs such as flow in (269).
Strictly Incremental Relations
The prototypical case of incremental themes are objects measuring out events; cf. (265)/(266).
For this, we can define, following Krifka (1998) and Beavers (2012), Strictly Incremental
Relations (SINCs) as in (270). SINCs θ-relate events and patients. By isomorphically tying
4.4. Algebra 155
the progress of an event to the extent of an object, the definition of SINCs in (270) formalizes
the idea of objects serving as incremental themes that measure out events. SINCs have the
property of mapping events to unique subobjects (MUSO) in (270a), and the property of
mapping objects to unique subevents (MUSE) in (270b).79,80
(270) Strictly Incremental Relation (SINC):
Event e is θ-related to patient x such that every unique part of e corresponds to a
unique part of x and vice versa, i.e. θ has the MUSO and MUSE properties:
a. Mapping-to-Unique-Subobjects (MUSO):∀x ∈ UP∀e, e′ ∈ UE[θ(x, e)∧ e′ <E e → ∃!x′[x′ <P x ∧ θ(x′, e′)]]
“For all x θ-related to e, for all e′ < e there is a unique θ-related x′ < x.”
b. Mapping-to-Unique-Subevents (MUSE):∀x, x′ ∈ UP∀e ∈ UE[θ(x, e)∧ x′ <P x → ∃!e′[e′ <E e ∧ θ(x′, e′)]]
“For all e θ-related to x, for all x′ < x there is a unique θ-related e′ < e.”
(Beavers 2012: 28)
Graphically, SINCs can be represented as in Figure 21.
e
x
θ
e′
x′
θ MUSEMUSO
Figure 21: MUSO and MUSE properties of SINC relations
With the notion of SINCs as defined above and with telicity as defined in (264), we can predict
the telicity of consumption verbs like eat and drink. Consumption verbs typically establish
79Note that Beavers’ (2012: 28) definition of SINCs can be considered to be a condensed version of Krifka’s
(1998: 210–213) definition of SINCs. In particular, MUSO is a combination of Krifka’s (1998: 212) Mapping-
to-Subobjects (MSO) and Uniqueness-of-Objects (UO) and MUSE is a combination of Krifka’s (1998: 211–212)
Mapping-to-Subevents (MSE) and Uniqueness-of-Events (UE).
80Note that MUSE has a flaw. Objects can often be decomposed in ways that do not correspond to natural
decompositions of events. Consider a pizza where one half is topped with cheese and the other half with
pepperoni. Assume you cut the pizza in four pieces such that there are two pieces with cheese and two with
pepperoni. The first piece you eat is a piece with cheese. Then you eat the two pieces with pepperoni and
finally you eat the last piece, which is the second piece with cheese. The two pieces with cheese together
can be considered a legitimate subpart of the pizza, namely the half with cheese. The unique subevent of the
event of eating the pizza that corresponds to the half with cheese is a temporally discontinuous event, which is
counterintuitive.
156 4. Semantics
SINCs. That is, the event of V-ing is θ-related to the internal argument of V. Consider the
clause in (271a) for which the classical telicity tests diagnose a telic predicate. The respective
semantic representation (without tense) is given in (271b).81
(271) a. Caesar drank two beers in/?for two hours.
b. λe∃b[drink(CAESAR, b, e)∧ two-beers(b)]
(Beavers 2012: 29)
The event e and the internal argument b are θ-related. That is, for any event e of drinking
two beers b, any non-initial or non-final subevent e′ < e is an event of drinking some b′ < b.
The predicate two beers has quantized reference, which means that no b′ < b qualifies for the
predicate. This means that no e′ qualifies for (271b). Basically, every e′ < e is only an event of
drinking less than two beers. This satisfies the telicity property in (264), and thus the clause is
predicted to be telic. Consider, in contrast, the clause in (272a), for which the classical telicity
tests diagnose an atelic predicate. The respective semantic representation is given in (272b).
(272) a. Caesar drank beer for/??in two hours.
b. λe∃b[drink(CAESAR, b, e)∧ beer(b)]
(Beavers 2012: 29)
Again, the event e and the internal argument b are θ-related. That is, for any event e of
drinking beer b, any non-initial or non-final subevent e′ < e is also an event of drinking some
b′ < b. In this case, the predicate beer does not have quantized reference, because any b′ < b
still qualifies for the predicate. This means that e′ < e qualifies for (272b). Every e′ < e is also
an event of drinking beer. This does not satisfy the telicity property in (264), and thus the
clause is predicted to be atelic.
Movement Relations
Movement along SPs (see Section 4.5) is also an instance of incrementality (Tenny 1995,
Jackendoff 1996) for which we can establish a thematic relation. Following Krifka (1998) and
Beavers (2012), we can define Strict Movement Relations (SMRs) in (273). Like SINCs, SMRs
formalize the idea of measuring out. SMRs have the adjacency property (ADJ) formalized in
(273a). It states that for all θ-related e and x, temporal adjacency of all subevents e′, e′′ < e is
preserved in spatial adjacency for the respective θ-related subpaths x′, x′′ < x. Furthermore,
SMRs have the property of mapping events to objects (MO) formalized in (273b). SMRs
81Note that the representations in (271b) and (272b) ignore the Voice Hypothesis (Kratzer 1996) according to
which the external argument – Caesar in this case – relates to the verb via a separate predicate, typically agent.
Nevertheless, for the point made here, this does not matter.
4.4. Algebra 157
also have the property that movement happens along connected paths (MCP) formalized in
(273c).82
(273) Strict Movement Relation (SMR):
Event e is θ-related to path x such that every unique part of e is θ-related to a
unique part of x and vice versa and temporally adjacency in e corresponds to spatial
adjacency in x and vice versa, i.e. θ has the ADJ, MO, and MCP properties:
a. Adjacency (ADJ):∀x, x′, x′′ ∈ PH∀e, e′, e′′ ∈ UE[θ(x, e)∧ e′, e′′ ≤E e∧ x′, x′′ ≤H x∧ θ(x′, e′)∧ θ(x′′, e′′)→[e′∞E e′′↔ x′∞H x′′]]
“For θ-related e and x, for any x′, x′′ ≤ x θ-related to e′, e′′ ≤ e respectively, x′ is
spatially adjacent to x′′ iff e′ is temporally adjacent e′′. ”
b. Mapping-to-Objects (MO):∀x ∈ UP∀e, e′ ∈ UE[θ(x, e)∧ e′ ≤E e → ∃x′[x′ ≤P x ∧ θ(x′, e′)]]
“For all θ-related e and x, for all e′ < e there is a θ-related x′ < x.”
c. Movement along Connected Paths (MCP):∀x ∈ UH∀e ∈ UE[θ(x, e)→ x ∈ PH]
“For all x θ-related to e, x is part of a connected path structure.”
(Beavers 2012: 30)
Let us now look at an example of an SMR. Consider the examples (274a) and (274b),
which both involve the verb hike. When occurring without an explicit path description, as in
(274a), the predicate is atelic. In contrast, when occurring with a bounded path description as
in (274a), the predicate is telic.
(274) a. Mary hiked for/*in a day.
b. Mary hiked the Vernal Falls Path in/*for a day.
(adopted from Krifka 1998: 224)
The definition of SMRs in (273) is too strict for a general account of movements. In general,
movements involve a range of continuous movements dubbed funny movements (Krifka
1998: 225) that are excluded by (273). In order to illustrate some funny movements, consider
again the toy model of paths in Figure 19, repeated here as Figure 22.
Assume that em ∞E en and em ≺E en for all n = m + 1, that is, we have a series of adjacent
events that precede one another (here: e1, e2, e3, ...). SMRs exclude movements with stops. In
(275a), for instance, the two paths c, d are θ-related to non-adjacent e3, e5. This violates the
ADJ property of SMRs. Likewise, SMRs exclude circular movements. In (275b), the paths
j, c are adjacent, but not the θ-related event e1, e6. This, again, violates the ADJ property of
82Here, a terminological note is in order. Beavers (2012) abbreviates ‘Movement along Connected Paths’ with
CP. By abbreviating ‘Movement along Connected Paths’ with MCP, I deviate from Beavers’ convention. The
reason is simply to avoid confusion with the syntactic abbreviation CP for complementizer phrase.
158 4. Semantics
a b c d e f g
j i
Figure 22: Toy model of (im)possible paths (repeated from Figure 19)
SMRs. Moreover, SMRs exclude movements with backups. In (275c), the events e3, e4 are not
θ-related to two adjacent paths, but to the same path. Telekinesis is generally disallowed. In
(275d), the two adjacent events e2, e3 θ-relate to the paths b, e that are not adjacent.
(275) a. Movements with stops (stop-n-go movements):
e.g. ⟨a, e1⟩, ⟨b, e2⟩, ⟨c, e3⟩, ⟨d, e5⟩, ⟨e, e6⟩, ⟨ f , e7⟩
b. Circular movements (Alcatraz movements):
e.g. ⟨c, e1⟩, ⟨d, e2⟩, ⟨e, e3⟩, ⟨ f , e4⟩, ⟨i, e5⟩, ⟨j, e6⟩,
c. Movements with backups (Echternach movements):
e.g. ⟨a, e1⟩, ⟨b, e2⟩, ⟨c, e3⟩, ⟨c, e4⟩, ⟨b, e5⟩
d. *Telekinesis:
e.g. ⟨a, e1⟩, ⟨b, e2⟩, ⟨e, e3⟩, ⟨ f , e4⟩
In order to account for funny movements of the types in (275a) to (275c) – while prohibiting
telekinesis in (275d), where the moving entity would be beamed in a futurist Star-Trek
manner – we can define Movement Relations (MRs) in (276). Essentially, an MR θ is the
smallest relation that embeds an SMR, and for any two events e ≺E e′ MR-related to tangential
x, x′, respectively, e⊕E e′ is MR-related to x⊕H x′. The condition in (276b) guarantees that
movements are continuous. That is, any two successive movements are such that “the second
movement must begin where the first movement ends” (Krifka 1998: 225).
(276) Movement Relation (MR):
θ is the smallest relation that embeds an SMR and for any two events e ≺E e′ MR-
related to tangential or identical paths x, x′ respectively, e ⊕E e′ is MR-related to
x⊕H x′, i.e.
a. There is a SMR θ′, and θ′ ⊆ θ
b. ∀x, x′ ∈ UH∀e, e′ ∈ UE[θ(x, e)∧ θ(x′, e′)∧ e ≺E e′ ∧∀e′′, e′′′ ∈ UE∀x′′, x′′′ ∈ UH[FINE(e′′, e)∧ INIE(e′′′, e′)∧ θ(e′′, x′′)∧ θ(e′′′, x′′′)→ TANGH(x′′, x′′′)]→ θ(x⊕H x′, e⊕E e′)]
(Beavers 2012: 32)
4.4. Algebra 159
Figure/Path Relations
Let us now briefly turn to the cases of double incremental themes in (269), where both the
boundedness of the Figure, which moves along a spatial path, and the boundedness of the
spatial path (SP), along which the Figure moves, determine the telicity of the predicate (cf.
Section 4.5 for SPs). Examples are given in (277) and (278), where boundedness is indicated
by underlining. The observation is that the predicate is telic only in the case where both
the Figure and the SP are bounded. Consider (277). The Figure can be bounded as in (277a)
and (277c) or unbounded as in (277b) and (277d). In particular, it is bounded if the DP has
quantized reference and it is unbounded if the DP has cumulative reference. In (277a) and
(277b), the SP is bounded (see Section 4.6 on boundedness of SPs). In (277c) and (277d), the
SP is implicit and thus unbounded.
(277) a. The liter of wine flowed onto the floor in/?for one minute.
b. Wine flowed onto the floor for/??in one minute.
c. The liter of wine flowed for/??in one minute.
d. Wine flowed for/??in one minute.
(Beavers 2012: 39, 43)
The examples in (278), where a book/books serve as Figures and off the shelf as the SP, are
parallel to the examples in (277). The difference is that the Figure in (277) occurs as the
subject of the intransitive verb flow, while the Figure in (278) occurs as the direct object of the
transitive verb shake.
(278) a. The earthquake shook a book off the shelf in/?for a few seconds.
b. The earthquake shook books off the shelf for/??in a few seconds.
c. The earthquake shook a book for/??in a few seconds.
d. The earthquake shook books for/??in a few seconds.
(Beavers 2012: 25)
In order to account for this, Beavers (2012) proposes ternary θ-relations that allow for dou-
ble, interdependent incremental themes. Beavers terms these ternary θ-relations Figure/Path
Relations (FPRs). In particular, he (2012: 37) proposes
[...] that motion is an inherently three-place, mutually constraining relation be-
tween a Figure x, a [spatial] path p, and an event e, where the motion event can
be decomposed into a series of motion subevents, each of which corresponds to
some part of x moving on some part of p via a MR and ending up at the goal of p
in e.
160 4. Semantics
Beavers (2012) defines FPRs as given in (279).83, 84
(279) Figure/Path Relation (FPR):
θ is the smallest relation where if θ(x, p, e) then for each xi ≤ x (1 ≤ i ≤ n) there is a
unique pair ei ≤ e and pi ≤ p where:
a. ei stands in a non-minimal MR to pi;
b. the goal of pi in ei is the goal of p in e;
c. for all such ei and pi, e = ∑ni=1 ei and p = ∑ni=1 pi.
(Beavers 2012: 38)
In this thesis, I follow Beavers (2012) in assuming that motion predicates are typically
FPRs, i.e. three-place, mutually-constraining relations between a Figure, a SP, and an event.
FPRs decompose an event e in two dimensions: (i) a dimension determined by the Figure x
and (ii) a dimension determined by the SP p. This can be graphically represented as illustrated
in Figure 23.
e
en
emnn...e
j
n...e1n
...ei
emii...e
j
i...e
1
i
...e1
em11...e
j
1...e
1
1 ⇕
e
e1
e11 ... e
1
i ... e
1
n1
... ej
ej1 ... e
j
i ... e
j
nj
... em
em1 ... e
m
i ... e
m
nm
The event:
By xi ≤ x:
By xi ≤ x, pji ≤ pi:
By pj ≤ p, xji ≤ xj:
By pj ≤ p:
The event:
Figure 23: Figure/Path Relation (Beavers 2012: 42)
Note at this point that my analyses of prepositions denoting SPs are straightforwardly
compatible with Beavers’ theory of Figure/Path Relations. However, they do not hinge on it.
4.5 Spatial paths
This section addresses spatial paths (SPs). Generally, SPs are one-dimensional line segments.
As described above in the context of algebraic structures and in particular in the context of
Figure/Path Relation, SPs can serve as semantic arguments of motion predicates. When they
are, SPs are also referred to as motion paths.
83Note that Beavers (2012: 33) assumes that movement with backtracking to the source is generally possible.
This requires that ei stands in a non-minimal MR to pi. An MR θ between event e and path p is minimal iff the
goal x on p in e is mapped to only one subevent of e.
84With regard to the notion of ‘goal’, I refer the reader to the respective discussion in Section 4.5.
4.5. Spatial paths 161
Regarding the conceptualization of SPs, we find two basic kinds of approaches.85 On the
one hand, axiomatic approaches take SPs as primitives (Piñón 1993, Krifka 1998, Eschenbach
et al. 2000, Beavers 2012). In axiomatic approaches in the spirit of Krifka (1998) and Beavers
(2012), SPs are typically elements of an undirected path structure H (Krifka 1998: 204). This
means that SPs do not have an inherent direction. Without an inherent direction, however,
both ‘ends’ of a SP are tails tantamount to one another. That is, if we look at the two tails,
then we cannot say which one corresponds to the starting point (source), and which one to
the end point (goal) of the SP. Therefore, sources and goals are not inherently identifiable on
SPs when they are assumed to be elements of an undirected path structure. Sources and goals
are identifiable only when SPs are mapped to events (Krifka 1998, Beavers 2012). Unlike
an undirected path structure H, an event structure E (Krifka 1998: 206) provides a direction
because it involves a time structure T (Krifka 1998: 205), which instantiates a directed path
structure D (Krifka 1998: 205). Spatial paths and are mapped to events in terms of a (strict)
movement relation θ, as defined in (273)/(276). That is, the direction of an event structure
imposes a direction on SPs by means of a θ-relation. From this direction imposed by a θ-
relation, we can derive source and goal as thematic roles. In particular, we can say that those
parts of SPs that relate to initial parts of events correspond to sources, and those parts of SPs
that correspond to final parts of events correspond to goals. Put differently, a source is where
movement begins, and a goal is where movement ends. Thus, in an axiomatic approach,
source and goal are thematic roles derived by θ-related mapping of SPs to event structure.
On the other side, constructive approaches take SPs as constructed objects; either as
nested sets or sequences of locations (Bierwisch 1988, Verkuyl and Zwarts 1992), or as func-
tions from some ordered domain to locations (Cresswell 1978, Zwarts 2005b). In constructive
approaches, SPs typically do have an inherent ordering from which sources and goals can be
derived independently from event structure. For example, Zwarts (2005b: 748) defines SPs
as “continuous functions from the real unit interval [0, 1] (the ‘indices’) to positions in some
model of space.86 The relation between paths and positions is straightforward: the starting
point of path p is p(0), the end point is p(1) and for any i ∈ [0, 1] p(i) is the corresponding
point of the path.” Under this view, “‘source’ and ‘goal’ are not thematic roles, but extremities
of paths (p(0) and p(1), respectively) that only play a role PP-internally” (Zwarts 2005b: 758).
Motivating a constructive approach to SPs, Zwarts (2005b: 748) claims that constructive ap-
proaches have the “advantage of making the relation between paths and places maximally
explicit and of being closer to our geometric intuitions.” With respect to geometry, Zwarts’
constructive approach relies on his vector space model (Zwarts 1997, 2003b, 2004, Zwarts and
Winter 2000) through which the respective positions in space, which the indices are mapped
to, can be described. That is, SPs are sequences of points in space that can be described by
vectors; or, SPs are series of vectors.
85I adopt the terms ‘axiomatic approach’ and ‘constructive approach’ from Zwarts (2005b: 748).
86Note that some parts of this discussion on spatial paths are repeated from the beginning of Section 4.3.
162 4. Semantics
In this thesis, I advocate an axiomatic approach to SPs in the spirit of Krifka (1998) and
Beavers (2012). I do this for two reasons, which I will briefly present in the following.
First, on a constructive approach to SPs, there is a flaw in the modeling of route prepo-
sitions (cf. Section 5.4.3) like over or through. In particular, constructive approaches do not
inherently preclude kinked SPs, i.e. SPs that are not rectilinear. Applying a vector space
model, Zwarts (2005b: 748) argues that constructive approaches can make spatial relations
maximally explicit. However, I think that constructive approaches are too explicit, as they ba-
sically allow natural language descriptions to express SPs with shapes of any kind. Consider
the examples in (280).
(280) a. John jumped over the fence.
b. John walked over the bridge.
Under an off-the-shelf constructed approach without further geometric rectilinearity con-
straints on SPs (e.g. Zwarts 2005b), the semantic representations of (280) do not exclude the
interpretations where John does not cross the fence or the bridge, respectively. On the telic
reading of these clauses,87 it is entailed that John arrived at the other side of the fence/bridge;
that is, the side where he arrived was not the one from which here started. Let us now
consider Zwarts’ definition of over as represented by the denotation of over the fence in (281).
(281) J over the fence K = {p ∶ there is an interval I ⊂ [0, 1] that includes neither
0 nor 1 and that consists of all the i ∈ [0, 1] for which p(i) is on/above the
fence}
(Zwarts 2005b: 763)
This definition correctly predicts that the source p(0) and the goal p(1) of paths denoted
by over the fence are not on/above the fence, while continuous intermediate points p(i) are
on/above the fence. However, it does not predict that the source and the goal must be
on different sides of the fence. (281) also allows situations where the SP starts on one side
outside of the on/above-region of the fence, then goes into the on/above-region of the fence,
and finally goes back to the very same side outside of the on/above-region of the fence
where the path started. However, such kinked paths are not entailed by over the fence. The
reason for this is that SPs qua sequences of locations are not restricted to rectilinear SPs
in constructive approaches. A sequence of locations could be rectilinear, of course, but it
could be also serpentine, spiral, dihedrally snapped, etc. Within an axiomatic approach, this
problem need not arise, because SPs are typically represented as rectilinear line segments that
function as minimal models of SPs as they are typically represented by underived motion
87Typically, route prepositions are ambiguous between a telic and an atelic reading. In line with Zwarts
(2005b), I assume that the telic reading is basic, and the atelic reading is somehow derived. (280a) is naturally
telic due to the achievement predicate jump. For (280b), however, both interpretations are possible. For the
argument here, only the telic interpretation is relevant.
4.5. Spatial paths 163
verbs combining with PPs. Such descriptions minimally commit to rectilinear line segments,
or at most to orthogonally related ones.
Second, axiomatic approaches to SPs are (representationally) more economic insofar as
they typically do not need extra-linguistic means in order to determine the direction of SPs.
Consider, for example, the constructive approach by (Zwarts 2005b). In order to determine
the direction of SPs, Zwarts incorporates the mathematical concept of the real unit interval
into the theory. In particular, he (2005b: 748) defines SPs as functions from the real unit
interval to positions in some model of space. That is, Zwarts’ approach to SPs hinges on an
additional non-linguistic concept, i.e. the real unit interval. In contrast, axiomatic approaches
to SPs are more economic in this regard, because they do not need an extra-linguistic concept,
such as the real unit interval, to determine the direction of SPs. Here, the direction is typically
determined by θ-related mapping to event structure. Such a mapping of SPs to event structure
in terms of a Movement Relation is needed independently from determining the direction of
SPs, namely for the determination of lexical aspect (cf. Section 4.4.2).
After having argued for an axiomatic approach to SPs, I now define SPs. In (282), I define
a SP as a one-dimensional, fundamentally rectilinear line segment that is an element of an
undirected path structure H (Krifka 1998: 203); cf. also (256)
(282) Spatial Path (SP):
A SP is a one-dimensional, fundamentally rectilinear line segment that is element of
a undirected path structure H (Krifka 1998: 203); cf. also (256)
Typically, path prepositions commit to SPs that are conceptualized as rectilinear line
segments. However, the route preposition um (‘around’) apparently denotes SPs that are
conceptualized as a non-rectilinear line segment.88 In Section 5.3.2, I define SPs denoted
by um as a minimal change of direction, to the effect that the core of an um-path are two
rectilinear line segments that are orthogonal to one another at endpoints, i.e. that form
a L-shaped right-angled SP. In that sense, SPs denoted by um can still be considered as
fundamentally rectilinear.
Let us now look at the concatenation of SPs. In line with Zwarts (2005b), Habel (1989),
and Nam (1995), I assume that concatenation is a natural sum operation over SPs. The
motivation for assuming concatenation as the sum operation over SPs, instead of plain
mereological sum formation, is that the former, but not the latter, preserves additivity and
commensurability of extensive measure functions. I assume that the concatenation operation?, as defined over extensive measure functions in (252) and (253), straightforwardly applies
to SPs (Krifka 1998: 201). If two SPs x, y are concatenated and thereby form the complex SP
z (i.e. x? y = z), then x, y – the concatenants (Zwarts 2005b: 750) – are subpaths of z – the
concatenation. Note that this definition of concatenation of SPs contrasts to the one by Zwarts
88Note at this point that the English preposition around involves the configurational element ‘round’. Thus, it
might be analyzed differently from German.
164 4. Semantics
(2005b). As he pursues a constructive approach taking SPs as functions from the real unit
interval to positions in space, Zwarts (2005b: 775) defines the concatenation of two SPs as
head-to-tail connection where the endpoint of one concatenant equals the starting point of
the other concatenant. That is, if the two SPs p, q are concatenated, then p(1) equals q(0).
Let us now look at sources and goals in two different axiomatic approaches to SPs. Recall
from the initial part of this section that there is a fundamental difference with regard to
sources and goals between axiomatic approaches to SPs, on the one hand, and constructive
approaches to SPs, on the other. Constructive approaches typically conceive sources and goals
as inherent extremities of SPs that are determined, for instance, by means of auxiliaries such
as the real unit interval (Zwarts 2005b: 758), while axiomatic approaches typically conceive
sources and goals as thematic roles that are determined by mapping to event structure
(Krifka 1998, Beavers 2012). In particular, sources are those locations that are mapped to
initial subevents, and goals are those locations that are mapped to final subevents. Even
though both authors pursue axiomatic approaches to SPs, Krifka’s and Beavers’ modeling
of sources and goals differ in one essential point. On the one hand, Krifka assumes that
sources and goals are not part of SPs but adjacent to them, while, on the other hand, Beavers
assumes that sources and goals are proper parts of SPs. Both Krifka and Beavers assume
that SPs correspond to elements of a path structure H (Krifka 1998: 204). However, plain
path structures H are undirected, and thus SPs do not have an inherent direction. That is, we
cannot tell which end of a SP is its source and which one its goal. In contrast to an undirected
path structure H, an event structure E (Krifka 1998: 206) is directed because it comprises
a time structure T (Krifka 1998: 205), which itself instantiates a directed path structure D
(Krifka 1998: 205). Hence, SPs obtain their direction by mapping to event structure. Krifka
(1998: 227–228) defines sources as those locations that are not part of SPs, but that are adjacent
to the beginning of a SP, i.e. that part of a SP that is θ-related to an initial part of an event; and
goals as those locations that are not part of a SP, but that are adjacent to the end of a SP, i.e.
that part of a SP that is θ-related to a final part of an event. In other words, for Krifka sources
and goals are adjacent to SPs, i.e. they are at the boundaries of SPs. Krifka (1998: 227–228)
defines the predicates SOURCE and GOAL as given in (283), where x is the source/goal at SP
w in event e. These definitions are diagrammed in Figure 24.
(283) If θ is a (Strict) Movement Relation for SP w and event e, then
a. ∀e, w, x[SOURCE(x, w, e) ↔ [¬x ≤H w ∧ ∀e′, w′[w′ ≤H w ∧ e′ ≤E e ∧ θ(w′, e′) →[[INIE(e′, e)→ w′∞H x]∧ [¬ INIE(e′, e)→ ¬w′∞H x]]]]]
“x is the source at w in e iff x is not a subpath of w but adjacent to a subpath
w′ ≤ w that is θ-related to an initial subevent e′ ≤ e”
b. ∀e, w, x[GOAL(x, w, e)↔ [¬x ≤H w ∧∀e′, w′[w′ ≤H w ∧ e′ ≤E e ∧ θ(w′, e′)→[[FINE(e′, e)→ w′∞H x]∧ [¬FINE(e′, e)→ ¬w′∞H x]]]]]
“x is the goal at w in e iff x is not a subpath of w but adjacent to a subpath w′ ≤ w
4.5. Spatial paths 165
that is θ-related to a final subevent e′ ≤ e”
(cf. Krifka 1998: 227–228)
x
e
w
e′
w′
θθ
24.a: “x is the source at w in e”
x
e
w
e′
w′
θ θ
24.b: “x is the goal at w in e”
Figure 24: Source and goal à la Krifka (1998: 227–228)
In contrast to Krifka (1998), Beavers (2012: 30) defines sources as those locations that
correspond to the parts of SPs that are θ-related to initial parts of events, and goals as those
locations that correspond to the parts of SP that are θ-related to final parts of events. In other
words, for Beavers source and goal are on (or contained in) SPs. Beavers (2012: 30) defines
the predicates SOURCE and GOAL as given in (284), where x is the source/goal on path w in
event e. These definitions are diagrammed in Figure 25.
(284) If θ is an (Strict) Movement Relation for path w and event e, then
a. ∀e, w, x[SOURCE(x, w, e)↔ [x ≤H w ∧∃e′∀e′′[[INIE(e′′, e)→ e′ ≤E e′′]∧ θ(e′, x)]]]
“x is the source on w in e iff x is θ-related to smallest initial e′ ≤ e.”
b. ∀e, w, x[GOAL(x, w, e)↔ [x ≤H w ∧∃e′∀e′′[[FINE(e′′, e)→ e′ ≤E e′′]∧ θ(e′, x)]]]
“x is the goal on w in e iff x is θ-related to smallest final e′ ≤ e.”
(cf. Beavers 2012: 30)
Note at this point that I will exploit – in Section 5.4.2 – the contrast between Krifka’s
and Beavers’ coneptualization of goals and sources in order to model an aspectual contrast
observed in the domain of source and goal prepositions. When combined with manner of
motion verbs, the goal preposition zu (‘to’) gives rise to accomplishment predicates, while
goal prepositions such as in (‘into’) or an (‘onto’) give rise to achievement predicates. In
particular, I will argue that an modified version of Krifka’s goal and source model underlies
prepositions such as zu (‘to’) and von (‘from’) (accomplishments), and that a modified version
of Beavers’ goal and source model underlies prepositions such as in (‘into’) and aus (‘out of’).
166 4. Semantics
ee′′e′
wx
θ θ
25.a: “x is the source on w in e”
e e′′ e′
w x
θθ
25.b: “x in the goal on w in e”
Figure 25: Source and goal à la Beavers (2012)
4.6 Prepositional aspect
This section discusses the notion of prepositional aspect as coined by Zwarts (2005b) and, in
particular, it discusses the appropriate algebraic closure property that characterizes preposi-
tional aspect. As observed by Jackendoff (1991), Verkuyl and Zwarts (1992), Piñón (1993),
Zwarts (2005b), a.o., PPs denoting spatial paths (SPs) can – unlike PPs denoting static loca-
tions – affect the aspectual properties of clauses, in particular when they serve as arguments.
Consider manner of motion verbs like run, swim, or drive, which are inherently atelic when
used as plain unergatives without internal arguments.
(285) John ran for/??in an hour.
Let us add a SP-denoting PP. In general, there are path prepositions, like to in (286a), that
give rise to a telic interpretation, and there are path prepositions, like towards in (286b), that
give rise to an atelic interpretation.
(286) a. John ran to the station in/?for an hour.
b. John ran towards the station for/??in an hour.
Interestingly, there are also path prepositions, like through in (287), that are ambiguous to the
effect that they give rise to both a telic interpretation and an atelic interpretation (Piñón 1993).
In fact, all morphologically-simplex route prepositions (in German) exhibit the ambiguity
illustrated with through.
(287) John ran through the forest in/for an hour.
Observing this behavior of SP-denoting PPs, Zwarts (2005b: 741–742) states that “the dis-
tinction between bounded and unbounded reference familiar from the verbal and nominal
4.6. Prepositional aspect 167
domain shows itself in the prepositional domain too (Jackendoff 1991, Verkuyl and Zwarts
1992, Piñón 1993).” Zwarts (2005b: 742) terms the property that a PP has of having either
bounded or unbounded reference prepositional aspect.89
What is the right closure property characterizing prepositional aspect? Section 4.4.1
introduces the three closure properties cumulativity, divisivity, and quantization, which are
informally repeated here in (288).
(288) a. A predicate is cumulative iff whenever it holds of two things,
it also holds of their sum.
b. A predicate is divisive iff whenever it holds of something,
it also holds of each of its proper parts.
c. A predicate is quantized iff whenever it holds of something,
it does not hold of any of its proper parts.
(Champollion and Krifka 2016: 524–526)
Krifka (1998) identifies quantization as the property that characterizes boundedness in
other domains. Take the bounded predicate three apples (Krifka 1998: 200). If the element x
falls under this predicate, then there is no proper part y < x that also falls under this predicate.
The question now is whether quantization is also the closure property that characterizes
bounded predicates in the prepositional domain. Zwarts (2005b: 754) shows that quantization
cannot be the right closure property characterizing bounded PPs. Take the bounded PP to the
station. If quantization was the closure property characterizing bounded PPs, then there must
not be a SP x that falls under the predicate to the station and that has a proper subpath y < x
that also falls under the predicate to the station. It can easily be shown that this is not the case.
Consider the SP x from A to B depicted in Figure 26. It clearly falls under the predicate to the
station. Obviously, we can find a proper subpath y < x (i.e. from A′ to B) that also falls under
the predicate to the station. Thus, quantization is not the right closure property characterizing
bounded PPs.
the
station
A BA′
y
x
Figure 26: Non-quantization of SPs to the station
Let us now see whether divisivity or cumulativity characterizes unbounded PPs. The
fundamental difference between these two closure properties is that divisivity is a downward-
89PPs that have bounded reference are referred to as bounded PPs, and those that have unbounded reference
as unbounded PPs. Prepositions that head bounded PPs are referred to as bounded prepositions, and those that
head unbounded PPs as unbounded prepositions.
168 4. Semantics
looking closure property based on the proper part relation <, while cumulativity is an
upward-looking closure property based on the sum relation ⊕.90
Piñón (1993) and Nam (2000) take the view that divisivity characterizes unboundedness
in the domain of SPs. Advocating a constructive approach to SPs, Zwarts (2005b) argues
that divisivity cannot be the closure property characterizing unbounded PPs. Take the
unbounded predicate towards the station (Zwarts 2005b: 751). If divisivity was the closure
property characterizing unbounded predicates in the prepositional domain, then it must be
the case that if the SP x falls under the predicate towards the station, then each subpath y < x
must also fall under the predicate towards the station. Let us first look at axiomatic approaches
to SPs, as, for instance, argued for by Piñón (1993), Krifka (1998). Here, SPs are typically
assumed to be rectilinear line segments. On such approaches, one of which is depicted in
Figure 27.a, divisivity correctly characterizes unbounded PPs. The SP x from A to B falls
under the predicate towards the station, and so does each of its proper subpaths. For instance,
the SP y < x from A′ to B′ also falls under the predicate towards the station. Let us now look at
constructive approaches to SPs, as, for instance, argued for by Zwarts (2005b). Recall from
Section 4.5 that Zwarts (2005b: 748) defines SPs as functions from the real unit interval [0, 1]
to positions in some model of space. This definition does not contain any constraints on the
shape of SPs, which is why they can have virtually any shape, as long as the locations are
spatially continuous. That is, SPs can virtually have any shape. Consider the SP x from A
to B in Figure 27.b, which falls under the predicate towards the station. Here, we can identify
subpaths that do not fall under the predicate towards the station. Take for instance the SP y < x
from A′ to B′. It clearly does not fall under the predicate towards the station.
the
station
A BA′ B′
y
x
27.a: Model with rectilinear SPs
the
stationA
A′
B′
B
y
x
27.b: Model with non-rectilinear SPs
Figure 27: (Non)-divisivity of SPs towards the station
Zwarts (2005b: 752) adduces a further argument against divisivity as the characteristic
property of unbounded PPs. Consider the unbounded PP along the river in (289).
90The terms ‘downward-looking’ and ‘upward-looking’ account for the intuition that divisivity looks
downward from the sum to the part, while cumulativity looks upward from the part to the sum.
4.6. Prepositional aspect 169
(289) Alex drove along the river (for/*in a day).
(Zwarts 2005b: 752)
Even though Zwarts assumes a constructive approach to SPs, this argument is straightfor-
wardly transferable to an axiomatic approach where SPs are considered to be rectilinear
line segments. Depending on the shape of the river, there might be configurations where
divisivity fails to characterize an unbounded PP such as along the river. In particular, there
can be (rectilinear) SPs that fall under the predicate along the river, but that also have proper
subpaths that do not fall under the predicate along the river. Imagine a meandering river as
illustrated in Figure 28. The SP x form A to B clearly falls under the predicate along the river.
There are, however, proper subpaths of x that do not fall under the predicate along the river.
Take for example the proper subpath y < x from A′ to B′; this path does not fall under the
predicate along the river.
the river
A A′ B′ B
y
x
Figure 28: Non-divisivity of (rectilinear) SPs along the river
Considering the examples illustrated the in Figures 27.b and 28, Zwarts (2005b: 752) con-
cludes that “divisivity is not the algebraic property that characterizes unbounded PPs.” Let
me add a further argument against divisivity as the characteristic closure property of un-
bounded PPs. The German route preposition um (‘around’) (cf. Section 5.4.3) is systematically
ambiguous between a telic (bounded) and an atelic (unbounded) interpretation (Piñón 1993,
Zwarts 2005b). Consider the example in (290).
(290) Hans
Hans
rannte
ran
in/für
in/for
zwei
two
Stunden
hours
um
around
den
the.ACC
Bahnhof.
station
‘Hans ran around the station in/for two hours.’
Even under an axiomatic approach to SPs, the minimal model of a SP denoted by um is not
entirely rectilinear. In Section 5.4.3, I propose that SPs denoted by um are minimally L-shaped
line segments (cf. Section 4.3.6) embracing the reference object. For example, the path x from
170 4. Semantics
A to B in Figure 29 falls under the predicate um den Bahnhof (‘around the station’).91 On such
a semi-rectilinear SP, we can easily identify a proper subpath that does not fall under the
denotation um den Bahnhof. Consider the SP y < x from A′ to B′, which does not fall under the
predicate um den Bahnhof. Thus, I follow Zwarts (2005b: 752) in assuming that divisivity is not
the right closure property that characterizes unbounded PPs.
the
station
A A′ B′
B
y
x
Figure 29: Non-divisivity of fundamentally rectilinear SPs
um den Bahnhof (‘around the station’)
Let us now look at cumulativity as the closure property characterizing unbounded PPs.
Unlike divisivity, which is based on the part relation, cumulativity is based on the sum
operation. The idea is that a predicate has unbounded reference iff for all two entities that
fall under the predicate also their mereological sum, if it exists, falls under the predicate.
With regard to SPs, Zwarts (2005b: 749–750) – following Habel (1989), Nam (1995) – proposes
that concatenation is a natural sum operation over SPs. Adopting a constructive approach,
Zwarts (2005b: 748) defines SPs as continuous functions from the real unit interval [0, 1]
to positions in some model of space. Based on this concept of SPs, he (2005b: 750) defines
the concatenation of two SPs x, y such that the endpoint of one concatenant corresponds
to the starting point of the other concatenant, i.e. x(1) = y(0). That is, the SPs x, y connect
head-to-tail. As I do not pursue a constructive approach to SPs, I cannot adopt Zwarts’
definition of concatenation of SPs. Instead, I adopt Krifka’s (1998: 201) definition of the
concatenation operation ? based on extensive measure functions; see (252) and (253) in
Section 4.4.1. An important precondition for assuming cumulativity as the characteristic
91Note that the English route preposition (a)round might commit to another minimal model than the German
route preposition um, even though the two prepositions are more or less direct translations of each other. English
(a)round apparently incorporates the morpheme ‘round’, which obviously refers to a geometric configuration.
In contrast, German um is frequently used as a particle in particle verb constructions describing ‘change of
direction scenarios’, e.g. etw. um-fahren (‘to knock sth. down, to hit sth.’) or etw. um-hauen (‘to chop/cut
down sth.’). In such particle verb constructions, um indicates a positional change of the direct object, e.g. from
an vertical to a horizontal position. This usage of um strongly corroborates the hypothesis that German um
minimally commits to some fundamental ‘change of direction’, which I capture in terms of semi-rectilinear
L-shaped line segments that contain at least one 90○ bend. Note that this is still in line with an axiomatic
approach to SPs. Even though L-shaped SPs have a geometrically complex modeling, they are indecomposable
primes at the level of semantic representation (DRS) at LF.
4.6. Prepositional aspect 171
property of unbounded PPs denoting SPs relates to the fact that cumulativity is based on the
mereological sum operation and the concatenation operation, respectively. We need to assume
that there is at least one concatenation of two SPs in the denotation of a PP. Otherwise, PP
denotations without any connecting SPs would be vacuously cumulative (Zwarts 2005b: 751).
Based on these considerations on cumulativity with respect to SPs, Zwarts (2005b: 751) defines
cumulative predicates over SPs as given in (291).
(291) A predicate Φ over SPs is cumulative iff
a. there are x, y ∈ Φ such that x? y exists and
b. for all x, y ∈ Φ, if x? y exists, then x? y ∈ Φ.
(cf. Zwarts 2005b: 753)
In fact, cumulativity based on concatenation appears to be the characteristic property
of unbounded PPs denoting SPs. Let us therefore revisit the cases discussed above in the
context of divisivity. The PP towards the station has unbounded reference. Consider again a
rectilinear model of SPs, as illustrated in Figure 30.a, and a non-rectilinear model of SPs, as
illustrated in Figure 30.b. In both models, both the SP x from A to B and the SP y from B to C
individually fall under the predicate towards the station, and so does their concatenation x? y
from A to C.
the
stationx y
A B C
30.a: Model with rectilinear SPs
the
station
A
B
C
x
y
30.b: Model with non-rectilinear SPs
Figure 30: Cumulativity of SPs towards the station
The same holds for the unbounded PP along the river. In Figure 31, both the SP x from
A to B and the SP y from B to C fall under the predicate along the river. Likewise, their
concatenation x? y from A to C falls under the predicate along the river.
What about German um (‘around’)? Consider again the minimal model of SPs denoted by
the PP um den Bahnhof (‘around the station’) depicted in Figure 32. Both the SP x from A to B
and SP y from B to C fall under the predicate um den Bahnhof, and so does their concatenation
x? y from A to C.
172 4. Semantics
the river
A B Cx y
Figure 31: Cumulativity of (rectilinear) SPs along the river
the
station
x
y
A
B
C
Figure 32: Cumulativity of fundamentally rectilinear SPs
um den Bahnhof (‘around the station’)
I conclude, in line with Zwarts, that cumulativity is the closure property that character-
izes unbounded PPs. In particular, Zwarts (2005b: 753) proposes the correlation between
cumulative reference and unboundedness in (292).
(292) a. A PP is unbounded iff it has cumulative reference.
b. A PP is bounded iff it does not have cumulative reference.
(Zwarts 2005b: 753)
I adopt (292) when modeling prepositional aspect.
4.7 Force-effective prepositions
This section addresses the concept of spatial support from below, which manifests itself as a
characteristic of the topological preposition auf (‘upon’) in German. Roughly speaking, I will
argue that auf describes situations where the Ground (the complement of the preposition)
4.7. Force-effective prepositions 173
must be capable of preventing the falling down of the Figure (the external argument of the
preposition); see Talmy (1975, 2000) and Section 4.2 for the notions Figure and Ground.92
Unlike German an (‘on’), the topological preposition auf (‘upon’) shows the force-dynamic
effect support from below. In their geometric usages, both topological prepositions an and
auf minimally commit to spatial contact between the Figure and the Ground. The difference
between the two prepositions is that auf, unlike an, commits to a configuration such that the
Ground supports the Figure from below. In order to understand the force-dynamic effect of
support from below, and thus the differences between an and auf, consider the two situations
depicted in Figure 33 below.
33.a: Apfel an Kiste (‘apple on box’) 33.b: Apfel auf Kiste (‘apple upon box’)
Figure 33: Support from below
Let us describe these situations with the topological prepositions an and auf such that
the position of the apple is described relative to the box; viz. the apple should serve as the
Figure, while the box should serve as the Ground (Talmy 2000: 312). The spatial configuration
in Figure 33.a can felicitously be described with an, as in (293a).93 The preposition auf is
unacceptable here. In contrast, the spatial configuration in Figure 33.b can straightforwardly
be described with auf, as in (293b). Interestingly, an is not unacceptable, but marked here.
Imagine a more complex situation where the apple is in a position as depicted in Figure 33.b.
But where it is not the box that carries the apple but some third party, e.g., if the apple
hangs on a rope but still touches the box. In such situations, the acceptability of auf seems to
decrease, and the acceptability of an seems to increase.
(293) a. Der
the
Apfel
apple
ist
is
an/*auf
on/upon
der
the
Kiste.
box
‘The apple is at the box.’ (as a description for Figure 33.a)
b. Der
the
Apfel
apple
ist
is
auf/?an
upon/on
der
the
Kiste.
box
‘The apple in upon the box.’ (as a description for Figure 33.b)
92Note that I use the notions Figure and Ground at the beginning of this section. These notions relate, sensu
stricto, to the cognitive domain of space. In fact, I replace them later in the course of this section by the notions
Agonist and Antagonist, which are the respective notions from the cognitive domain of force (Talmy 2000).
93Note that the projective (non-topological) preposition neben (‘beside’) would also be possible here. We can
consider this as another way to express this configuration. For the sake of argument, however, we will ignore
this possibility here.
174 4. Semantics
That is, auf does not only require spatial contact between the Figure and the Ground like
an, but also that the Ground carries the Figure to the effect that it prevents the Figure from
falling down. Under normal conditions on earth, all material objects are subject to gravity
and thus would fall down if not supported by something or kept going away from gravity
because of a kinetic momentum. In order to prevent the Figure from falling down to earth, it
can, for instance, be located at the upper side of the Ground, i.e. on that part of the surface of
the Ground that steadily prevents the Figure from being accelerated by gravity. This kind of
configuration where the Ground carries the Figure so that the Figure does not fall down to
earth can be understood as the force-dnyamic effect support from below.
Advocating a unified model of space and force in terms of vector spaces, Zwarts (2010a)
argues that the Dutch prepositions op (‘upon’), aan (‘on’), and in (‘in’) – which roughly
correspond to the German prepositions auf, an, and in, respectively – are forceful; that is, that
they are force-dynamically active. While I agree with Zwarts that some prepositions might
show a force-dynamic effect, I take the view that prepositions have a rather passive status
with regard to force-dynamics. I am convinced that verbs can speak of forces. Prototypical
instances of such verbs are push and pull in English or drücken and ziehen in German; see
also Zwarts (2010a). However, I assume that prepositions, unlike verbs, do not primarily
speak of forces, but rather can be selected by certain forceful verbs. Consider the following
data corroborating this assumption. If a force-dynamically relevant discourse referent, i.e. a
force, was present in the representation the preposition auf, then it should be accessible for
measurement – even in a context where the verb does not speak of forces. In such contexts,
however, it is apparently impossible to measure a force with an adverb like schwer (‘heavily’),
which is a prototypical adverb for measuring forces. Consider the data in (294) involving
PPs headed by auf. Interestingly, if the verb does not speak of a force, as in (294b) and
(294c), an adverb such as schwer that measures forces is ungrammatical. Only if the verb
is force-dynamically active, as for instance the verb lasten (‘weigh’) in (294a), is the adverb
felicitous.
(294) a. Die
the
Vase
vase
war
was
(*schwer)
heavily
auf
upon
dem
the
Tisch.
table
b. Die
the
Vase
vase
stand
stood
(??schwer)
heavily
auf
upon
dem
the
Tisch.
table
c. Die
the
Vase
vase
lastete
weighed
(schwer)
heavily
auf
upon
dem
the
Tisch.
table
I conclude from these data that the preposition auf is intrinsically not force-dynamically
active. However, acknowledging the fact that it can show a force-dynamic effect, I assume
instead that it is force-effective. To understand what I mean by this, let me now present
some basic concepts of force-dynamics as discussed by Talmy (1975, 2000).
4.7. Force-effective prepositions 175
To begin, let us define the two force entities Agonist and Antagonist that are elementary
for force-dynamic analyses. Note that I adhere in this regard to Talmy’s original terms, even
though many scholars apply terms that are essentially borrowed from other domains.
(295) a. Agonist:
The Agonist is the force entity that is singled out for focal attention. The salient
issue in the force interaction is whether the Agonist is able to manifest its force
tendency or is overcome. It is the force entity for which the resultant is assessed.
b. Antagonist:
The Antagonist is the force entity that is in force interaction with the Agonist.
The Antagonist is opposing the Agonist.
(Talmy 2000: 413,415)
Talmy schematizes the Agonist as a circle and the Antagonist as a concave figure. Force
entities can have an intrinsic force tendency, either toward action or toward rest. A tendency
toward action is indicated by an angle bracket (>), while a tendency toward rest is indicated
by a bullet (●). A further factor is the balance between the force of the Agonist and the force
of the Antagonist, i.e. the relative strength of the opposing forces. Typically, the stronger
force entity is marked with a plus sign (+), while the weaker force entity is unmarked. The
opposing force entities yield a resultant which is either of action or of rest. The resultant is
assessed only for the Agonist, as it is the force entity whose circumstance is at issue. The
resultant is schematized as a line beneath the Agonist. Talmy (1988, 2000) identifies four
basic steady-state force-dynamic patterns, which are illustrated in the diagrams in Figure 34.
The pattern in Figure 34.a involves an Agonist with a tendency toward rest that is opposed
by a stronger Antagonist. Thus, the Agonist’s tendency towards rest is overcome, which
results in action. An example of this pattern is given in (296a). The pattern in Figure 34.b
involves an Agonist with a tendency toward rest. It is ineffectively opposed by a weaker
Antagonist, which results in rest. An example of this pattern is given in (296b). The pattern
in Figure 34.c involves an Agonist with a tendency toward action. It is opposed by a weaker
Antagonist, which results in action. An example of this pattern is given in (296c). The pattern
in Figure 34.d involves an Agonist with a tendency towards action. It is opposed by a stronger
Antagonist, which results in rest. An example of this pattern is given in (296d).
(296) a. The ball kept rolling because of the wind blowing on it.
b. The shed kept standing despite the gale wind blowing against it.
c. The ball kept rolling despite the stiff grass.
d. The log kept lying on the incline because of the ridge there.
(Talmy 2000: 416)
The gravitational attraction of the earth gives weight to material objects. Being attracted
by the gravity of the earth, material objects fall down to the ground, moving along the vertical
176 4. Semantics
●+
>
34.a
●+
●
34.b
>+
>
34.c
> +
●
34.d
Figure 34: The basic steady-state force-dynamic patterns (Talmy 2000: 415)
axis. Let us assume that this is conceptualized to the effect that gravity endows material
objects with their own intrinsic force, or, put differently, that gravity literally ‘enforces’
material objects. That is, material objects (on earth) are typically conceptualized as Agonists,
in that they tend to fall to earth; they have an intrinsic force tendency toward action by virtue
of gravity.
Let us now look again at the ‘apple-upon-box’ situation, i.e. the prototypical instance of
the preposition auf (‘upon’) that is depicted in Figure 33.b and described by the clause in
(293b). With regard to the cognitive domains of space and force, I claim that this situation is
conceptualized as follows. As for space (297a), we can say that the apple serves as the Figure,
while the box serves as the Ground. As for force (297b), the apple is the force entity that is
singled out for focal attention. It is conceptualized as the Agonist that has a disposition to fall
down. In contrast, the box is the force entity that is in force interaction with the apple; it is
conceptualized as the Antagonist. The box prevents the apple from falling down so that the
apple stays put. The Antagonist provides a stronger counterforce overcoming the Agonist’s
intrinsic force tendency toward action, which results in rest. This instantiates the steady-state
force-dynamic pattern depicted in Figure 34.d.
(297) a. Space: [Figure Der Apfel ] ist [PP auf [Ground der Kiste ]].
b. Force: [Agonist Der Apfel ] ist [PP auf [Antagonist der Kiste ]].
the apple is upon the box
In order to account for the force-dynamic effect that manifests itself in the geometric usage
of the preposition auf (‘upon’), I do not draw on Zwarts’ (2010a) integrated vector space
model of space and force. Instead, I model the force-dynamic concept of support from below
in terms of the two-place predicate sfb. It is informally sketched in (298). In particular, I leave
4.8. Summary 177
the model-theoretic explication of sfb for future research. The predicate sfb is adopted in the
definition of auf-regions in (334); cf. Section 5.3.3.
(298) The force entity x supports the force entity y from below “sfb(x, y)”:
a. By virtue of gravity, the force entity y has an intrinsic force tendency toward
action. The force direction is downward. The force entity y is conceptualized as
an Agonist.
b. The force entity x provides a counterforce that overcomes the Agonist’s ten-
dency to fall down. The force entity x is conceptualized as an Antagonist.
c. This equilibrium of forces takes place along the vertical axis and leads to rest as
resultant.
d. The canonical configuration for this is that the Agonist is on top of the Antago-
nist.
Note that the geometric usage of auf typically commits to spatial contact between the
Agonist and the Antagonist. This is accounted for by the way auf-regions are defined. In
particular, the definition of auf-regions in (334) involves the condition x ⊃⊂ y, where x is the
region occupied by the Agonist, y is the region occupied by the Antagonist, and ⊃⊂ means
‘has spatial contact with’ (cf. Section 4.3.5).
4.8 Summary
This chapter explored the semantic branch of the Y-model of grammar, that is Logical Form
(LF). In this thesis, I adopted the tenets of Discourse Representation Theory (DRT) (Kamp
and Reyle 1993, 2011, Kamp et al. 2011) to model LF. As for a model of space, I followed
Kamp and Roßdeutscher (2005). As for algebraic structures, I followed Krifka (1998), Beavers
(2012).
Section 4.1 presented the semantic construction algorithm. At LF, each terminal node
of a syntactic structure receives a context-dependent interpretation. Compositionally, the
interpretations of the terminal nodes are combined bottom-up along the syntactic structure
by means of unification-based composition rules. As for the representation of LF, Discourse
Representation Theory (DRT) (Kamp and Reyle 1993, 2011, Kamp et al. 2011) was chosen; cf.
Section 4.1.2. One of the features of DRT is that interpretation involves a two-stage process:
(i) the construction of semantic representations referred to as Discourse Representation
Structures (DRSs), i.e. the LF-representation proper; and (ii) a model-theoretic interpretation
of those DRSs. Section 4.1.3 illustrated the semantic construction algorithm by reproducing a
textbook example, involving aspectual information.
Section 4.2 briefly discussed the general conceptualization of ‘Figure’ and ‘Ground’ in
language, as introduced by Talmy (1975, 2000).
178 4. Semantics
Section 4.3 focused on the model-theoretic aspects relevant for the semantic modeling
of spatial prepositions. I presented two models of three-dimensional space: (i) the vector
space model of space, as advocated by Zwarts (1997, 2003b, 2005b), Zwarts and Winter (2000);
and (ii) the perception-driven model of space, as advocated by Kamp and Roßdeutscher
(2005), who base their approach on principles formulated by Lang (1990). In this thesis, I
adopted Kamp and Roßdeutscher’s (2005) parsimonious, perception-driven model of space.
Section 4.3.1 discussed material objects, which can be conceptualized as being one-, two-
, or three-dimensional. Section 4.3.2 focused on the spatial ontology. In particular, the
notions ‘region’, ‘point’, ‘line’, ‘line segment’, ‘direction’, ‘directed line segment’, and ‘plane’
were introduced. Then, Section 4.3.3 introduced the Primary Perceptual Space (PPS), which
spans a three-dimensional space on the basis of our perceptual input (Lang 1990, Kamp
and Roßdeutscher 2005). The PPS consists of three axes that are orthogonal to one another:
(i) the vertical axis determined by gravity, (ii) the observer axis determined by vision, and
(iii) the transversal axis derived from the other two axes as being orthogonal to both. Six
orientations are identified on the three axes: up and down are orientations of the vertical axis;
fore and back are orientations of the observer axis; and left and right are orientations of the
transversal axis. Section 4.3.4 addressed boundaries of material objects and regions and how
they can be used to determine the inside and the outside of a material object. Section 4.3.5
briefly discussed how ‘spatial contact’ of two regions can be modeled. Then, Section 4.3.6
discussed conditions on line segments that figure in the modeling of spatial paths denoted by
route prepositions. Two types of conditions are proposed: (i) boundary conditions and (ii)
configurational conditions. Boundary conditions manifest themselves to the effect that a line
segment is either completely inside or completely outside the material object, i.e. an internal
or external line segment of a material object. A crucial property of both boundary conditions
is that one must be able to drop a perpendicular from the boundary of the material object
onto every point of the line segment. Configurational conditions describe the configuration
of line segments as related to material objects or the shape of line segments; three such
configurational conditions of line segments are proposed: (i) an L-shaped line segment is
a line segment that involves an orthogonal change of direction; (ii) a plumb-square line
segment of a material object is a line segment that is horizontally aligned and above the
material object (NB: the term is borrowed from a carpentry tool); and (iii) a spear-like line
segment of a material object is a line segment that is orthogonal to a cross section of the
material object.
Section 4.4 discussed the algebraic foundations. Section 4.4.1 presented the mereological
structures that figure for the modeling of spatial paths. In particular, plain/undirected
path structures H (Krifka 1998: 203) and directed path structures D (Krifka 1998: 203) were
presented. Spatial paths can serve as incremental themes measuring out events (Dowty 1979,
1991, Tenny 1992, Jackendoff 1996, Krifka 1998, Beavers 2012); thus, Section 4.4.2 presented
incremental relations mapping spatial paths to event. I briefly presented Beavers’ (2012)
Figure/Path Relations (FPRs) that account for double incremental themes.
4.8. Summary 179
Section 4.5 focused on spatial paths. I briefly presented two approaches to spatial paths:
(i) an axiomatic approach, where spatial paths are taken as primitives in the universe of
discourse (Piñón 1993, Krifka 1998, Beavers 2012); and (ii) a constructive approach, where
spatial paths are defined as continuous functions from the real unit interval [0, 1] to positions
in some model of space (Zwarts 2005b: 748). The two approaches have different implications
on the notions ‘goal’ and ‘source’. In axiomatic approaches, ‘goal’ and ‘source’ are thematic
notions that typically derive when motion events and their spatial projections map onto one
another. In constructive approaches, ‘goal’ and ‘source’ are inherent extremities of spatial
paths (Zwarts 2005b: 758). In this thesis, I opted for an axiomatic approach to spatial paths.
Section 4.6 explored the notion of ‘prepositional aspect’. Zwarts (2005b: 742) relates
prepositional aspect to the distinction between bounded and unbounded reference, which
is familiar from the verbal domain, e.g., and which shows itself also in the domain of PPs
denoting spatial paths (Jackendoff 1991, Verkuyl and Zwarts 1992, Piñón 1993). Following
Zwarts (2005b: 753), I assume that cumulativity is the algebraic property characterizing
prepositional aspect: unbounded PPs have cumulative reference, while bounded PPs nodes
not have cumulative reference.
Section 4.7 discussed the force-dynamic effect of the German topological preposition
auf (‘upon’), which can be characterized as ‘support from below’. In contrast to (Zwarts
2010a), who takes the view that prepositions can be forceful, I argued that prepositions
are not forceful but can show force-dynamic effects. Using Talmy’s (2000: 413, 415) terms
‘Agonist’ and ‘Antagonist’ for the force entities at issue, the force-dynamic effect of auf can be
characterized to the effect that the complement of the preposition serves as an Antagonist
providing a counterforce of an Agonist’s tendency to fall down. The equilibrium of forces
takes place along the vertical axis and leads to a resultant toward rest.
180 4. Semantics
Chapter 5
Spatial prepositions at the interfaces
This chapter will spell out the syntax, semantic, morphology of spatial prepositions in
German. It is the core of this thesis because it illustrates how spatial prepositions can be
implemented in the Y-model of grammar. The structure of this chapter is as follows. First,
Section 5.1 will classify spatial preposition according to several criteria. Section 5.1.1 will
introduce the distinction between place prepositions, on the one hand, and path prepositions,
on the other. Path prepositions are further subdivided into directed path prepositions (goal
and source prepositions) and undirected path prepositions (route prepositions) (Jackendoff
1983, Piñón 1993, Zwarts 2006, a.o.). Section 5.1.2 will propose a geometry-based classifi-
cation of spatial prepositions that is orthogonal to the place/path typology. I propose that
spatial prepositions can be (i) geometric prepositions, (ii) pseudo-geometric prepositions, or
(iii) non-geometric prepositions. Section 5.1.3 will classify path prepositions into bounded
and unbounded path prepositions. Section 5.1.4 will map these classifications to syntactic
structure. Then, Section 5.2 will briefly touch upon the cartographic decomposition of spatial
prepositions (Svenonius 2006, 2010, Pantcheva 2011). Then, Section 5.3 will introduce three
abstract Content features that relate to geometric concepts and that figure in the derivation of
the geometric prepositions: [ℵ] relating to interiority in Section 5.3.1; [ℶ] relating to contiguity
in Section 5.3.2; and [ℷ] relating to verticality in Section 5.3.3. Then, Section 5.4 will derive the
lexical structure of spatial prepositions and spell out PF-instructions for their morphophono-
logical realization and LF-instructions for their semantic interpretation. Then, Section 5.5 will
derive the functional structure of spatial prepositions and spell out PF-instructions for their
morphophonological realization and LF-instructions for their semantic interpretation. Then,
Section 5.6 will illustrate how a fully-fledged PP, i.e. a prepositional CP, headed by a spatial
preposition can be integrated in various verbal contexts. Finally, Section 5.7 will summarize
this chapter.
181
182 5. Spatial prepositions at the interfaces
5.1 Classifying spatial prepositions
5.1.1 Place and path prepositions
Generally, we find two types of prepositions expressing spatial configurations. On the one
hand, place prepositions denote static locations relative to the Ground (regions) and the
Figure is located in this location. On the other hand, path prepositions denote dynamic
locations with respect to the Ground (spatial paths) along which the Figure changes its
position or moves. Path prepositions can be directed/oriented or undirected/non-oriented.
Directed path preposition denote either a spatial path from a location relative to the Ground
(source preposition) or a spatial path to a location relative to the Ground (goal preposition).
Undirected path prepositions denote spatial paths where the location relative to the Ground
serves neither as source nor as goal (route prepositions). This gives rise to the typology of
spatial prepositions given in Figure 35, which is widely accepted in the literature (e.g. Jack-
endoff 1983, Piñón 1993, Zwarts 2006, Gehrke 2008, Kracht 2008, Svenonius 2010, Pantcheva
2011). The typology in Figure 35 includes examples from English.
spatial prepositions
place prepositions
(in)
path prepositions
directed
source prepositions
(out of )
goal prepositions
(into)
undirected
route prepositions
(through)
Figure 35: Typology of spatial prepositions
5.1.2 Prepositions and geometry
This section establishes three classes of spatial prepositions in German. Generally, spatial
prepositions express spatial relations. Some of these spatial relations can be characterized in
geometric terms, while others cannot. A crucial characteristic of the three classes that I argue
for is whether the respective prepositions involve a geometric level of description or not.
Essentially, this gives rise to two classes, geometric prepositions, i.e. those prepositions that
involve a geometric level, as opposed to non-geometric prepositions, i.e. those prepositions
that do not involve a geometric level. In addition, I argue for a third class which I refer to
5.1. Classifying spatial prepositions 183
as pseudo-geometric prepositions. Superficially, they look like geometric prepositions, but,
crucially, they lack a geometric level. This is shown by certain aspects of their behavior.
In this thesis, I conceive geometry in a broader sense including geometry in the narrow
sense as well as topology. Thus ‘geometric prepositions’ is a term covering both prepositions
expressing relations that are best understood in terms of topological terms (topological
prepositions) and prepositions expressing relations that are best understood in terms of
projection onto one of the three perpendicular axes of the Primary Perceptual Space (Lang
1990, Kamp and Roßdeutscher 2005), i.e. onto the vertical axis, onto the observer axis, or onto
the horizontal axis (projective prepositions). I focus on topological prepositions. Projective
prepositions behave in many – but not in all – respects like topological prepositions. For
instance, projective prepositions behave like topological propositions with respect to case
assignment – which is central in this thesis –, while projective prepositions behave differently
from topological prepositions with respect to licensing postpositional elements – which is not
central in this thesis. Thus, for the sake of clarity, I concentrate on topological prepositions. In
German, these include an (‘at, on’), auf (‘upon’), aus (‘out of’), and in (‘in’).94 As for projective
prepositions, which include über (‘above’), unter (‘under’), vor (‘in front of’), hinter (‘behind’),
and neben (‘next to’), I refer the reader to Herskovits (1986), Lang (1993), Zwarts (1997, 2010b),
Zwarts and Winter (2000), Svenonius (2006, 2010), Hying (2009), and references therein. Note
that I also omit zwischen (‘between’), the behavior ov which is parallel to that of projective
prepositions.
Note that the geometry that is crucial for geometric prepositions can be modeled in
serveral ways. For example, we can model geometry in terms of a simple geometric model
of space in the spirit of Kamp and Roßdeutscher (2005), a vector space model in the spirit
of Zwarts (1997) and Zwarts and Winter (2000), or any other model of space; cf. Section 4.3.
Topological relations can be modeled, for instance, as described by Egenhofer (1989, 1993).
Note, however, that the way in which geometric relations are modeled is not crucial here.
I argue that it is crucial to distinguish between geometric prepositions and non-geometric
prepositions. As opposed to geometric prepositions, the spatial relations conveyed by
non-geometric prepositions are best understood not in geometric but in other terms. Non-
geometric prepositions differ from geometric prepositions not only with respect to the spatial
relation conveyed, but also in some other respects, such as (lexical) aspect or case assignment.
The non-geometric prepositions include the prepositions bei (‘at’), zu (‘to’), von (‘from’),
auf ... zu (‘towards’), its archaic from gen (‘towards’), and von ... weg (‘away from’). Note
that auf ... zu and von ... weg are fixed combinations of a preposition and a postposition.
Nevertheless, I avoid the term ‘circumposition’ because, under certain conditions, these
combinations can occur in reverse order as a combination of prepositions, i.e. zu auf and
weg von.
94Often, the spatial prepositions discussed here cannot be translated one to one into English. Thus the
translations appear sometimes awkward.
184 5. Spatial prepositions at the interfaces
In order to illustrate the non-geometricality of these prepositions, take the non-geometric
preposition zu (‘to’) in (299a). Essentially, it does not provide any geometric information
insofar as we do not know where exactly Hans ended up with respect to the forest. Did
he enter the interior of the forest? Or did he stop at the forest boundary or at a location
somewhere near the forest? (299a) does not specify this information. All we know is that
he ran to a location that is somehow related to and at least near the forest. In contrast, the
geometric preposition in (‘into’) in (299b) provides geometric information insofar as we know
that Hans ended up in the interior of the forest.
(299) a. Hans
Hans
rannte
ran
zu
to
einem
a.DAT
Wald.
forest
‘Hans ran to a forest.’
b. Hans
Hans
rannte
ran
in
in
einen
a.ACC
Wald.
forest
‘Hans ran into a forest.’
Table 3 maps this geometry/non-geometry divide to the typology of spatial prepositions
shown in Figure 35, that is, to place prepositions and to path prepositions (source, goal, and
route). Note that route prepositions cut across the geometric/non-geometric divide.
geometric non-geometric
place an (‘on’),
auf (‘upon’),
in (‘in’)
bei (‘at’)
path dir. source aus (‘out of’),
(von an ‘from on’),
(von auf ‘from upon’),
(von in ‘from in’)
von (‘from’),
von ... weg (‘away from’)
goal an (‘onto’),
auf (‘up onto’),
in (‘into’)
zu (‘to’),
auf ... zu (‘towards’)
undir. route um (‘around’),
über (‘across, over’),
durch (‘through’)
Table 3: Geometric and non-geometric prepositions in German
The geometric prepositions are an, auf, and in occur, on the one hand, as place prepositions,
and on the other hand, as goal prepositions. Note that they take a dative complement
when serving as place prepositions and an accusative complement when serving as goal
prepositions. This is the well-known place/goal alternation (or dative/accusative alternation)
of German prepositions. Note also that the projective prepositions, which I omit here, are
likewise subject to the place/goal alternation.
The geometric source prepositions can either have a synthetic form or an analytic form.
The synthetic geometric source preposition in German is aus. The analytic forms are com-
5.1. Classifying spatial prepositions 185
binations of the (non-geometric) source preposition von plus an, auf, or in.95 Note that the
analytic forms are generally dispreferred, yet not ungrammatical. Note in this regard that the
projective prepositions pattern with an and auf.
The geometric route prepositions have forms distinct from the other geometric preposi-
tions. Interestingly, the topological route prepositions um, über, and durch are the only morpho-
logically simplex route prepositions in German.96 In particular, there are no morphologically-
simplex projective route prepositions.
The number of non-geometric prepositions is relatively low compared to the number of
geometric prepositions. There is only bei serving as a place preposition. For both source and
goal respectively, there are two prepositions: von and von ... weg as well as zu and auf ... zu. In
fact, this dichotomy mirrors the bounded/unbounded divide addressed in Section 5.1.3.
In addition to the geometric/non-geometric divide, I argue for a third class of prepositions
that I refer to as pseudo-geometric prepositions. Pseudo-geometric prepositions can be
considered as the prototypical place and path prepositions used with a certain DP providing
a ‘functional locative’ interpretation. That is, pseudo-geometric prepositions are functional
locative prepositions. Superficially, pseudo-geometric prepositions look and in some respects
also behave like geometric prepositions, but, crucially, pseudo-geometric prepositions lack an
explicit geometric level of description. Instead, they denote locations that have a functional
character. The pesudo-geometric prepositions involve the topological prepositions an (‘on/at,
onto/to’), auf (‘upon/at, up onto/to’), in (‘in/at, into/to’) – in both their place and path
version – and additionally the path preposition nach (‘to’).
With common nouns, often both pseudo-geometric and geometric prepositions are possi-
ble, which leads to an ambiguity. Consider the examples in (300) involving the preposition
auf and the common noun Standesamt (‘civil registry office’). In (300a), auf serves as a place
preposition, while it serves as a path preposition (goal) in (300b).
(300) a. Hans
Hans
war
was
auf
upon
dem
the.DAT
Standesamt.
civil registry office
b. Hans
Hans
ging
went
auf
upon
das
the.ACC
Standesamt.
civil registry office
Both the place preposition and the path preposition are at least two-way ambiguous. On
the first reading, the geometric reading that is available with geometric prepositions, Hans
literally was on/went onto the civil registry office, because he was a roofer, for instance.
On the other reading, the general locative reading that is available with pseudo-geometric
prepositions, Hans was at/went to the civil registry office, for instance, because he was a
groom. I refer to this ambiguity as the roofer/groom ambiguity. Note that the preposition
auf in (300) is best translated into English as ‘on, onto’ on the geometric usage, and as ‘at, to’
95The source prepositional combination von in (‘from in’) is semantically tantamount to aus (‘out of’). The
combination von in is not ungrammatical, but highly dispreferred, which is, I think, due to the existence of aus.
96The preposition über is highly ambiguous. It is not only a geometric route preposition, it can also be a
projective place (and goal) preposition meaning ‘above’ (and ‘to above’).
186 5. Spatial prepositions at the interfaces
on the pseudo-geometric usage. Note also that the geometric meaning of these prepositions
could also be referred to as the literal meaning of the prepositions.
The roofer/groom ambiguity is of course also influenced by the internal and external
context of the PP. Let us look at the internal context, i.e. the complement of the preposition, e.g.
auf. Several Ground DPs can be subject to regular polysemy, i.e. they can be conceptualized
in different ways.97 A DP like Standesamt (‘civil registry office’), for instance, can either be
conceptualized as an institution (abstract) or as a building (concrete). Here, the availability
of the geometric reading of the preposition auf seems to correlate with the building-reading
of the civil registry office. If we take a Ground DP that is not subject to regular polysemy in
that way, the geometric reading of the preposition is (almost) unavailable. Consider (301)
involving the noun Party (‘party’), which cannot be conceptualized as a concrete entity. Here,
auf typically has the meaning ‘at’ (place) or ‘to’ (goal).
(301) a. Hans
Hans
war
was
auf
at
der
the.DAT
Party.
party
b. Hans
Hans
ging
went
auf
to
die
the.ACC
Pary.
party
Nevertheless, the external context of the preposition also influences the reading of the
preposition. Let us look at the choice of the verb that can take a PP headed by auf as an
argument. In (300) the verbs have a rather unspecific or general meaning. In fact, this seems
to favor the availability of the general locative reading with pseudo-geometric prepositions.
If we choose a verb with a more specific manner component, e.g. klettern (‘climb’) in (302),
pseudo-geometric preposition with the general locative reading is pretty unlikely.
(302) Hans
Hans
kletterte
climbed
auf
up onto
das
the.ACC
Standesamt.
civil registry office
‘Hans climbed up onto the civil registry office.’
Due to the fact that many common nouns can be conceptualized in several distinct
ways, the roofer/groom ambiguity is indeed common, but often unnoticed. Many instances
can remain undisambiguated and thus blur the borderline between geometric and pseudo-
geometric prepositions. However, pseudo-geometric prepositions can often be identified
as such when they occur in contexts where geometric prepositions are blocked. Typical
contexts of this sort are provided by toponyms, i.e. names of topological entities (countries,
cities, islands, etc.), are – under normal conditions – always pseudo-geometric prepositions. I
refer to pseudo-geometric prepositions that occur with toponyms as toponymic prepositions.
Toponymic prepositions are paradigmatic instances of pseudo-geometric prepositions. This
thesis discusses toponymic prepositions as a case study of pseudo-geometric prepositions.
97Ora Matushansky (pc) pointed out that pseudo-geometric could be licensed in the context of weak definites
(Aguilar Guevara 2014). I leave this question for future work.
5.1. Classifying spatial prepositions 187
In German, geometric and pseudo-geometric prepositions behave differently in at least
two ways. First, geometric prepositions license a so-called echo extension, i.e. a postpositional
element involving the very same preposition, while pseudo-geometric prepositions do not
license echo extensions. Second, geometric prepositions are subject to free choice, i.e. as long
as semantic selection restrictions are obeyed, any preposition could be used depending on
the spatial relation the speaker wants to express, while pseudo-geometric prepositions are
not subject to free choice, i.e. they are fixed with respect to a DP.
Let us first look at the licensing ability of echo extensions. An echo extension is an optional
postpositional element consisting of a deictic element and a recurrence of the preposition.
Abraham (2010: 265) terms these optional postpositional elements echo extensions, because
they contain a recurrence of the preposition. Geometric prepositions typically allow an echo
extension (303).98
(303) a. Hans
Hans
stand
stood
an
on
der
the.DAT
Wand
wall
(dr-an).
there-on
‘Hans stood at the wall.’
b. Hans
Hans
saß
sat
auf
upon
dem
the.DAT
Tisch
table
(dr-auf).
there-upon
‘Hans sat upon the table.’
c. Hans
Hans
lag
lay
in
in
der
the.DAT
Kiste
box
(dr-in).
there-in
‘Hans lay in the box.’
d. Hans
Hans
kam
came
an
onto
die
the.ACC
Wand
wall
(her-an).
hither-on
‘Hans came to the wall.’
e. Hans
Hans
sprang
jumped
auf
up onto
den
the.ACC
Tisch
table
(hin-auf).
thither-upon
‘Hans jumped on the table.’
f. Hans
Hans
schlenderte
strolled
aus
out of
dem
the.DAT
Zimmer
room
(her-aus)
hither-out
‘Hans strolled out of the room.’
g. Hans
Hans
rannte
ran
in
into
das
the.ACC
Zimmer
room
(hin-ein)
thither-in
‘Hans ran into the room.’
In contrast to geometric prepositions, pseudo-geometric prepositions do not allow echo
extensions (304).
(304) a. Hans
Hans
wohnte
lived
an
on
der
the.DAT
Ostsee
Baltic Sea
(*dr-an).
there-on
‘Hans lived at the Baltic Sea.’
98Note that not all geometric prepositions allow echo extension. Topological place and path prepositions, as
well as route prepositions allow echo extension, while projective prepositions do not allow echo extensions.
188 5. Spatial prepositions at the interfaces
b. Hans
Hans
war
was
auf
upon
den
the.DAT
Kanaren
Canary Islands
(*dr-auf).
there-upon
‘Hans was in the Canary Islands.’
c. Hans
Hans
war
was
in
in
der
the.DAT
Mongolei
Mongolia
(*dr-in)
there-in
‘Hans was in Mongolia.’
d. Hans
Hans
wanderte
hiked
an
onto
den
the.ACC
Bodensee
Lake Constance
(*her-an)
hither-on
‘Hans hiked to Lake Constance.’
e. Hans
Hans
flog
flew
auf
up onto
die
the.ACC
Azoren
Azores
(*hin-auf)
thither-upon
‘Hans flew to the Azores.’
f. Hans
Hans
reiste
traveled
aus
out of
der
the.DAT
DDR
GDR
(*her-aus).
hither-out
‘Hans traveled out of the GDR.’
g. Hans
Hans
fuhr
drove
in
into
die
the.ACC
Schweiz
Switzerland
(*hin-ein).
thither-in
‘Hans drove to Switzerland.’
h. Hans
Hans
trampte
hitchhiked
nach
to
Berlin
Berlin
(*hin-nach).
thither-to
‘Hans hitchhiked to Berlin.’
With respect to echo extensions, non-geometric prepositions pattern with pseudo-geometric
prepositions. Here it only makes sense to look at the non-geometric place preposition bei (‘at’)
and the non-geometric path prepositions von (‘from’) and zu (‘to’), because the non-geometric
prepositions von ... weg (‘away from’) and auf ... zu (‘towards’) consist of a prepositional part
and a non-echo postpositional part anyway. Non-geometric prepositions do not allow an
echo extension (305).
(305) a. Hans
Hans
stand
stood
bei
at
der
the.DAT
Hütte
hut
(*da-bei).
there-at
‘Hans stood at the hut.’
b. Hans
Hans
fuhr
drove
zu
to
der
the.DAT
Hütte
hut
(*hin-zu).
thither-to
‘Hans drove to the hut.’
c. Hans
Hans
kam
came
von
from
der
the.DAT
Hütte
hut
(*her-von).
hither-from
‘Hans came from the hut.’
Note that the constructions bei ... dabei and zu ... hinzu do in fact exist. However, both
constructions do not have a spatial but rather a comitative interpretation. They thus fall
outside the scope of this thesis.
(306) a. Die
The
Rechnung
bill
war
was
bei
at
der
the
Lieferung
delivery
da-bei.
there-at
‘The delivery came with the bill included.’
5.1. Classifying spatial prepositions 189
b. Hans
Hans
schüttete
pours
Wasser
water
zu
to
der
the
Sauce
sauce
hin-zu.
thither-to
‘Hans added water to the sauce.’
Let us now look at the second difference between geometric prepositions on the one hand
and pseudo-geometric prepositions on the other. While geometric prepositions are subject to
free choice, pseudo-geometric prepositions are not subject to free choice. Here, free choice
refers to the choice of geometric configuration. Obviously, the choice of a genuine geometric
preposition depends on the geometric configuration that is to be expressed. As long as the
semantic selection restrictions are obeyed, any geometric prepositions can combine with any
kind of Ground. As an example of geometric prepositions, consider the topological place
prepositions in (307a) and the corresponding goal prepositions in (307b). Each preposition
in (307) contributes distinct spatial information. In particular, the choice of the preposition
depends on what kind of spatial relation the speaker intends to express (307).
(307) a. Hans
Hans
stand
stood
an/auf/in
on/upon/in
der
the.DAT
Hütte.
hut
‘Hans stood at/on/in the hut.’
b. Hans
Hans
sprang
jumped
an/auf/in
onto/up onto/into
die
the.ACC
Hütte.
hut
‘Hans jumped to/onto/into the hut.’
To a certain extent, this is similar to the free choice of the subject and the object in (308).
Depending on what situation the speaker wants to describe, they might equally have chosen
shark and fish as subject and object (308a), or the other way around (308b).
(308) a. The shark chased the fish.
b. The fish chased the shark.
(Harley and Noyer 2000: 7)
The picture is different with pseudo-geometric prepositions. Unlike geometric preposi-
tions, pseudo-geometric prepositions are restricted to the effect that the Ground determines
the preposition. In fact, it seems that the conceptualization of the Ground rather than the
intended spatial relation determines the preposition. That is, the choice of the preposition is
not free but depends on the Ground argument. In each of the examples in (309), only one
preposition is possible.
(309) a. Hans
Hans
war
was
in/*auf/*an
in/upon/on
dem
the.DAT
Iran.
Iran
‘Hans was in Iran.’
b. Hans
Hans
flog
flew
auf/*in/*an/*nach
up onto/into/onto/to
die
the.ACC
Balearen.
Balearic Islands
‘Hans flew to the Balearic Islands.’
190 5. Spatial prepositions at the interfaces
c. Hans
Hans
fuhr
drove
an/*in/*auf/*nach
onto/into/up onto/to
die
the.ACC
Nordsee.
North Sea
‘Hans drove to the North Sea coast.’
d. Hans
Hans
raste
raced
nach/*in/*auf/*an
to/into/up onto/onto
München.
Munich
‘Hans raced to Munich.’
By definition, non-geometric prepositions do not involve a geometric level of description
and thus non-geometric prepositions do not correspond to any of the various geometric
relations the way geometric prepositions do. As a consequence, the question concerning
free choice does not arise for non-geometric prepositions. Nevertheless, the choice of a
non-geometric preposition seems to be determined by the absence of any spatial Content
feature.
Table 4 summarizes how geometric, pseudo-geometric, and non-geometric prepositions
behave with respect to echo extensions and with respect to the question of free choice.
geometric pseudo-geometric non-geometric
prepositions prepositions prepositions
echo extensions yes no no
free choice yes no –
Table 4: Properties of non-geometric, geometric, and pseudo-geometric prepositions
Note that I attribute this behavior to the presence or absence of Content material in
Root position within the prepositional head. That is, while geometric prepositions involve
Content material in Root position, pseudo-geometric and non-geometric prepositions do
not. For a detailed discussion of the lexical derivations of geometric, pseudo-geometric, and
non-geometric prepositions, I refer the reader to Section 5.4. For a further discussion of echo
extensions, I refer the reader to Section 5.5, which addresses the functional prepositional
structure hosting echo extensions.
5.1.3 Prepositions and aspect
Following Jackendoff (1991), Verkuyl and Zwarts (1992), Piñón (1993), Zwarts (2005b), I
consider prepositional aspect as being correlated to the distinction between bounded and
unbounded reference familiar from the verbal and nominal domain (Bach 1986, Jackendoff
1991). Both place and path prepositions – or rather the phrases they ultimately project – can
serve as heads of arguments of verbs. But while place prepositions are like state descriptions
inasmuch as they are aspectually neutral, path prepositions can contribute to the aspectual
properties of a clausal predicate (Zwarts 2005b: 741). Take manner of motion verbs like walk,
run, or swim, which typically give rise to an atelic interpretation when they are used all by
themselves (310a). Let us add a path preposition – goal, for instance. While the addition of the
goal preposition to leads to a telic interpretation (310b), the addition of the goal preposition
towards preserves the atelic interpretation of the manner of motion verb (310c).
5.1. Classifying spatial prepositions 191
(310) a. John swam for/??in 30 minutes.
b. John swam to the island in/?for 30 minutes.
c. John swam towards the island for/??in 30 minutes.
As already mentioned, I assume that this is due to the fact that spatial paths denoted by
prepositions like to are conceptualized as bounded, i.e. as having boundaries in space, while
the spatial paths denoted by prepositions like towards are conceptualized as unbounded, i.e.
as having no boundaries in space.
Let us look at how the notion of boundedness of paths relates to the typology of spatial
prepositions in Figure 35 Of particular interest here are the three types of path prepositions:
source, goal, and route prepositions. Recall that source and goal prepositions are directed,
and that route prepositions are undirected. Distinguishing between bounded and unbounded
paths, Jackendoff (1991) accounts for unbounded directed paths (directions) and unbounded
undirected paths (routes) on the one hand, and for bounded directed paths on the other hand.
That is, he assumes that only unbounded paths can be undirected. Put differently, bounded
paths are always directed in his system. Consider the typology of (spatial) paths in Figure 36.
paths
bounded
source
(from)
goal
(to)
unbounded
directed
source
(away from)
goal
(toward)
undirected
routes
(via)
Figure 36: Typology of paths according to Jackendoff (1991)
Assuming that boundedness in the conceptualization of paths correlates to telicity in the
verbal domain, Piñón (1993) takes this typology as a starting point. Applying the well-known
aspectual tests involving compatibility with in/for-adverbials, Piñón confirms the general
division into bounded and unbounded paths of goal (and source) prepositions (311a)/(311b)
and that there are route prepositions that do not denote bounded paths (311c).
(311) a. Mary walked to the library {in ten minutes, #for ten minutes}.
b. John skipped towards the park {for ten minutes, #in ten minutes}.
c. The dog ran along the river {for ten minutes, #in ten minutes}.
(Piñón 1993: 298)
192 5. Spatial prepositions at the interfaces
However, Piñón observes that some route prepositions show a variable behavior when tested
for their aspectual class. In particular, the route prepositions in (312) give rise to both a telic
and an atelic interpretation.
(312) a. The insect crawled through the tube {for two hours, in two hours}.
b. The procession walked by the church {for 45 minutes, in 45 minutes}.
c. Mary limped across the bridge {for ten minutes, in ten minutes}.
(Piñón 1993: 298)
Piñón (1993) concludes that paths denoted by route prepositions can be conceptualized as
unbounded and as bounded paths. Piñón thus proposes the enriched, symmetrical typology
of paths in Figure 37. In particular, both directed path prepositions (goal and source) and
undirected path prepositions (route) can denote bounded and unbounded paths.
paths
bounded
directed
source
(from)
goal
(to)
undirected
route
(through)
unbounded
directed
source
(away from)
goal
(toward)
undirected
route
(through)
Figure 37: Symmetrical typology of paths according to Piñón (1993)
Kracht’s (2002, 2008) system comprises the same six types of paths: bounded source
paths are coinitial paths, bounded goal paths are cofinal paths, bounded route paths are
transitory paths, unbounded source paths are recessive paths, unbounded goal paths are
approximative paths, and unbounded route paths are static paths. These six classes of
paths are given in Table 5, together with prototypical English examples. Note that I refer to
Pantcheva (2011) for further discussion concerning classifications of paths.
directed undirected
source goal (route)
bounded coinitial cofinal transitory
from to past
unbounded recessive approximative static
away from towards along
Table 5: Kracht’s (2002, 2008) classification of paths
5.1. Classifying spatial prepositions 193
Let us now fill this table with German path prepositions. In German, recessive and
approximative paths are typically not expressed by simplex spatial prepositions. For instance,
a common way of expressing approximative paths is by using the prepositional construction
in Richtung (von) (lit.: in direction ‘towards, in the direction of’) involving a nominal element.
Thus, recessive and approximative path descriptions fall outside the scope of this thesis.
Nevertheless, I briefly touch upon the construction auf ... zu (‘towards’) in Section 5.5.3.
directed undirected
source goal (route)
bounded coinitial cofinal transitory
aus (‘out of’),
(von an ‘from on’),
(von auf ‘from upon’),
(von in ‘from in’),
von (‘from’)
in (‘into’),
an (‘onto’),
auf (‘up onto’),
nach (‘to’),
zu (‘to’)
durch (‘through’),
über (‘across, over’),
um (‘around’)
unbounded recessive approximative static
von ... weg
(‘away from’)
auf ... zu (‘towards’) durch (‘through’),
über (‘across, over’),
um (‘around’)
Table 6: Bounded and unbounded German path prepositions
Before closing this section, I should like to mention the spatial usage of the preposition
bis (‘till, until, up’). Surprisingly, bis does not seem to be a proper spatial preposition on par
with other goal prepositions. Structurally, it seems to ‘depend’ on other goal prepositions.
In particular, I assume that it marks delimited paths in the sense of Pantcheva (2011). The
preposition bis can occur in two contexts. On the one hand, bis can be used optionally in
combination with every German cofinal preposition resulting in a so-called terminative path
description (Pantcheva 2011: 59). See (313a) for an example with the non-geometric goal
preposition zu (‘to’) and (313b) for an example with the geometric goal preposition under
(‘under’).
(313) a. Hans
Hans
fuhr
drove
(bis)
up
zu
to
der
the.DAT
alten
old
Messestadt.
trade fair city
‘Hans drove until the old trade fair city.’
b. Hans
Hans
fuhr
drove
(bis)
up
unter
under
das
the.ACC
Dach.
roof
‘Hans drove until he was under the roof.’
(adapted from Eisenberg et al. 1998: 393)
On the other hand, bis can occur with determinerless toponyms as in (314).
(314) Hans
Hans
fuhr
drove
bis
until
Frankfurt
Frankfurt
‘Hans drove until Frankfurt.’
194 5. Spatial prepositions at the interfaces
In this thesis, I assume that the usage of bis with toponyms in (314) is in fact parallel to its
usages in (313). Consider the fact that bis can optionally co-occur with toponymic nach as in
(315a) or with toponymic in as in (315b). Indicating delimited paths, bis in (315) behaves like
in (313).
(315) a. Hans
Hans
fuhr
drove
(bis)
up
nach
to
Frankfurt
Frankfurt
‘Hans drove until Frankfurt.’
b. Hans
Hans
fuhr
drove
(bis)
up
in
in
die
the.ACC
Schweiz.
Switzerland
‘Hans drove until Switzerland.’
Nevertheless, toponymic nach is special when used with bis because it can be omitted as in
(316a), giving rise to (314). Interestingly, only the toponymic preposition nach can be omitted.
Other toponymic goal prepositions like in (‘to, into’) in (316b) cannot be omitted when used
with bis.
(316) a. Hans
Hans
fuhr
drove
bis
up
(nach)
to
Frankfurt.
Frankfurt
‘Hans drove until Frankfurt.’
b. Hans
Hans
fuhr
drove
bis
up
*(in)
in
die
the.ACC
Schweiz.
Switzerland
‘Hans drove until Switzerland.’
Note that this is all I have to say about bis in this thesis.
5.1.4 Categories and syntacticosemantic features in prepositions
This section briefly discusses how the classes of prepositions discussed in the previous
sections map to prepositional structure. Let us first determine the general structure of fully-
fledged prepositions. Generally, I assume that every preposition involves the lexical category
P, which takes a DP-complement and which can generate a Root position; cf. Section 2.3.
Furthermore, I assume that some prepositions can additionally involve the light category Q
above P. In line with Den Dikken (2010), a.o., I assume that every fully-fledged PP involves
the functional categories Asp (for aspect), Dx (for deixis), and C (for complementizer) above Q;
or directly above P, if Q is absent. Ignoring the ultimate surface linearization (cf. Section 3.2),
we can determine the general structure of fully-fledged prepositions as given in (317).
5.1. Classifying spatial prepositions 195
(317) CP
DxP
AspP
(QP)
PP
DPP○
P○∅
(Q○)
Asp○
Dx○
C○
The categories of the structure in (317) can host various syntacticosemantic (synsem) fea-
tures. The category P can host one of the synsem features [LOC] (for locative), [AT], or [±NINF]
(for non-initial, non-final). The feature [LOC] characterizes (pseudo)-geometric prepositions,
while the feature [AT] characterizes non-geometric prepositions. The feature [±NINF] (for
non-initial, non-final) characterizes undirected path prepositions, i.e. route prepositions.
Place prepositions involve the category P hosting either [LOC] or [AT]; place prepositions
may not involve the category Q. The category Q above P derives directed path prepositions
from place prepositions.99 Q can host the synsem feature [±TO]. In both (pseudo)-geometric
and non-geometric contexts, Q[+TO] derives goal prepositions and Q[−TO] derives source
prepositions. Table 7 summarizes these considerations the according to the schema of Table 3.
(pseudo)-geometric non-geometric
place P[LOC] P[AT]
path dir. source P[LOC] < Q[−TO] P[AT] < Q[−TO]
goal P[LOC] < Q[+TO] P[AT] < Q[+TO]
undir. route P[±NINF]
Table 7: Categories and features of (pseudo)-geometric and non-geometric prepositions
Generally, path prepositions can be bounded or unbounded (cf. Section 5.1.3). I assume
that bounded and unbounded aspect of directed path prepositions (source and goal preposi-
tions) relate to the synsem feature [±UNBD] (for unbounded) hosted by the functional category
99The idea that path-related features are structurally higher than place-related features is a common assump-
tion in the literature (Jackendoff 1983, Koopman 2000, 2010, Folli 2008, Gehrke 2008, Mateu 2008, Svenonius
2008, 2010, Noonan 2010, Den Dikken 2010, Pantcheva 2011, a.o.).
196 5. Spatial prepositions at the interfaces
Asp above Q; [+UNBD] leads to unbounded source and goal prepositions, and [−UNBD] leads
to bounded source and goal prepositions. In contrast, bounded and unbounded aspect
of undirected path prepositions (route prepositions, cf. Section 5.4.3) relate to the value of
the synsem feature [±NINF] hosted by P; [−NINF] leads to bounded route prepositions and[+NINF] leads to unbounded route prepositions. Note that directed (pseudo)-geometric path
prepositions denote transitional paths and are thus necessarily bounded; cf. Sections 5.4.2.1
and 5.4.2.2. That is, directed (pseudo)-geometric path prepositions, which are characterized by
Q[±TO] above P[LOC], are uninterpretable with Asp[+UNBD]. Directed non-geometric path
prepositions denote non-transitional paths and hence they can be bounded or unbounded; cf.
Section 5.4.2.3. That is, directed non-geometric path prepositions, which are characterized
by Q[±TO] (above P[AT]), are interpretable either with Asp[−UNBD] or with Asp[+UNBD].
Table 8 summarizes these considerations according to the schema of Table 6.
directed undirected
source goal (route)
bounded Q[−TO] < Asp[−UNBD] Q[+TO] < Asp[−UNBD] P[−NINF]
unbounded Q[−TO] < Asp[+UNBD] Q[+TO] < Asp[+UNBD] P[+NINF]
Table 8: Aspectually-relevant features in path prepositions
Furthermore, I propose that the difference between geometric prepositions and pseudo-
geometric prepositions relates to the filling of the prepositional Root position. I particular, I
assume that geometric prepositions contain an abstract Content feature in their Root position,
while pseudo-geometric prepositions (and also non-geometric prepositions) do not contain
an abstract Content feature in their Root position. Section 5.3 addresses the abstract Content
features that are relevant for the topological prepositions this thesis focuses on.
The functional category Dx dominates Asp and can host the synsem features [+PROX]
for proximal deixis or [−PROX] for non-proximal (distal) deixis. The functional category
C dominates Dx and can host the synsem features [+MOTION] for path prepositions or[−MOTION] for place prepositions.
5.2 On the cartographic decomposition of prepositions
Even though I do not pursue a cartographic analysis of German prepositions in this thesis,
it is worth to briefly present some work on spatial prepositions that is embedded in the
cartographic enterprise. Generally, Cartography aims at exploding syntactic structures in
order to obtain articulated and fine-grained hierarchical structures of features (Cinque 1999,
Cinque and Rizzi 2008, Shlonsky 2010, and the contributions in Cinque 2002, Rizzi 2004,
Belletti 2004, Cinque 2006, Benincà and Munaro 2010, Cinque and Rizzi 2010). Cartographic
approaches typically necessitate the assumption that multiple syntactic terminals can be
realized jointly by one indecomposable morphophonological exponent. Relating to this,
Nanosyntax assumes phrasal spell-out; cf. Starke (2009). A cartographic decomposition in
5.2. On the cartographic decomposition of prepositions 197
Distributed Morphology, however, would require spanning; cf. Svenonius (2016), Alexiadou
(2016).
The domain of (spatial) prepositions is often the subject of cartographic research (see
in particular the contributions in Asbury et al. 2008, Cinque and Rizzi 2010). Based on
conceptual considerations by Jackendoff (1983), many scholars assume that features related to
directional path semantics (PATH), if present, are in general structurally superior to features
related to locative place semantics (PLACE) (e.g. Jackendoff 1983, Koopman 2000, 2010,
Folli 2008, Gehrke 2008, Mateu 2008, Svenonius 2008, 2010, Noonan 2010, Den Dikken 2010,
Pantcheva 2011, a.o.). Thus, the basic cartographic decomposition of spatial prepositions in
(318) is often assumed.
(318) Basic cartographic decomposition of spatial prepositions:
PATH > PLACE
Focusing on complex spatial prepositions of the type in front of, as in (319), Svenonius
(2006, 2010) argues for a cartographic decomposition of the PLACE component.
(319) There was a kangaroo in front of the car.
Svenonius observes that the determinerless nominal element front in (319) cannot be analyzed
as a straightforward nominal complement of the preposition in, like the one in (320), involving
a determiner. Consider the more or less transparent interpretations of (320). While (320a)
is interpreted to the effect that a kangaroo was in one of the front seats of the car, (320b) is
interpreted to the effect that a kangaroo is in contact with the surface of the front part of the
car. However, (319) has a different interpretation, namely that the kangaroo is located in the
space projected forward from the car.
(320) a. There was a kangaroo in the front of the car.
b. There was a kangaroo on the front of the car.
Interestingly, while the core preposition in can be replaced in (320a), as done in (320b), in
cannot be replaced in (319); (321) is ungrammatical.
(321) *There was a kangaroo on front of the car.
Further, the usage of front with a determiner in (322a) allows pluralization, while the deter-
minerless usage in (322b) does not.
(322) a. There were kangaroos in the fronts of the cars.
b. *There were kangaroos in fronts of the cars.
198 5. Spatial prepositions at the interfaces
Moreover, while adjectival modification of the nominal front is possible in the usage with
a determiner in (323a), adjectival modification is impossible in the determinerless usage in
(323b).
(323) a. There was a kangaroo in the smashed-up front of the car.
b. *There was a kangaroo in smashed-up front of the car.
Considering these data, Svenonius concludes that the preposition in does not simply embed a
DP, but that the nominal element must realize some different syntactic position. Proposing a
cartographic decomposition of prepositions, Svenonius (2006) allocates this syntactic position
within the prepositional domain. In particular, Svenonius argues that the feature [AXPART]
within prepositions can host nominal elements such as front. For PPs such as in front of the
house, he (2010: 131) offers the analysis in (324), where the core preposition in realizes a feature
termed [LOC], the nominal element the feature [AXPART], and of a further feature termed[K].
(324) [ LOC=in [ AXPART=front [ K=of DP=the house ]]]
(adapted from Svenonius 2010: 131)
Considering further features – which I do not discuss here – Svenonius (2010) ultimately
proposes the cartographic decomposition of PLACE as given in (325).
(325) Svenonius’ cartographic decomposition of PLACE:
DEG > DEIX > LOC > AXPART > K
(Svenonius 2010: 133, 144)
Recently, Svenonius (2017) has argued that a full (cartographic) spine of features, as given
in (325), should not be assumed in the case of topological prepositions; simply because
there is, cross-linguistically, no syntacticosemantic or morphosyntactic evidence for this. For
instance, he assumes that topological prepositions, such as English in, on, and at, do only
project [LOC] above [K] – ignoring Svenonius’ (2003) little p at this point. I take the view
that Svenonius’ (2010) cartographic feature [K] roughly corresponds to the lexical category
feature P in the approach outlined in this thesis. Similarly, Svenonius’ cartographic feature[LOC] roughly corresponds to the synsem features [LOC] and [AT] that I assume in this thesis
for (pseudo)-geometric and non-geometric prepositions. Instead of a hierarchical structuring
of the category feature P and the synsem features [LOC] and [AT], I assume that the former
can host one of the latter.
Pantcheva (2011) cartographically decomposes PATH. Pantcheva argues for the carto-
graphic decomposition of PATH, as given in (326).
5.2. On the cartographic decomposition of prepositions 199
(326) Pantcheva’s cartographic decomposition of PATH:
ROUTE > SOURCE > GOAL
(Pantcheva 2011: 63)
Adopting Zwarts’ (2008) semantics of paths,100 Pantcheva argues that directional prepositions
are minimally goal prepositions (e.g. into), which contain the feature [GOAL]. This feature is
interpreted as a transitional predicate to the effect that there is a path that ends at a certain
location (positive phase of the path), but, crucially, does not start at this location (negative
phase of the path) (327a). In the case of source prepositions (e.g. out of ), the feature [GOAL]
is dominated by the feature [SOURCE] interpreted as a reversal operator. It operates on
goal paths to the effect that the path starts at a certain location but does not end at this
location. That is, it turns around the positive and the negative phase of a path (327b). In the
case of route prepositions (e.g. through), the feature [SOURCE] is dominated by the feature[ROUTE] that semantically appends a positive phase in front of a source path. That is, it
yields bi-transitional paths that go into a certain location and out of that location, and thus
do not start and end at that location, see (327c).
(327) a. Goal path− − − − − + + + + +
0 1
(Zwarts 2008: 84, Pantcheva 2011: 68)
b. Source path+ + + + + − − − − −
0 1
(Zwarts 2008: 84, Pantcheva 2011: 71)
c. Route path− − − − + + + + − − − −
0 1
(Zwarts 2008: 84, Pantcheva 2011: 72)
In this thesis, I refrain from a cartographic analysis for path prepositions, and also for
place prepositions. Assuming a compositional semantics along the syntactic structure, it
follows from Pantcheva’s (2011) cartographic decomposition of route prepositions that their
semantics contain the semantics of goal and source prepositions. However, in Section 5.4.3,
I will argue that this appears not to be the case, at least in German. Thus, I do not commit
to Pantcheva’s analysis that route prepositions structurally derive from goal and source
prepositions.
100Note that in Zwarts’ approach paths are functions from the real unit interval [0, 1] to positions in some
model of space (Zwarts 2005b: 748). Thus, paths always start at 0 and end at 1.
200 5. Spatial prepositions at the interfaces
5.3 Abstract Content features
This thesis focuses on spatial prepositions that express topological relations. In order to
account for the topological relations described by the geometric prepositions in (‘in’), aus
(‘out of’), durch (‘through’), an (‘on’), um (‘around’), auf (‘upon’), and über (‘over, across’), I
assume non-generative, abstract Content features that relate to general topological concepts.
The topological concepts that figure in this respect are (i) interiority, (ii) contiguity, and (iii)
verticality. The corresponding abstract Content features are [ℵ] relating to interiority, [ℶ]
relating to contiguity, and [ℷ] relating to verticality.101
At this point, we should look at cross-linguistic differences with respect to the choice of
(geometric) preposition when describing topological relations. Consider the situations (a) to
(f) in Table 9 below. Almost all languages taken into account have prepositions with which
these situations can be described; only Japanese does not have prepositions for describing the
situations in (b)–(e). However, as for the choice of preposition, the languages given in Table 9
show great variation. Let us briefly look at English, Dutch, German, and Spanish. While
the situation in (f) can be described by using the preposition in and similarly functioning
words in most other languages, (a)–(e) can be described by using varying prepositions in
different languages. For describing (a)–(e), English has only the preposition on. For the same
situations, Dutch and German have op/auf and aan/an, respectively, although with different
distributions. Spanish – in contrast to English, Dutch, and German – does not have special
prepositions for the situations depicted in (a)–(e). Instead, Spanish uses the same preposition
as it does for (f). I take this cross-linguistic variation as indication of a language-specific
treatment of the underlying features, which are arguably [ℵ], [ℶ], and [ℷ]. Therefore, these
features should not reside in the Lexicon proper, which is fed by UG; instead, I propose that
these abstract features should reside in the Content.
Generally, I assume that Content features can enter structures at Root positions. In
particular, I assume that the abstract Content features [ℵ] (relating to interiority), [ℶ] (relating
to contiguity), and [ℷ] (relating to verticality) can enter the prepositional structure at the
Root position of P. Moreover, I assume that an abstract Content feature is integrated into the
feature bundle of P, when inserted into the Root position of P. The basic P-structure before
and after insertion of an abstract Content feature (here: [ℵ]) is illustrated in (328a) and (328b),
respectively.
101In this thesis, I represent the abstract topological Content features by means of the first three letters of the
Semitic abjads: ℵ (aleph), ℶ (beth), and ℷ (gimel).
5.3. Abstract Content features 201
(a) (b) (c) (d) (e) (f)
cup bandaid picture handle apple apple
on table on leg on wall on door on twig in bowl
English on in
Japanese ue ∅ naka
Dutch op aan in
Berber x
di
Spanish en
German auf an in
Table 9: Cross-linguistic differences in expressing topological relations
(Bowerman and Choi 2001: 485)
(328) a. P-structure before insertion of Content feature:
PP
DPP○[uD]
P○[uD]∅
b. P-structure after insertion of Content feature:
PP
DPP○[uD,ℵ]
P○[uD]√[ℵ]
The PF- and LF-interface rules apply to the higher P○-node. By assumption, insertion of
Content features takes place at Spell-Out. At this level, the feature [uD] that licenses the
complement DP of the preposition is checked and thus it deletes. The Full Interpretation
constraint states that “the structure to which the [...] interface rules apply contains no
uninterpretable features” (Adger 2003: 85; cf. (56) on page 38). According to this constraint,
the PF- and LF-interface rules may only target the structurally higher P○ node, i.e. the one
that potentially contains a Content feature.
202 5. Spatial prepositions at the interfaces
Section 5.1.4 proposes three distinct P-contexts with regard to synsem features: P[LOC] is
characteristic for (pseudo)-geometric prepositions (place, goal and source), P[AT] is character-
istic for non-geometric prepositions (place, goal and source), and P[±NINF] is characteristic
for route prepositions. I propose that the abstract Content features can, in principle, enter
P-structures containing all of these three synsem features. However, in Section 5.4.1.3, I argue
that the interpretation of P[AT] is incompatible with one of the abstract Content features
presented above. That is, abstract Content features can enter P-structures that contain either
P[LOC] or P[±NINF]. The former can additionally co-occur with the light preposition Q,
which can host the synsem feature [+TO] for a goal interpretation, or [−TO] for a source inter-
pretation. In sum, this yields four distinct contexts into which the abstract Content features[ℵ], [ℶ], and [ℷ] can be inserted: (i) place prepositions, (ii) goal path prepositions, (iii) source
path prepositions, and (iv) route prepositions.102 I propose that the abstract Content features
relate to these four structural contexts in the way shown in Table 10. Note that the respective
structures yield geometric prepositions by means of insertion of Content features.103
place goal path source path route path
prepositions prepositions prepositions prepositions
PP
DPP○
P○[LOC]∅
QP
PP
DPP○
P○[LOC]∅
Q○[+TO]
QP
PP
DPP○
P○[LOC]∅
Q○[−TO]
PP
DPP○
P○[±NINF]∅
[ℵ] in (‘in’) in (‘into’) aus (‘out of’),
(von in ‘from in’)
durch (‘through’)
[ℶ] an (‘on’) an (‘onto’) (von an ‘from on’) um (‘around’)[ℷ] auf (‘upon’) auf (‘up onto’) (von auf ‘from upon’) über (‘over, across’)
Table 10: Abstract Content features in P-structures
Generally, there are two major prepositional contexts into which the abstract Content
features can be inserted: (i) P[LOC] for place, goal and source prepositions; and (ii) P[±NINF]
for route prepositions.104 The next sections describe how the abstract Content features[ℵ] relating to interiority, [ℶ] relating to contiguity, and [ℷ] relating to verticality manifest
themselves semantically in these two prepositional contexts.
102Actually, there would have been five different contexts, if one would have kept P[−NINF] and P[+NINF]
apart. However, the ultimate difference between these two structures (i.e. bounded vs. unbounded route
prepositions) is not crucial here.
103With regard to Roots, one could say that the Content feature [ℵ] is interpreted as the Root √durch when it
is inserted in the Root position of P[±NINF], as the Root √aus when it is inserted in the Root position of P[LOC]
dominated by Q[−TO], and as √in when it is inserted in the Root position of any other P[LOC]; cf. Section 2.3.
104At this point it should be mentioned that each of the predicates defined for route prepositions consists of
two conditions: a boundary condition (i.e. intlis or extlis) and a configurational condition (i.e. spear-like, L-shaped,
or plumb-square); cf. Section 4.3.6.
5.3. Abstract Content features 203
As for route prepositions, I will propose the three LF-predicates durch-bar, um-bar, and
ueber-bar. The reason for labeling these predicates with the extension ‘-bar’ is that they
contribute some intermediate geometric predication. They do not function as geometric
predicates of route paths, but of ‘internal’ parts of route paths, viz. NINF-path (non-initial,
non-final paths).
5.3.1 Interiority
Both the place and goal preposition in (‘in, into’) and the route preposition durch (‘through’)
conceptually relate to interiority. I assume that these two prepositions share a common
feature that refers to the concept of interiority, viz. the abstract Content feature [ℵ]. In
the two prepositional contexts, the concept of interiority manifests itself in different ways.
In the case of the place and goal preposition in, the concept of interiority manifests itself
as the region that is inside the Ground, while, in the case of the route preposition durch,
the concept of interiority manifests itself as a spatial path that lies spear-like inside the
Ground. For the former configuration, I assume the two-place LF-predicate in(r, x) holding
between a region r and a material object x, and for the latter configuration, I assume the
two-place LF-predicate durch-bar(v, x) holding between a spatial path v and a material object
x. Structurally, the place and goal preposition in is characterized by P[LOC] and the route
preposition durch is characterized by P[±NINF]. Hence, I assume that [ℵ] is interpreted as
specifying an in-region of a material object when inserted into the Root position of P[LOC],
while it is interpreted as specifying a durch-bar-path of a material object when inserted into the
Root position of P[±NINF]. The following subsections define the model-theoretic denotations
of the LF-predicates in and durch-bar, which both relate to interiority.
in-regions
I propose that the two-place predicate in(r, x) holding between a region r and a material
object x is the core semantic interpretation of the geometric preposition in (‘in, into’). The
predicate is a prime at LF. In (329), I define that an in-region r of a material object x is included
in (i) the three-dimensional inside region of x if x is conceptualized as three-dimensional, or
(ii) the two-dimensional inner surface of x if x is conceptualized as two-dimensional. In order
to distinguish between three- and two-dimensional material objects, we can exploit the fact
that material objects that are conceptualized as three-dimensional have a ball-like surface,
while material objects that are conceptualized as two-dimensional have a disc-like surface.
For a discussion of the respective geometric predicates, I refer the reader to Section 4.3.4.
(329) ∀r, x[in(r, x)↔ reg(r)∧ obj(x)∧∃z[reg(z)∧ r ⊆ z∧∀y[ball-like(y)∧ surf(y, x)→ inside(z, y)]∧∀y[disc-like(y)∧ surf(y, x)→ insurf(z, y)]]]
“r is an in-region of a material object x iff r is included in a region z, and for all y if y
204 5. Spatial prepositions at the interfaces
is a ball-like surface of x then z is the inside region of y, and for all y if y is a disc-like
surface of x then z is the inner surface of y”
durch-bar-paths
I propose that the two-place predicate durch-bar(v, x) holding between a spatial path v and a
material object x is the core semantic interpretation of the geometric route preposition durch
(‘through’). The predicate is a prime at LF. In (330), I define a durch-bar-path v of a material
object x as an internal and spear-like line segment of the material object x. Both the respective
predicates intlis (boundary condition) and spear-like (configurational condition) are defined in
Section 4.3.6.
(330) durch-bar-paths:∀v, x[durch-bar(v, x)↔ intlis(v, x)∧ spear-like(v, x)]
“v is a durch-bar-path of material object x iff v is an internal and spear-like line
segment of x”
5.3.2 Contiguity
Both the place and goal preposition an (‘on, onto’) and route preposition um (‘around’)
conceptually relate to contiguity. I assume that these two prepositions share a common
feature that refers to the concept of contiguity, viz. the abstract Content feature [ℶ]. In the
two prepositional contexts, the concept of contiguity manifests itself in different ways. In
the case of the place and goal preposition an, the concept of contiguity manifests itself as
the region of the Ground where a Figure has spatial contact with the Ground, while, in
the case of the route preposition um, the concept of contiguity manifests itself as a spatial
path that is external and tangential to the Ground and that changes its direction by 90○ in
order to keep tangentiality. For the configuration expressed by an, I assume the two-place LF-
predicate an(r, x) holding between a region r and a material object x, and for the configuration
expressed by um, I assume the two-place LF-predicate um-bar(v, x) holding between a spatial
path v and a material object x. Structurally, the place and goal preposition an is characterized
by P[LOC] and the route preposition um is characterized by P[±NINF]. Hence, I assume
that [ℶ] is interpreted as specifying an an-region of a material object when inserted into the
Root position of P[LOC], while it is interpreted as specifying a um-bar-path of a material
object when inserted into the Root position of P[±NINF]. The following subsections define
the model-theoretic denotations of the LF-predicates an and um-bar, which both relate to
contiguity.
an-regions
I propose that the two-place predicate an(r, x) holding between a region r and a material
object x is the basic semantic interpretation of the geometric preposition an (‘on, onto’). The
5.3. Abstract Content features 205
predicate is a prime at LF. In (331), I define an an-region r of a material object x as a region
that is in spatial contact with the region y, which is the region that x occupies. Section 4.3.5
discusses the notion of spatial contact.
(331) an-regions:∀r, x[an(r, x)↔ reg(r)∧ obj(x)∧∃!y[reg(y)∧ occ(x, y)∧ r ⊃⊂ y]]
“r is an an-region of a material object x iff y is the region that x occupies,
and r is in spatial contact with y”
um-bar-paths
I propose that the two-place predicate um-bar(v, x) holding between a spatial path v and a ma-
terial object x is the basic semantic interpretation of the geometric preposition um (‘around’).
The predicate is a prime at LF. In (332), I define a um-bar-path v of a material object x as an
external line segment of x that is L-shaped. This configuration is illustrated in Figure 38. Both
the respective predicates extlis (boundary condition) and L-shaped (configurational condition)
are defined in Section 4.3.6.
(332) um-bar-paths:∀v, x[um-bar(v, x)↔ extlis(v, x)∧ L-shaped(v)]
“v is an um-bar-path of material object x iff v is an external line segment of x that is
L-shaped”
x v
z′
w′
p′ z′′w′′ p′′
Figure 38: um-bar(v, x)
Generally, I take the view that the German morpheme um fundamentally expresses some
change of direction that relates to an L-shaped form.105 This hypothesis is corroborated by
various verbal constructions that um can enter. In addition to its usage as a route preposition,
105For other proposals for the German route preposition um (‘around’), I refer the reader to Wunderlich (1993),
who proposes that um can be semantically represented in terms of the geometric condition of enclosure.
206 5. Spatial prepositions at the interfaces
um can also serve as a verbal prefix (inseparable verbal construction) as illustrated in (333a)
or as a verbal particle (separable verbal construction) as illustrated in (333b).
(333) a. Hans
Hans
um-fuhr
around.PREFIX-drove
den
the.ACC
Baum.
tree
‘Hans drove around the tree.’
b. Hans
Hans
fuhr
drove
den
the.ACC
Baum
tree
um.
around.PARTICLE
‘Hans knocked down the tree.’
When used as a verbal prefix in combination with the verb fahren (‘drive’) as illustrated in
(333a), the semantic interpretation of um is similar to the interpretation of um as a route
preposition. The interpretation of the prefix verb um-fahren in (333a) is such that Hans takes
a detour around the tree. However, when used as a verbal particle in combination with
the same base verb as illustrated in (333b), the semantic interpretation of um is such that it
expresses a fundamental positional change of the entity denoted by internal argument, i.e.
the tree. In particular, the interpretation of the particle verb um-fahren in (333b) is such that
the tree is understood as changing its position from a vertical (upright) to a horizontal (lying)
position. Obviously, this positional change can also be described by means of an L-shaped
configuration.
Summarizing, we can say that an L-shaped configuration generalizes over the various
interpretations of um described above. But how does an L-shaped configuration relate to
the abstract Content feature [ℶ], which refers to contiguity in the first place? All usages
of um discussed above relate in some way or another to spatial paths, which I consider
to be instances of line segments. I assume that these spatial paths are to be contiguous to
a contextually implicit or explicit reference point. Two things are important to note here.
First, a line segment is a one-dimensional spatial entity, while a point is a zero-dimensional
spatial entity. Second, a line segment is relatively contiguous to a point if one can drop a
perpendicular from every point of the line segment onto that point. All in all, this means that
the line segment must change its direction in order to be contiguous to the reference point in
its entire length. Two line segments that are orthogonally chained together in an L-shaped
way such that the two legs enfold the reference point arguably constitute such a minimal
model of concentric change of direction. Such an L-shaped line segment that is concentric to
a reference point is sketched in Figure 39.
In the case of the route preposition and the verbal prefix um, the shape of the denoted
spatial paths takes the form of an L. The reference point is explicit. It is given by the Ground
argument in the case of the route preposition um or by the internal argument of the verb in
the case of the verbal prefix um. In contrast, in the case of the verbal particle um, it is the
major orientation of the entity denoted by the internal argument of the verb that changes
from being aligned with one leg of the L to being aligned with the other leg of the L. That is,
the entity tilts by 90 degrees. Here, the reference point is implicit.
5.3. Abstract Content features 207
Figure 39: Generalized model of concentric change of direction
At this point, a brief note on the English route preposition (a)round, which is the closest
translation of the German route preposition um, is in order. English (a)round might commit to
another minimal model than German um. Unlike German um, English (a)round apparently
incorporates the morpheme ‘round’ that obviously refers to the geometric configuration
of circularity. See also footnote 91 on page 170. For an semantic representation of English
(a)round in terms of a vector space model, I refer the reader to Zwarts (2003a, 2004).
5.3.3 Verticality
Both the place and goal preposition auf (‘upon, up onto’) and route preposition über (‘over,
across’) conceptually relate to verticality. I assume that these two prepositions share a
common feature that refers to the concept of verticality, viz. the abstract Content feature[ℷ]. In the two prepositional contexts, the concept of verticality manifests itself in different
ways. In the case of the place and goal preposition auf, the concept of verticality manifests
itself as a region adjacent to the Ground in which the Ground can support a Figure from
below. The ‘support’ component in the meaning of auf entails that there also must be
contact between the Ground and the Figure, or more precisely, between the region that is
occupied by the Ground and the region that is occupied by the Figure. In the case of the
route preposition über, the concept of verticality manifests itself as a spatial path that is above
the Ground in a horizontal orientation. For the configuration expressed by auf, I assume
the two-place LF-predicate auf(r, x) holding between a region r and a material object x, and
for the configuration expressed by über, I assume the two-place LF-predicate ueber-bar(v, x)
holding between a spatial path v and a material object x. Structurally, the place and goal
preposition auf is characterized by P[LOC] and the route preposition über is characterized by
P[±NINF]. Hence, I assume that [ℷ] is interpreted as specifying an auf-region of a material
object when inserted into the Root position of P[LOC], while it is interpreted as specifying
an ueber-bar-path of a material object when inserted into the Root position of P[±NINF]. The
following two subsections define the model-theoretic denotations of the LF-predicates auf
and ueber-bar, which both relate to verticality.
208 5. Spatial prepositions at the interfaces
auf-regions
I propose that the two-place predicate auf(r, x) holding between a region r and a material
object x is the basic semantic interpretation of the geometric preposition auf (‘upon, up onto’).
The predicate is a prime at LF. Generally, the definition of the predicate auf parallels the
predicate an (cf. Section 5.3.2). In addition to the predicate an, the predicate auf expresses
the force-dynamic effect that the complement of the preposition auf provides support from
below. This is achieved by integrating the force-dynamic predicate sfb(x, z), i.e. “x supports y
from below”. The material object x, which serves as the Ground in spatial terms, serves as an
Antagonist in force-dynamic terms. It is identified with the complement of the preposition.
The opponent of the Antagonist, i.e. the Agonist, which serves as the Figure in spatial terms,
is identified with the external argument of the PP. The Antagonist x provides support from
below for the Agonist z, a material object that makes contact with x in such a way that x can
support it from below. The Agonist is conceptualized as endowed with a downward force
(imposed on it by gravity), which would make it fall down in the absence of the support by
the Antagonist x. The Antagonist x and the Agonist z force-dynamically interact so that the
respective forces level each other out, i.e. the resultant is toward rest. The force-dynamic
predicate sfb is discussed in more detail in Section 4.7; see in particular (298) on page 177.
Note that spatial contact is discussed in Section 4.3.5. In (334), I define an auf-region r of a
material object x.
(334) auf-regions:∀r, x[auf(r, x)↔ reg(r)∧ obj(x)∧∃!y[reg(y)∧ occ(x, y)∧ r ⊃⊂ y∧∃z[obj(z)∧ occ(z, r)∧ sfb(x, z)]]]
“r is an auf-region of a material object x iff y is the region that x occupies,
and r is in spatial contact with y, and r is the region that is occupied by a material
object z that is supported by z from below”
ueber-bar-paths
I propose that the two-place predicate ueber-bar(v, x) holding between a spatial path v and
a material object x is the basic semantic interpretation of the geometric route preposition
über (‘over, across’). The predicate is a prime at LF. In (335), I define an ueber-bar-path
v of a material object x as an external line segment of x that is also a plumb-square line
segment above x. Both the respective predicates extlis (boundary condition) and plumb-square
(configurational condition) are defined in Section 4.3.6.
(335) ueber-bar-path:∀v, x[ueber-bar(v, x)↔ extlis(v, x)∧ plumb-square(v, x)]
“v is an ueber-bar-path of material object x iff v is an external line segment of x and v
is a plumb-square line segment above x”
5.4. Lexical prepositional structure 209
The relation between the concept of verticality [ℷ] and the configuration expressed by the
predicate ueber-bar is straightforward. Its definition involves the predicate plumb-square that
directly makes reference to the downward orientation, i.e. one of the two orientations on the
vertical axis; see (248) on page 144.
5.4 Lexical prepositional structure
This section discusses the lexical structure of the spatial prepositions. That is, the structure
projected by the lexical category P. For convenience, I also address the optional light preposi-
tion Q in this section. Section 5.4.1 addresses place prepositions, Section 5.4.2 directed path
prepositions (i.e. goal and source prepositions), and Section 5.4.3 undirected path prepo-
sitions (i.e. route prepositions). The general lexical and light structure of prepositions is
depicted in (336).
(336) (QP)
PP
DPP○[uD]
P○[uD]∅
(Q○)[uP]
5.4.1 Place prepositions
This section presents the lexical derivation of place prepositions. Section 5.4.1.1 addresses
geometric place prepositions, Section 5.4.1.2 addresses pseudo-geometric place prepositions,
and Section 5.4.1.3 addresses non-geometric place prepositions.
5.4.1.1 Geometric prepositions
An example of a geometric place preposition is in (‘in’) as for instance given in (337).
(337) Hans
Hans
war
was
in
in
einem
a.DAT
Wald.
forest
‘Hans was in a forest.’
The lexical structure of the PP in (337) is depicted in (338). The category P hosts the synsem
feature [LOC], which is characteristic for locative prepositions, and a u-prefixed D-feature, i.e.
210 5. Spatial prepositions at the interfaces
[uD], which triggers Merge with the DP-complement of the preposition. Once P has merged
with its DP-complement, it projects a PP and the u-prefixed D-feature deletes. At the outset of
the derivation, P[LOC, uD] undergoes Primary Merge and thereby generates a prepositional
Root position; cf. Section 2.3. At Spell-Out, this prepositional Root position serves as the
insertion site for abstract Content features. In the case of the geometric place preposition in,
it is the abstract Content feature [ℵ] relating to interiority that enters the structure at the Root
position of P[LOC].
(338) PP
DPP○[LOC,ℵ, uD]
P○[LOC, uD]√in[ℵ]
Let us now look at the interpretation of this structure at the interfaces. Let us start
with LF. The higher P○-node is subject to interpretation at LF. It hosts the synsem feature[LOC] together with the abstract Content feature [ℵ]. I propose that German provides an
LF-instruction to the effect that P[LOC,ℵ] is interpreted as specifying an in-region r′ of an
anticipated material object x. The discourse referent r′ serves as the referential argument of P○.
In this example, the DP is interpreted as specifying a forest-entity x′. The discourse referent x′
serves as the referential argument of the DP and instantiates the anticipated discourse referent
x. The PP is interpreted to the effect that r′ is an in-region of the forest x′. The discourse
referent r′ is the referential argument of the PP. The semantic interpretation of the structure
at LF is depicted in (339).
(339) PP
r′ x′
in(r′, x′)
forest(x′)
DP
x′
forest(x′)
P○[LOC,ℵ]
r′
in(r′, x)
The derivations of the other two geometric place prepositions an (‘on’) and auf (‘upon’)
differ from the derivation of in (‘in’) in the choice of the abstract Content feature. While in
5.4. Lexical prepositional structure 211
comprises [ℵ] relating to interiority, an comprises [ℶ] relating to contiguity, and auf comprises[ℷ] relating to verticality. As for these three geometric place prepositions, we can now
formulate the LF-instructions for P in (340).106 When P hosts the synsem feature [LOC]
paired with the abstract Content feature [ℵ], it is interpreted as providing an in-region of the
material object provided by the complement DP. When [LOC] pairs with the abstract Content
feature [ℶ], P is interpreted as providing an an-region of the material object provided by the
complement DP; and when [LOC] pairs with the abstract Content feature [ℷ], P is interpreted
as providing an auf-region of the material object provided by the complement DP.
(340) LF-instructions for P (first version):
a. P ↔ r′
in(r′, x) / _ [LOC,ℵ]
b. ↔ r′
an(r′, x) / _ [LOC,ℶ]
c. ↔ r′
auf(r′, x) / _ [LOC, ℷ]
Let us now turn to the morphophonological realizations of P at PF. I propose that German
provides a PF-instruction to the effect that P[LOC,ℵ] is realized as /In/, which is illustrated in
(341).
(341) PP
DPP○[LOC,ℵ]
/In/
As for the three geometric place prepositions, we can now formulate the PF-instructions
for P in (342).107 When P hosts the synsem feature [LOC] paired with the abstract Content
feature [ℵ], it is realized as /In/. When [LOC] pairs with the abstract Content feature [ℶ], P is
realized as /an/; and when [LOC] pairs with the abstract Content feature [ℷ], P is realized as
/au<f/.
(342) PF-instructions for P (first version):
a. P ↔ /In/ / _ [LOC,ℵ]
b. ↔ /an/ / _ [LOC,ℶ]
c. ↔ /au<f/ / _ [LOC, ℷ]
106Note that the LF-instructions for P as given (340) are incomplete; they will be extended in the next sections.
107Note that the PF-instructions for P as given (342) are incomplete; they will be extended in the next sections.
212 5. Spatial prepositions at the interfaces
5.4.1.2 Pseudo-geometric prepositions
This section discusses the derivation of the pseudo-geometric place prepositions in, an, and
auf. Recall from Section 5.1.2 that I argue that pseudo-geometric prepositions share the
morphological form with geometric prepositions but that they do not have an geometrically-
grounded interpretation, but that they give rise to a functional locative interpretation. For
an example, consider the clause in (343) with a PP headed by auf. The clause is ambiguous
between (i) a reading where Hans is understood as being literally upon (the building of) the
civil registry office, e.g., because he works there as a roofer (→ roofer reading), and (ii) a
reading where Hans is understood as being at (the institution of) the civil registry office, e.g.,
because he is a groom and about to contract a civil marriage there (→ groom reading). The
two readings of the clause correspond to two readings of the preposition auf. Under the
roofer reading, the preposition has a geometrically-grounded interpretation. It refers to the
surface region of the building of the civil registry office that provides support from below. In
contrast, under the groom reading, the preposition has a functional locative interpretation.
It refers to the functionally relevant space of the institution of the civil registry office where
one can carry out official things. This contrast with respect to geometry motivates the terms
geometric preposition and pseudo-geometric preposition. Note that the two readings of
auf correspond also to two different translations in English. In this example, the geometric
preposition auf is best translated as on top of, while the pseudo-geometric preposition auf is
best translated as at.
(343) Hans
Hans
war
was
auf
on
dem
top
Standesamt
of/at the.DAT civil registry office
a. auf as a geometric preposition (roofer reading):
‘Hans was on top of (the building of) the civil registry office.’
b. auf as a pseudo-geometric preposition (groom reading):
‘Hans was at (the institution of) the civil registry office.’
With regard to the space denoted by the preposition, the contrast between the geometric
and the pseudo-geometric preposition auf in (343) is relatively clear. Typically, the space
where one carries out official things at the civil registry office is not upon the building.
However, some common nouns do not require the pseudo-geometric preposition auf, like
Standesamt does, but in.108 In these cases, the contrast between geometric and pseudo-
geometric readings of the preposition is often not that clear. Consider the clause in (344),
which is comparable to (343) in this respect. The clause is ambiguous between (i) a reading
where Hans is understood to be literally inside (the building of) the pub, e.g. because he
seeks shelter from the rain (344a), and (ii) a reading where Hans is understood to be at (the
institution of) the pub, e.g. because he works there as a waiter (344b).
108Note that I assume that the choice of geometric prepositions is determined by the intention of the speaker
(depending on the geometric relation that they want to express), while the choice of pseudo-geometric preposi-
tions is determined by the conceptualization of the complement of the pseudo-geometric preposition.
5.4. Lexical prepositional structure 213
(344) Hans
Hans
war
was
in
in/at
der
the.DAT
Kneipe.
pub
a. in as a geometric preposition (cf. roofer reading):
‘Hans was in(side) the pub (e.g. seeking shelter from the rain).’
b. in as a pseudo-geometric preposition (cf. groom reading):
‘Hans was at the pub (e.g. working there as a waiter).’
The difference to auf in (343) is that the space of a pub where one works as a waiter is typically
inside the pub. That is, the distribution of the geometric and the pseudo-geometric readings
of in is often intuitively not as clear as it is for auf.
Common nouns are thus a difficult environment to exemplify pseudo-geometric preposi-
tions. This is due to the fact that many common nouns can be conceptualized in various ways,
where one conceptualization goes together with a geometric preposition, while another goes
together with a pseudo-geometric preposition, like Standesamt (‘civil registry office’) in (343)
or Kneipe (‘pub’) in (344). There is, however, an environment where geometric prepositions
are ruled out, but pseudo-geometric prepositions are straightforwardly possible. Spatial
prepositions co-occurring with toponyms, i.e. names of topological entities like countries,
cities, islands, etc., are – under normal conditions – always pseudo-geometric prepositions. I
refer to these pseudo-geometric prepositions as toponymic prepositions.
An example of a pseudo-geometric (toponymic) place preposition is auf as for instance
given in (345). Note at this point that, in combination with the DP Hispaniola (‘Hispaniola’),
which refers to the island of Hispaniola, auf is the only locative place preposition possible; in
is ungrammatical.
(345) Hans
Hans
war
was
auf/*in
upon/in
Hispaniola
Hispaniola
‘Hans was on Hispaniola.’
The lexical structure of the PP in (345) is depicted in (346). I assume that it is generally
parallel to the structure of a geometric place preposition but with the difference that the Root
position is empty. That is, no abstract Content feature is inserted into the Root position of
P[LOC] at Spell-Out.
(346) PP
DPP○[LOC, uD]
P○[LOC, uD]∅
214 5. Spatial prepositions at the interfaces
Recall from the discussion in Section 5.1.2, especially from the examples in (303) and (304),
that geometric prepositions allow echo extensions, while pseudo-geometric prepositions
disallow them. Take (347a) as an example for a geometric place preposition, and (347b) as an
example for a pseudo-geometric place preposition.
(347) a. Hans
Hans
war
was
auf
upon
dem
the.DAT
Tisch
table
(dr-auf).
there-upon
‘Hans was upon the table.’
b. Hans
Hans
war
was
auf
upon
den
the.DAT
Kanaren
Canary Islands
(*dr-auf).
there-upon
‘Hans was on the Canary Islands.’
This distribution of echo extensions can be explained if we assume that the presence of
abstract Content features in the Root position of P is a necessary condition for the availability
of echo extensions. Geometric prepositions have a Root position filled with abstract Content
features, while pseudo-geometric prepositions have an empty Root position. For a further
discussion on echo extensions, I refer the reader to Section 5.5.1.
Before we look at the PF-realization of this structure and at the question of how the surface
form of the preposition is determined, let us first have a look at the interpretation of this
structure at LF. Again, the higher P○-node is subject to interpretation at LF. It hosts the
synsem feature [LOC]. I propose that German provides an LF-instruction to the effect that
plain P[LOC] is interpreted as specifying a functional region r′ of an anticipated material
object x. For functional regions, I use the predicate func. I assume that a func-region is a
region that is geometrically unspecific, i.e. it is not geometrically but rather functionally
grounded. The discourse referent r′ serves as the referential argument of P○. In this example,
the DP Hispaniola is interpreted as specifying an entity x′ that has the property of being
the Caribbean island Hispaniola. For this, I use the one-place predicate Island-of-Hispaniola.
The discourse referent x′ serves as the referential argument of the DP and instantiates the
anticipated discourse referent x. The PP is compositionally interpreted to the effect that r′ is a
functional region of the island Hispaniola x′, i.e. some location on the island of Hispaniola.
The discourse referent r′ is the referential argument of the PP. The semantic interpretation of
the structure at LF is depicted in (348).
5.4. Lexical prepositional structure 215
(348) PP
r′ x′
func(r′, x′)
Island-of-Hispaniola(x′)
DP
x′
Island-of-Hispaniola(x′)
P○[LOC]
r′
func(r′, x)
Consider now another example of a pseudo-geometric (toponymic) place preposition in
(349). Here, the DP Haiti (‘Haiti’), which refers to the state of Haiti, can only combine with
the locative place preposition in (‘in, at’); auf is ungrammatical.109
(349) Hans
Hans
war
was
in/*auf
in/upon
Haiti
Haiti
‘Hans was in Haiti.’
As for the structure the PP in (349), I propose that it is parallel to the one in (346). Again, P
hosts the feature [LOC] and the Root position is empty. P[LOC] is interpreted as specifying
a functional region r′ of an anticipated material object x. In this example, the DP Haiti is
interpreted as specifying an entity x′ that has the property of being the Caribbean state Haiti.
For this, I use the one-place predicate State-of-Haiti. The PP is compositionally interpreted to
the effect that r′ is a functional region of the state Haiti x′, i.e. some location in the national
territory of the Republic of Haiti. The semantic interpretation of the structure at LF is depicted
in (350).
(350) PP
r′ x′
func(r′, x′)
State-of-Haiti(x′)
DP
x′
State-of-Haiti(x′)
P○[LOC]
r′
func(r′, x)
109Note that Haiti was the name of the island that has today the name Hispaniola. In this context, auf Haiti is
grammatical.
216 5. Spatial prepositions at the interfaces
In order to account for the interpretation of P[LOC] as a functional region, we can update
the LF-instructions for P in (340) with the rule in (351d).
(351) LF-instructions for P (second version):
a. P ↔ r′
in(r′, x) / _ [LOC,ℵ]
b. ↔ r′
an(r′, x) / _ [LOC,ℶ]
c. ↔ r′
auf(r′, x) / _ [LOC, ℷ]
d. ↔ r′
func(r′, x) / _ [LOC]
Note that the LF-instructions in (351) model some kind of geometric bleaching effect of
the locative P. When the locative feature [LOC] occurs in combination with a certain abstract
Content feature, i.e. (351a)–(351c), the interpretation of P is geometrically specific. In contrast,
when the locative feature [LOC] occurs in isolation, i.e. (351d), the interpretation of P is
geometrically unspecific.
Let us now look at the conceptual differences between nouns Hispaniola and Haiti, which, I
argue, explain the different realizations of the pseudo-geometric (topoynmic) P at PF. In (345)
we saw that the DP Hispaniola, which refers to the island of Hispaniola, can go together only
with the toponymic place preposition auf ; and in (349) we saw that the DP Haiti, which refers
to the state of Haiti, can go together only with the toponymic place preposition in. In order
to approach this phenomenon, I first have to clarify the assumptions I make with regard to
the invariant, idiosyncratic core underlying nouns like Hispaniola and Haiti. In particular,
I assume that the idiosyncratic core of nouns like Hispaniola and Haiti are (idiosyncratic)
Content features, say [©HISPANIOLA] and [©HAITI]. These Content features, which I mark
with the copyright symbol ©, relate, in a rather abstract way, to the respective conceptual
entities. Now, we have to look at the conceptual differences between Hispaniola (island) and
Haiti (state). I assume that islands are conceptualized as planes or discs on the surface of
the water that provide support from below, while states are conceptualized as containers
with an interior. Support from below relates to the abstract Content feature [ℷ] for verticality;
and containment relates to the abstract Content feature [ℵ] for interiority. I propose that
idiosyncratic Content features can pair with abstract Content feature and thereby reflect
various aspects of possible conceptualizations. That is, the island-denoting noun Hispaniola
contains the Content feature bundle [©HISPANIOLA, ℷ], while the state-denoting noun Haiti
contains the Content feature bundle [©HAITI,ℵ]. The respective lexical PP-structures look as
depicted in (352) and (353).
5.4. Lexical prepositional structure 217
(352) PP
DP
[©HISPANIOLA, ℷ]
P○[LOC]
(353) PP
DP
[©HAITI,ℵ]
P○[LOC]
In order to achieve the different realizations of P in these two contexts, I propose that abstract
Content features can be copied from within a DP to the dominating P○-node at PF. That is,
abstract Content features behave like dissociated features to the effect that they can be copied
at PF (Embick and Noyer 2007: 309); cf. also Section 3.3 and, in particular, (114) on page 72. In
the examples at issue, P[LOC] extends to P[LOC, ℷPF] in the context of [©HISPANIOLA, ℷ] and
P[LOC] extends to P[LOC,ℵPF] in the context of [©HAITI,ℵ]. Note that I use the subscript PF
in the feature structure of P in order to indicate that the respective abstract Content feature is
visible only at PF. This leads to the representations in (354) and (355). Now the PF-instructions
for P formulated in (342) straightforwardly apply. This leads to the correct realizations of the
pseudo-geometric place prepositions.
(354) PP
DP
[©HISPANIOLA, ℷ]
P○[LOC, ℷPF]
/au<f/
(355) PP
DP
[©HAITI,ℵ]
P○[LOC,ℵPF]
/In/
At this point a word on the underlying structure of the respective nominals as well as its
LF-interpretation and PF-realization is in order. We could assume that N undergoes Primary
Merge and thereby generates a nominal Root position as sketched in (356) (De Belder and
Van Craenenbroeck 2015; cf. Section 2.3). At Spell-Out, Content feature bundles can fill in
218 5. Spatial prepositions at the interfaces
these Root positions and thereby become Roots. For instance, the Content feature bundle[©HISPANIOLA, ℷ] in a nominal Root position is interpreted as the Root √Hispaniola, which
is illustrated in (357); and the Content feature bundle [©HAITI,ℵ] in a nominal Root position
is interpreted as the Root
√
Haiti, which is illustrated in (358).
(356) N○/NP
N○∅
(357) N○/NP
N○√Hispaniola[©HISPANIOLA, ℷ]
(358) N○/NP
N○√Haiti[©HAITI,ℵ]
Now, the questions arise which Content feature pairings are possible and what restricts the
parings. Note that the system outlined here does not preclude Content feature pairings that
are not interpretable. In principle, there could be a Content feature pairing [©HISPANIOLA,ℵ]
which led to the interpretation of Hispaniola as a state (or a city); or there could be a Content
feature pairing [©HAITI, ℷ] which led to the interpretation of Haiti as an island. However,
I assume that the respective interpretations are not available at LF because they cannot be
justified in our world, i.e. there is no state named Hispaniola and there is no island named
Haiti nowadays.110 This could be formalized as sketched in (359). The LF-instructions in
(359a) and (359b) are justified and thus available, while the ones in (359c) and (359d) are
not. The crucial point here is that, as from a grammatical point of view, such restrictions are
arbitrary.
(359) LF-instructions for the nouns Hispaniola and Haiti:
a. N ↔ x′
Island-of-Hispaniola(x′) / _ [©HISPANIOLA, ℷ]
b. ↔ x′
State-of-Haiti(x′) / _ [©HAITI,ℵ]
110In fact, the island of Hispaniola officially had the name Haiti between 1804 and 1844. Considering this,[©HAITI, ℷ] leading to auf Haiti is perfectly fine.
5.4. Lexical prepositional structure 219
c. ↔ # x′
State-of-Hispaniola(x′) / _ [©HISPANIOLA,ℵ]
d. ↔ # x′
Island-of-Haiti(x′) / _ [©HAITI, ℷ]
Figure 40: Historical map of the Greater Antilles
Consider Kuba (‘Cuba’). Unlike Hispaniola and Haiti, Kuba is the name for an island and
for a state.111 Consequently, both the toponymic preposition auf for the island reading (360a)
and the toponymic preposition in for the state reading (360b) are possible.
(360) a. Hans
Hans
war
was
auf
upon
Kuba.
Cuba
‘Hans was on the island of Cuba.’
b. Hans
Hans
war
was
in
in
Kuba.
Cuba
‘Hans was in the state of Cuba.’
The respective feature structures underlying the DP Kuba are sketched in (360); (361a) for the
island reading and (361b) for the state reading. Note that, in this system, there are ultimately
two distinct Roots:
√
Kuba1 for the island and
√
Kuba2 for the state.
111Note that the island of Cuba and the state of Cuba physically overlap almost entirely. Only the area of the
US Guantanamo Bay Naval Base is part of the island of Cuba, but not of the state of Cuba.
220 5. Spatial prepositions at the interfaces
(361) a. N○/NP
N○√Kuba1[©CUBA, ℷ]
b. N○/NP
N○√Kuba2[©CUBA,ℵ]
The LF-instructions for the noun Kuba could be formulated as given in (362).
(362) LF-instructions for the noun Kuba:
a. N ↔ x′
State-of-Cuba(x′) / _ [©CUBA,ℵ]
b. ↔ x′
Island-of-Cuba(x′) / _ [©CUBA, ℷ]
Let us now briefly look at the PF-instructions for the nouns Hispaniola, Haiti, and Kuba.
They could be formulated as given in (363). For these nouns, the abstract Content features
are immaterial at PF.
(363) PF-instructions for the nouns Hispaniola, Haiti, and Kuba:
a. N ↔ /hIsp"ani
“
o:la/ / _ [©HISPANIOLA]
b. ↔ /ha"i:ti/ / _ [©HAITI]
c. ↔ /"ku:ba/ / _ [©CUBA]
Let me close this discussion with a cross-linguistic remark. I assume that the way in which
Content features can pair with each other and how they are interpreted at LF or realized at
PF is language-dependent. For instance, in order to account for the phenomenon discussed
above, we could formulate Content rules for Standard German as follows: When occurring
in a nominal Root position, (i) pairings of toponymic Content features with [ℵ] give rise
to interpretations as states, cities, etc.; (ii) pairings of toponymic Content features with [ℷ]
give rise to interpretations as islands, squares, etc.; and (iii) pairings of toponymic Content
features with [ℶ] give rise to interpretations as rivers, lakes, etc.
As I assume that the pairing of Content features is language-dependent, cross-linguistic
variation is expected. In fact, a similar phenomenon can be observed in Norwegian Bokmål.
While most cities co-occur with i (‘in’) as the toponymic place preposition, some cities co-occur
with på (‘upon’). Textbooks on Norwegian Bokmål state the rule of thumb that Norwegian
5.4. Lexical prepositional structure 221
inland cities are used with på as in (364b), while Norwegian coastal cities and normally
non-Norwegian cities are used with i as in (364a).
(364) a. Jeg
I
bor
live
på
upon
Lillehammer.
Lillehammer
‘I live in Lillehammer’
b. Jeg
I
bor
live
i
in
Oslo/Berlin.
Oslo/Berlin
‘I live in Oslo/Berlin’ (cf. Aas 2012: 22)
A city’s property of being located in the Norwegian inland should arguably not correspond
to a grammatical property of Norwegian Bokmål. In particular, we cannot identify obvious
syntactic, semantic, or morphological properties of the Norwegian toponyms that determine
the choice of the respective toponymic place preposition. I thus propose that Norwegian
Bokmål has Content rules to the effect that Content features relating to Norwegian inland
cities pair with [ℷ] leading to the PF-realization of P as /po:/, i.e. på, while Content feature
relating to other cities pair with [ℵ] leading to the PF-realization of P as /i:/, i.e. i.112 From a
grammatical point of view, such distinctions are rather arbitrary or idiosyncratic.
5.4.1.3 Non-geometric prepositions
The region described by the non-geometric place preposition bei (‘at’) is special in various
ways. It has been noted by several scholars that it denotes a general, unspecified location
with respect to a Ground object (Li 1994, Nüse 1999, Levinson and Meira 2003, Zwarts 2010b).
The (pseudo)-geometric place prepositions refer to regions that relate to certain spatial parts
of the Ground object: (i) geometric in (‘in’) relates to the interior of the Ground, (ii) geometric
an (‘on’) relates to the surface of the Ground, (iii) geometric auf (‘upon’) relates to that part of
the surface of the Ground that provides support from below, and (iv) pseudo-geometric in,
an, and auf relate to a functional region of the Ground. In contrast, the non-geometric place
preposition bei (‘at’) refers to the Ground as a whole (Li 1994). Zwarts (2010b: 987) argues
that what he calls the AT-location (i.e. the region denoted by German bei ‘at’) “is relevant
with objects that have no interior or surface, or for which these spatial parts are not relevant.”
This conforms to the observations by Schröder (1986) that bei is preferred for general and
rather unspecific location descriptions as in (365a), for animated Ground objects as in (365b)
and (365d) (sphere of influence), and for workplaces (365c). Nevertheless, ‘normal’ Ground
nouns like Wald (‘forest’) as in (365e) are also straightforwardly acceptable.
(365) a. Lützen
Lützen
liegt
lies
bei
at
Leipzig.
Leipzig
‘Lützen is located near Leipzig.’
112For a conceptual explanation of this phenomenon, I refer the reader to Szyman´ska (2010: 174) who claims
that i is conceived as relating to containment, while på is conceived as relating to support from below.
222 5. Spatial prepositions at the interfaces
b. Er
he
wohnte
lived
noch
still
bei
at
seinen
his.DAT
Eltern.
parents
‘He still stayed with his parents.’
c. Er
he
arbeitet
works
bei
at
der
the.DAT
Bahn.
railroad
‘He is employed by the railroad.’
(Schröder 1986: 85, 86)
d. Hans
Hans
war
was
bei
at
seiner
his.DAT
Oma.
granny
‘Hans was with his granny.’
e. Hans
Hans
war
was
bei
at
einem
a.DAT
Wald.
forest
‘Hans was at a forest.”
In Section 5.4.2.3, I will put forth the hypothesis that the German goal preposition zu (‘to’)
relates to the non-geometric place preposition bei (‘at’) in that both refer to at-regions (cf.
Zwarts’ 2010b AT-location). That an at-region is special can thus also be seen with certain
usages of the non-geometric goal preposition zu. Consider the example (366), which is a
slogan used by the Green Party for the 1996 Baden-Württemberg state election; the original
campaign poster is given in Figure 41.
(366) Warum
why
fahren
drive
immer
always
so
so
viele
many
zum
to.the.DAT
Stau?
traffic jam
‘Why do so many people deliberately drive to traffic jams?’
The usage of the non-geometric goal preposition zum (contracted form of zu dem ‘to the.DAT’)
in combination with the noun Stau (‘traffic jam’) and the motion verb fahren (‘drive’) is not
straightforward because it implies that one would deliberately ‘drive to a traffic jam.’This is of
course not what a typical traffic participant intends to do, which is what the slogan amusingly
provokes. Typically, we can derive an intentional motion description when zu heads the path-
argument of a motion verb. In contrast, when a (pseudo)-geometric path preposition heads
the path-argument of a motion verb, intentionality cannot be derived.113 As for intentionality
in the context of motion verbs, I refer the reader to Roßdeutscher (2000: 183). I take this
observation as a further clue that an at-region referred to by the German non-geometric
prepositions bei (‘at’) and zu (‘to’) must be functionally determined rather than geometrically
(or pseudo-geometrically). In (366), the at-region must apparently be such that the subject of
fahren, i.e. the Figure, is aware of driving there, and maybe that it has relevance for the Figure
to go there.
These considerations motivate the synsem feature [AT]. In particular, I assume that the
non-geometric place preposition bei (‘at’) contains the synsem feature [AT] instead of [LOC];
note that the same also holds for the non-geometric goal and source prepositions zu (‘to’)
113In fact, a straightforward, unmarked description of an event of getting unintentionally into a traffic jam
would involve the pseudo-geometric preposition in (‘into’).
5.4. Lexical prepositional structure 223
Figure 41: Campaign poster by Green Party (1996 Baden-Württemberg state election)
and von (‘from’). As for the structure of the non-geometric place preposition bei, I assume
that it is parallel to the structure of (pseudo)-geometric place prepositions, except for the
fact that P hosts [AT] instead of [LOC]. Furthermore, I assume that the Root position of
non-geometric (place) prepositions is empty, like it is for pseudo-geometric prepositions. The
lexical structure of the non-geometric place preposition bei (‘at’) is illustrated in (367).
(367) PP
DPP○[AT, uD]
P○[AT, uD]∅
Recall from the discussion in Section 5.1.2, especially from the examples in (305), that
non-geometric prepositions – like pseudo-geometric prepositions, but unlike geometric
prepositions – disallow echo extensions. Take (368) as an example.
224 5. Spatial prepositions at the interfaces
(368) Hans
Hans
stand
stood
bei
at
der
the.DAT
Hütte
hut
(*da-bei).
there-at
‘Hans stood at the hut.’
The explanation I propose for why zu-PPs do not allow echo extensions is the same as I
gave for the absence of echo extensions of in PPs with pseudo-geometric prepositions (cf.
Section 5.4.1.2): echo extensions are possible only, when the Root position of P is non-empty;
but since zu is a non-geometric preposition, its Roos position cannot contain any abstract
Content features. Hence, the unavailability of echo extensions straightforwardly follows.
Let us begin by looking at the semantic interpretation of this structure at LF. The P○-node
hosts the synsem feature [AT]. I assume that this is interpreted as the two-place predicate
at(r′, x), which provides an at-region r′ of an anticipated material object x. The discourse
referent r′ serves as the referential argument of P○. Consider (365e) as an illustrative example.
Here, the DP is interpreted as specifying a forest-entity x′. The discourse referent x′ serves as
the referential argument of the DP and instantiates the anticipated discourse referent x. The
PP is compositionally assigned the interpretation that r′ is an at-region of the forest x′. The
discourse referent r′ is the referential argument of the PP. The semantic interpretation of the
structure at LF is depicted in (369).
(369) PP
r′ x′
at(r′, x′)
forest(x′)
DP
x′
forest(x′)
P○[AT]
r′
at(r′, x)
In order to account for the interpretation of P[AT] as an at-region, we can simply expand
the LF-instructions for P by the rule in (370e).
(370) LF-instructions for P (third version):
a. P ↔ r′
in(r′, x) / _ [LOC,ℵ]
b. ↔ r′
an(r′, x) / _ [LOC,ℶ]
c. ↔ r′
auf(r′, x) / _ [LOC, ℷ]
5.4. Lexical prepositional structure 225
d. ↔ r′
func(r′, x) / _ [LOC]
e. ↔ r′
at(r′, x) / _ [AT]
Let us now turn to the morphophonological realizations of P at PF. I propose that the
structure in (367) is realized as in (371). That is, the exponent /bai</ (for bei, ‘at’) is inserted in
P[AT].
(371) PP
DPP○[AT]
/bai</
In order to account for the proper realization of P[AT], we can expand the PF-instructions
for P by the rule in (372d).
(372) PF-instructions for P (second version):
a. P ↔ /In/ / _ [LOC,ℵ]
b. ↔ /an/ / _ [LOC,ℶ]
c. ↔ /au<f/ / _ [LOC, ℷ]
d. ↔ /bai</ / _ [AT]
5.4.2 Goal and source prepositions
I take the view that goal and source prepositions, i.e. directed path prepositions, derive from
place prepositions. In this section I propose that a light preposition, which I label Q, above
P derives goal and source prepositions from place prepositions. That is, source and goal
prepositions generally have the structure depicted in (373).
226 5. Spatial prepositions at the interfaces
(373) QP
PP
DPP○[uD]
P○[uD]∅
Q○[uP]
Let us first revisit the goal and source prepositions this thesis focuses on. The (pseudo)-
geometric goal prepositions are an (‘onto’), auf (‘up onto’), and in (‘into’).114 At this point, I
should mention again that the place/goal alternation manifests itself as a case alternation.
Leaving their forms unchanged, the (pseudo)-geometric place prepositions take a dative com-
plement, while the (pseudo)-geometric goal prepositions take an accusative complement. I
should also mention here the goal preposition nach (‘to’), which can be considered as a special
case. It is the pseudo-geometric goal preposition that occurs with determinerless comple-
ments. The (pseudo)-geometric source prepositions come in two versions, either as a synthetic
(one-word) form or as an analytic (two-word) form. The synthetic (pseudo)-geometric source
preposition is aus (‘out of’); the analytic (pseudo)-geometric source prepositions are von an
(‘from on’), von auf (‘from upon’), and von in (‘from in’).115 The non-geometric goal and
source prepositions are zu (‘to’) and plain von (‘from’), respectively.
As for synsem features, I assume that the light preposition Q can host the synsem feature[+TO] leading to a goal interpretation, or the synsem feature [−TO], leading to a source
interpretation. Recall that Section 5.4.1 discussed two types of place prepositions. On the one
hand, P[LOC] characterizes the (pseudo)-geometric place prepositions an (‘on’), auf (‘upon’),
and in (‘in’), while, on the other hand, P[AT] characterizes the non-geometric place preposition
bei (‘at’). In this section, I argue that the distinction between (pseudo)-geometric and non-
geometric prepositions is also valid in the domain of goal and source prepositions. One crucial
difference between the two types of prepositions is that (pseudo)-geometric goal and source
prepositions denote spatial paths that are conceptualized as punctual, while non-geometric
goal and source prepositions denote spatial paths that are conceptualized as extended In
particular, spatial paths denoted by (pseudo)-geometric goal and source prepositions can
be characterized by a transitional change with regard to some spatial configuration (e.g. a
spatial path denoted by the PP into X can roughly be described as a transition from ‘not in X’
114Note that the English place prepositions in and on correspond to the morphologically complex goal
prepositions in-to and on-to. I consider the morpheme -to in these forms as cross-linguistic evidence for the light
preposition Q.
115Note that many German speakers do not like these analytic source prepositions.
5.4. Lexical prepositional structure 227
to ‘in X’), while spatial paths denoted by non-geometric goal and source prepositions can be
characterized by their starting point (source) or end point (goal) (e.g. a spatial path denoted
to X can roughly be described as one that has its starting point not at X and its end point at X).
In order to account for this contrast, I propose that the synsem feature [±TO] hosted by Q can
give rise to different interpretations depending on the synsem features hosted by P below. In
particular, I will propose that Q[±TO] above P[LOC] is interpreted as denoting transitional
spatial paths that are conceptualized as punctual, while Q[±TO] above [AT] is interpreted as
denoting non-transitional spatial paths that are conceptualized as extended.
The aspectual difference, as indicated above, becomes visible when the two types of
goal and source PPs serve as arguments of motion verbs. For instance, when combined
with manner of motion verbs, (pseudo)-geometric goal and source prepositions give rise
to achievement predicates, while non-geometric goal and source prepositions give rise to
accomplishment predicates. For English, Beavers (2002), Denis (2003), Denis et al. (2003),
Zwarts (2005b) have observed that paths denoted by goal prepositions like into ((pseudo)-
geometric) are conceptualized as punctual, while paths denoted by the goal preposition to
(non-geometric) are conceptualized as extended. In particular, Denis (2003) applies several
established aktionsart tests all of which show that goal PPs headed by into give rise to
achievement predicates, when combined with manner of motion verbs, while goal PPs
headed by to give rise to accomplishment predicates. The aktionsart test applied by Denis
(2003) are: (i) the punctual adverbial test, (ii) the frame adverbial test, (iii) the perfective-to-
imperfective entailment test, and (iv) the halfway through test.116 In the following I reproduce
these aktionsart tests for German goal prepositions.117 In addition, I apply (v) Kratzer (2004)
Kratzer (2004)’s aktionsart test involving weiter (‘further’). Note that most of the tests involve
the agentive manner motion verb laufen (‘walk’) which gives rise to an atelic predicate
(activity) when it is used without a goal PP as can be seen in (374).
(374) Hans
Hans
lief
walked
für/??in
for/??in
zwei
two
Stunden.
hours.
The first aktionsart test involves punctual adverbials like um 18:02 Uhr (‘at 6.02 pm’) or
um Mitternacht (‘at midnight’). Such adverbials give rise to a straightforward interpretation
with punctual situation types such as achievements (375a). They specify the point in time
when the event happens. With accomplishments, however, punctual adverbials normally
provoke an inceptive reading, i.e. a reading where the event is understood to start at the
specified point in time; see (375b).
116Note that I omit Denis’s spend/take an hour as it is difficult to reproduce in German.
117Note that I focus here on goal prepositions and leave source prepositions aside. Within this thesis, I assume
that the aktionsart differences that we observe with goal prepositions are similar or even parallel for source
prepositions. In fact, tentative tests suggest this. Nevertheless, I leave a detailed analysis of the aspectual
behavior of source prepositions for further research.
228 5. Spatial prepositions at the interfaces
(375) a. Hans
Hans
erreichte
reached
um
at
18:02
6.02
Uhr
o’clock
den
the
Gipfel.
summit
‘Hans reached the summit at 6.02 pm.’
b. Hans
Hans
baute
built
um
at
18:02
6.02
Uhr
o’clock
eine
a
Sandburg.
sandcastle
‘Hans built a sandcastle at 6.02 pm.’
In combination with (pseudo)-geometric goal prepositions as in (376a), punctual adverbials
give rise to a punctual reading, as is the case with achievement predicates. The adverbial
specifies the point in time when Hans enters the interior of the supermarket. In contrast, with
the non-geometric goal preposition zu punctual adverbials give rise to an inceptive reading,
as is the case with accomplishment predicates. The natural interpretation of (376b) is that
Hans starts walking to the supermarket at 6.02 pm.
(376) a. Hans
Hans
lief
walked
um
at
18:02
6.02
Uhr
o’clock
in
into
den
the.ACC
Supermarkt.
supermarket
‘Hans walked into the supermarket at 6.02 pm.’
b. Hans
Hans
lief
walked
um
at
18:02
6.02
Uhr
o’clock
zu
to
dem
the.DAT
Supermarkt.
supermarket
‘Hans walked to the supermarket at 6.02 pm.’
The second aktionsart test involves the temporal frame adverbial in an hour. It is well
known that temporal in-PPs are felicitous with telic predicates, that is, with accomplishments
and achievements. There is, however, an interpretative difference of temporal in-PPs with
these two situation types. With accomplishments, a temporal in-PP measures the duration of
the event up to the culmination point where the event ends. With achievements, in contrast,
a temporal in-PP does not measure the event itself but a preparatory phase. This preceding
process is conceptually detached from the event expressed by the verb (Dowty 1979, Smith
1991). Consider an example of an achievement predicate in (377a) and an example of an
accomplishment predicate in (377b)
(377) a. Hans
Hans
erreichte
reached
in
in
einer
an
Stunde
hour
den
the
Gipfel.
summit
‘Hans reached the summit in an hour.’
b. Hans
Hans
baute
built
in
in
einer
an
Stunde
hour
eine
a
Sandburg.
sandcastle
‘Hans built a sandcastle in an hour.’
Let us now apply the frame adverbial test to the goal prepositions under discussion. The
test shows that (pseudo)-geometric goal prepositions behave like achievements, while the
non-geometric goal preposition zu behaves like accomplishments. In (378a), the event of
walking into the supermarket is expressed to happen after one hour has elapsed, while in
(378a), the event of walking to the supermarket is expressed to last one hour.
5.4. Lexical prepositional structure 229
(378) a. Hans
Hans
lief
walked
in
in
einer
an
Stunde
hour
in
into
den
the.ACC
Supermarkt.
supermarket
‘Hans walked into the supermarket in an hour.’
b. Hans
Hans
lief
walked
in
in
einer
an
Stunde
hour
zu
to
dem
the.DAT
Supermarkt.
supermarket
‘Hans walked to the supermarket in an hour.’
The third aktionsart test concerns the perfective-to-imperfective entailment depicted in
(379). The perfective-to-imperfective entailment is typically licensed by accomplishments but
not by achievements (Dowty 1979: 59, Denis 2003: 8, Rothstein 2004: 26).
(379) X VP-ed in an hour⇒ X was VP-ing during that hour
Unlike English, Standard German does not have a morphologically overt progressive form.
Thus, this test needs to be adapted for German. Instead of the progressive, we can use
the construction dabei sein etwas zu tun (‘to be in the act of doing sth.’) in order to express
imperfective aspect. That is, an achievement as in (377a) does not entail (380a), while an
accomplishment as in (377b) entails (380b).
(380) a. Hans
Hans
war
was
während
during
dieser
that
Stunde
hour
dabei
at
den
the
Gipfel
summit
zu
to
erreichen.
reach
‘Hans was reaching the summit during that hour.’
b. Hans
Hans
war
was
während
during
dieser
that
Stunde
hour
dabei
at
eine
a
Sandburg
sandcastle
zu
to
bauen.
build
‘Hans was building a sandcastle during that hour.’
(381) a. (377a) /⇒ (380a)
b. (377b)⇒ (380b)
When applied to the goal prepositions under discussion, the perfective-to-imperfective entail-
ment test shows that (pseudo)-geometric goal prepositions give rise to achievement predi-
cates, while the non-geometric goal preposition zu gives rise to accomplishment predicates.
In particular, (378a) does not entail (382a). In contrast, (378b) entails (382b).
(382) a. Hans
Hans
war
was
während
during
dieser
that
Stunde
hour
dabei
at
in
into
den
the.ACC
Supermarkt
supermarket
zu
to
laufen.
walk
‘Hans was walking into the supermarket during that hour.’
b. Hans
Hans
war
was
während
during
dieser
that
Stunde
hour
dabei
at
zu
to
dem
the.DAT
Supermarkt
supermarket
zu
to
laufen.
walk
‘Hans was walking to the supermarket during that hour.’
(383) a. (378a) /⇒ (382a)
b. (378b)⇒ (382b)
The fourth aktionsart test involves the progressive construction be halfway through
doing sth., which is possible with accomplishments but not with achievements (Denis 2003: 9,
230 5. Spatial prepositions at the interfaces
Rothstein 2004: 44). As Standard German does not have a straightforward progressive form
like English, we need to adapt this test to German. Instead of the progressive plus halfway
through, we can use the construction es zur Hälfte geschafft haben etw. zu tun (lit.: it to.the half
accomplished have sth. to do). In fact, achievements as in (384a) are ungrammatical, while
accomplishments as in (384b) are grammatical.
(384) a. *Hans
Hans
hat
has
es
it
zur
to.the
Hälfte
half
geschafft
accomplished
den
the
Gipfel
summit
zu
to
erreichen.
reach
*‘Hans was halfway through reaching the summit.’
b. Hans
Hans
hat
has
es
it
zur
to.the
Hälfte
half
geschafft
accomplished
eine
a
Sandburg
sandcastle
zu
to
bauen.
build
‘Hans was halfway through building a sandcastle.’
When applied to the goal prepositions under discussion, the halfway through test shows
that (pseudo)-geometric goal prepositions give rise to achievement predicates, while the
non-geometric goal preposition zu gives rise to accomplishment predicates. That is, (385a) is
ungrammatical, while (385b) is grammatical.
(385) a. *Hans
Hans
hat
has
es
it
zur
to.the
Hälfte
half
geschafft
accomplished
in
into
den
the.ACC
Supermarkt
supermarket
zu
to
laufen.
walk
*‘Hans was halfway through walking into the supermarket.’
b. Hans
Hans
hat
has
es
it
zur
to.the
Hälfte
half
geschafft
accomplished
zu
to
dem
the.DAT
Supermarkt
supermarket
zu
to
laufen.
walk
‘Hans was halfway through walking to the supermarket.’
The fifth aktionsart test involves the German verb particle weiter (‘further’), which
is straightforwardly interpretable with accomplishments but strange with achievements
(Kratzer 2004). Compare the achievement in (386a), which is ungrammatical with weiter, with
the accomplishment in (386b), which is grammatical with weiter.
(386) a. ??Hans
Hans
konnte
could
den
the
Gipfel
summit
weiter-erreichen.
further-reach
??‘Hans could continue to reach the summit.’
b. Hans
Hans
konnte
could
die
the
Sandburg
sandcastle
weiter-bauen.
further-build
‘Hans could continue to build the sandcastle.’
When applied to the goal prepositions under discussion, the weiter test shows that (pseudo)-
geometric goal prepositions give rise to achievement predicates, while the non-geometric
goal preposition zu gives rise to accomplishment predicates. (387a) is marked, while (387b) is
straightforward.
(387) a. ??Hans
Hans
konnte
could
in
into
den
the.ACC
Supermarkt
supermarket
weiter-laufen.
further-walk
??‘Hans could continue to walk into the supermarket.’
5.4. Lexical prepositional structure 231
b. Hans
Hans
konnte
could
zu
to
dem
the.DAT
Supermarkt
supermarket
weiter-laufen.
further-walk
‘Hans could continue to walk to the supermarket.’
All aktionsart tests applied above have shown that (pseudo)-geometric goal (and source)
prepositions contrast with non-geometric goal (and source) prepositions such that – when
combined with manner of motion verbs – the former give rise to achievement predicates,
while the latter give rise to accomplishment predicates. My conclusion from this is that
(pseudo)-geometric goal and source prepositions (e.g. in ‘into’ and aus ‘out of’) denote spatial
paths that are conceptualized as punctual, i.e. as spatially not extended, while, on the other
hand, non-geometric goal and source prepositions (i.e. zu ‘to’ and von ‘from’) denote spatial
paths that are conceptualized as spatially extended. Section 4.5 discussed two different
conceptualizations of goals and sources in axiomatic approaches to (spatial) paths. Krifka
(1998: 227–228) defines sources and goals as being adjacent to paths, while Beavers (2012: 30)
defines them as being parts of paths. I propose that this distinction can be exploited to
model the aspectual difference between (pseudo)-geometric and non-geometric goal and
source prepositions. In particular, I take the view that Krifka’s conceptualization of goals and
sources can be used to model extended spatial paths denoted by non-geometric goal and
source prepositions, while Beavers’ conceptualization of goals and sources can be used, in a
modified way, to model transitional spatial paths denoted by (pseudo)-geometric goal and
source prepositions.
Let us first look at transitional spatial paths denoted by (pseudo)-geometric goal and
source prepositions. Beavers’ idea of sources and goals as being on paths combined with
Krifka’s (1998: 230) analysis of instantaneous movements, viz. achievements as minimal
final (and initial) subevents, gives rise to the definitions of the two three-place LF-predicates
leave(w, r, e) and enter(w, r, e) in (388). The model for a transitional path w leaving a region r
in e is displayed in Figure 42.a; the model for a transitional path w entering a region r in e is
displayed in Figure 42.b.
(388) If θ is an (Strict) Movement Relation for spatial path w and event e, then
a. ∀e, r, w[leave(w, r, e)↔
w ⊆ r ∧ θ(w, e) ∧ ∃e′, w′[e < e′ ∧ θ(w′, e′) ∧ INI(e, e′) ∧ ∀e′′[INI(e′′, e′) → e ≤ e′′] ∧∀w′′[w′′ ≤ w′ ∧¬w′′ ⊗w → ¬w′′ ⊆ r]]]
“path w leaves region r in e iff w is contained in r and w is θ-related to the
minimal initial e < e′ such that e′ is θ-related to w′ and all other subpaths
w′′ < w′ that do not overlap with w are not contained in r”
b. ∀e, r, w[enter(w, r, e)↔
w ⊆ r ∧ θ(w, e) ∧ ∃e′, w′[e < e′ ∧ θ(w′, e′) ∧ FIN(e, e′) ∧ ∀e′′[FIN(e′′, e′) → e ≤ e′′] ∧∀w′′[w′′ ≤ w′ ∧¬w′′ ⊗w → ¬w′′ ⊆ r]]]
“path w enters region r in e iff w is contained in r and w is θ-related to the
232 5. Spatial prepositions at the interfaces
minimal final e < e′ such that e′ is θ-related to w′ and all other subpaths w′′ < w′
that do not overlap with w are not contained in r”
e′e′′e
w′w w′′r
θθ
42.a: “path w leaves region r in e”
e′ e′′ e
w′ ww′′ r
θ θ
42.b: “path w enters region r in e”
Figure 42: Transitional goal and source paths
Let us now look at extended spatial paths denoted by non-geometric goal and source
prepositions. I basically adopt Krifka’ (1998: 227–228) definitions of goals and sources in
order to model spatial paths denoted by non-geometric goal and source prepositions. Note
that I ‘relabel’ Krifka’s goal and source as the two three-place LF-predicates to(w, r, e) and
from(w, r, e), respectively. In order to ensure that to-paths and from-paths are extended, I
assume additionally that they are non-minimally complex objects (non-mco) as proposed by
Beavers (2002: 19), see (389). Non-minimally complex objects are divisible into at least thee
unique, non-overlapping subobjects.
(389) ∀x[non-mco(x)↔ ∃x′, x′′, x′′′[x = x′ ⊕ x′′ ⊕ x′′′ ∧¬x′ ⊗ x′′ ∧¬x′′ ⊗ x′′′ ∧¬x′ ⊗ x′′′]]
(Beavers 2002: 19)
The model for a path w from a region r in e is displayed in Figure 43.a; the model for a path w
to a region r in e is displayed in Figure 43.b.
(390) If θ is a (Strict) Movement Relation for spatial path w and event e, then
a. ∀e, r, w[from(w, r, e)↔ ¬w ⊆ r ∧ non-mco(w)∧ θ(w, e)∧∀e′, w′[w′ ≤ w∧ e′ ≤ e∧ θ(w′, e′)→ [[INI(e′, e)→ w′∞ r]∧ [¬ INI(e′, e)→ ¬w′∞ r]]]]
“w is a path from r in e iff w is not contained in r but all subpaths w′ ≤ w that
are θ-related to initial subevents e′ ≤ e are adjacent to r”
b. ∀e, r, w[to(w, r, e)↔ ¬w ⊆ r ∧ non-mco(w)∧ θ(w, e)∧∀e′, w′[w′ ≤ w∧ e′ ≤ e∧ θ(w′, e′)→ [[FIN(e′, e)→ w′∞ r]∧ [¬FIN(e′, e)→ ¬w′∞ r]]]]
“w is a path to r in e iff w is not contained in r but all subpaths w′ ≤ w that are
θ-related to final subevents e′ ≤ e are adjacent to r”
(adapted from Krifka 1998: 227–228)
5.4. Lexical prepositional structure 233
r
e
w
e′
w′
θθ
43.a: “w is a path from region r in e”
r
e
w
e′
w′
θ θ
43.b: “w is a path to region r in e”
Figure 43: Extended goal and source paths
The following sections address the derivations as well as the LF-interpretations and the PF-
realizations of geometric, pseudo-geometric and non-geometric goal and source prepositions.
5.4.2.1 Geometric prepositions
A prototypical example of the geometric goal preposition in (‘into’) is given in (391a); a
prototypical example of the geometric source preposition aus (‘out of’) is given in (391b).
(391) a. Hans
Hans
rannte
ran
in
into
einen
a.ACC
Wald.
forest
‘Hans ran into a forest.’
b. Hans
Hans
rannte
ran
aus
out of
einem
a.DAT
Wald.
forest
‘Hans ran out of a forest.’
I assume that both geometric goal and geometric source prepositions share the lexical
structure with geometric place prepositions. That is, up to the level of PP, the structure
in (392) is identical to the structure in (338) on page 210. The category P hosts the synsem
feature [LOC] and a u-prefixed D-feature that triggers Merge with the DP-complement of
the preposition. Once P has merged with its DP-complement it projects a PP and the u-
prefixed D-feature deletes. At the outset of the derivation, the category P undergoes Primary
merge and thereby generates a prepositional Root position, cf. Section 2.3. At Spell-Out, this
prepositional Root position serves as the insertion site for abstract Content features. In the
case of the geometric goal and source prepositions in and aus, it is the abstract Content feature[ℵ] relating to interiority that enters the structure at the Root position of P[LOC]. The light
preposition Q derives goal and source prepositions from place prepositions. Q can host the
synsem feature [+TO] for a goal interpretation; and [−TO] for a source interpretation. That is,
the structure of the geometric goal preposition in (‘into’) in (391a) and the structure of the
geometric source preposition aus (‘out of’) in (391b) looks as depicted in (392).
234 5. Spatial prepositions at the interfaces
(392) QP
PP
DPP○[LOC, uD,ℵ]
P○[LOC, uD]√in[ℵ]
Q○[±TO, uP]
Let us now look at the interpretation of this structure at LF. Up to the level of PP, the
interpretation is parallel to the interpretation of the respective geometric place preposition
depicted in (369). The higher P○-node is subject to interpretation at LF. It hosts the synsem
feature [LOC] together with the abstract Content feature [ℵ]. P[LOC,ℵ] is interpreted as
specifying an in-region r′ of an anticipated material object x. In this example, the DP is
interpreted as specifying a forest-entity x′, which instantiates x. That is, the PP is interpreted
to the effect that r′ is an in-region of the forest x′.
I assume that the light preposition Q above PP derives goal and source prepositions. In the
case of the geometric goal preposition in (‘into’) as in (391a), Q hosts the synsem feature [+TO].
This is interpreted to the effect that it introduces the three-place predicate enter(w, r, e); see
the definition of the predicate in (388b). An anticipated spatial path w, which is a transitional
spatial path that is conceptualized as punctual, enters an anticipated region r in an anticipated
event e. The in-region-denoting discourse referent r′ is the referential argument of the PP.
It instantiates the anticipated region r of Q. That is, QP is compositionally interpreted as
denoting an in-region r′ of the forest x′ that is entered by an anticipated spatial path w in an
anticipated event e.118 The LF-representation of the PP in (391a) is given in (393).
118The anticipated spatial path w will be instantiated at the functional level of the derivation by the referential
argument of the functional prepositional category C, while the anticipated event e will be instantiated by the
referential argument of the verb. An example of this is given in (488) and (489) in Section 5.6.2.
5.4. Lexical prepositional structure 235
(393) QP
r′ x′
in(r′, x′) enter(w, r′, e)
forest(x′)
PP
r′ x′
in(r′, x′)
forest(x′)
DP
x′
forest(x′)
P○[LOC,ℵ]
r′
in(r′, x)
Q○[+TO]
enter(w, r, e)
In the case of the geometric source preposition aus (‘out of’) as in (391b), the structure is
basically identical. The only difference is that Q hosts the synsem feature [−TO]. This is
interpreted to the effect that it introduces the three-place predicate leave(w, r, e); see the
definition of the predicate in (388a). The QP is compositionally interpreted as denoting an
in-region r′ of the forest x′ that is left by an anticipated spatial path w in an anticipated event
e. The LF-representation of the QP in (391b) is given in (394).
(394) QP
r′ x′
in(r′, x′) leave(w, r′, e)
forest(x′)
PP
r′ x′
in(r′, x′)
forest(x′)
DP
x′
forest(x′)
P○[LOC,ℵ]
r′
in(r′, x)
Q○[−TO]
leave(w, r, e)
236 5. Spatial prepositions at the interfaces
In order to account for the respective interpretations, we can formulate the LF-instructions
for Q as given in (395). The contexts are formulated to the effect that the interpretation rules
apply only in the context of (pseudo)-geometric prepositions, which involve the synsem
feature [LOC]. Note at this point that these instructions will be extended in the context of non-
geometric goal and source prepositions, cf. Section 5.4.2.3. Note also that the LF-instructions
for P as formulated in (340), (351), and (370) straightforwardly apply to the geometric goal
and source prepositions.
(395) LF-instructions for Q (first version):
a. Q ↔
enter(w, r, e) / [ _ [+TO] ... P[LOC]]
b. ↔
leave(w, r, e) / [ _ [−TO] ... P[LOC]]
Let us now look at the possible PF-realizations of the structure in (392). The PF-instructions
for P formulated in (342) and (372) straightforwardly apply for the geometric goal prepositions
in (‘into’), an (‘onto’), and auf (‘up onto’). Unlike in English, the German morphological forms
of the geometric goal prepositions are identical to the morphological forms of the respective
geometric place prepositions. Instead, German shows a case alternation; cf. the place/goal
alternation (or dative/accusative alternation) discussed in Section 5.1.2. Geometric (and also
pseudo-geometric) place prepositions have a dative complement, while the corresponding
(pseudo)-geometric goal prepositions have an accusative complement. Note that I do not
address this alternation at this point. Section 6.4 discusses case in the prepositional domain.
At PF, the analysis of geometric source prepositions is more complex than the analysis of
geometric goal prepositions. Let us first look at the surface forms of the geometric source
prepositions in German; cf. Section 5.1.2 and, in particular, Table 3 on page 184. The geometric
source preposition that corresponds to the geometric goal preposition in (‘into’) has a synthetic
form, namely aus (‘out of’). In addition, German has the analytic source prepositions von an
(‘from on’), von auf (‘from upon’), and von in (‘from in’), which are, however, judged as
marginal or even ungrammatical by many German speakers. It appears that the source
preposition von (‘from’), which is actually a non-geometric source preposition, is usually
preferred.
In order to account for the synthetic source preposition aus (‘out of’), I posit a morphologi-
cal movement operation to the effect that the Q○-node morphologically lowers to and fuses
with the P○-node.119 Coming from Spell-Out, we start, at PF, with the structure depicted in
(396a). Then, the Q○-node lowers to the P○-node as depicted in (396b). Technically, this step
takes the form of adjunction. Finally, the Q○-node and the P○-node fuse to the node P○/Q○ as
119See Sections 3.4 and 3.5 for a presentation of the respective morphological operations.
5.4. Lexical prepositional structure 237
depicted in (396c). At the same time, the synsem-feature bundles they host individually fuse
to one synsem-feature bundle, i.e. [LOC,ℵ,−TO].
(396) a. QP
PP
DPP○[LOC,ℵ]
Q○[−TO]
b. QP
PP
DPP○
P○[LOC,ℵ]Q○[−TO]
c. QP
PP
DPP○/Q○[LOC,ℵ,−TO]
I propose the morphological rule of Q-to-P-Lowering and subsequent P/Q-Fusion, as
formulated in (397).
(397) Q-to-P-Lowering and subsequent P/Q-Fusion:
Q○ lowers to and fuses with P○.
Now, we can formulate the PF-instructions for P and Q in order to account for synthetic
geometric source and goal prepositions. Q/P[LOC,ℵ,−TO] is realized as /au<s/ (or aus). This
motivates the addition of the special rule in (398a) to the PF-instructions for P. I mentioned
above that the non-geometric source preposition von (‘from’) is often used instead of analytic
source prepositions. I thus add the rule in (398b). Note that this rule is independent of
whether P hosts the synsem feature [LOC] for (pseudo)-geometric prepositions or [AT] for
238 5. Spatial prepositions at the interfaces
non-geometric prepositions. However, it must be ranked higher than the rules involving the
synsem feature [LOC].
(398) PF-instructions for P (third version):
a. P ↔ /au<s/ / _ [LOC,ℵ,−TO]
b. ↔ /fOn/ / _ [−TO]
c. ↔ /In/ / _ [LOC,ℵ]
d. ↔ /an/ / _ [LOC,ℶ]
e. ↔ /au<f/ / _ [LOC, ℷ]
f. ↔ /bai</ / _ [AT]
Let us finally look at the analytic source prepositions von an (‘from on’), von auf (‘from
upon’), and von in (‘from in’). I take the view that they are the result of the non-application
of the morphological rule of Q-to-P-Lowering and subsequent P/Q-Fusion. In this case, the
P○-node is realized straightforwardly as a geometric place preposition and the synsem feature[−TO] triggers the realization of Q as /fOn/, i.e. von. The PF-instructions for Q are given in
(399). Q is realized as /fOn/ iff it hosts the synsem feature [−TO] and Q-to-P-Lowering and
subsequent P/Q-Fusion has not taken place (i.e. ¬∃P○/Q○). If [−TO] is hosted by P○/Q○ as a
result of Q-to-P-Lowering and subsequent P/Q-Fusion, P is realized as /fOn/ and Q is silent.
(399) PF-instructions for Q:
a. Q ↔ /fOn/ / _ [−TO] ∧ ¬∃P○/Q○
b. ↔ ∅ elsewhere
Note in this context that I assume that, in German, Q-to-P-Lowering and subsequent P/Q-
Fusion always take place at PF by default. Only if speakers want to express a source path
that can only be described by an analytic source preposition (e.g. by von auf ‘from upon’),
they can suppress Q-to-P-Lowering and subsequent P/Q-Fusion.
5.4.2.2 Pseudo-geometric prepositions
This section addresses the derivation of pseudo-geometric (toponymic) goal and source
prepositions and their interpretation at LF as well as their realization at PF. A prototypical
example of the toponymic goal preposition in (‘to, into’) is given in (400).
(400) Hans
Hans
fuhr
drove
in
into
die
the.ACC
Schweiz.
Switzerland
‘Hans drove to Switzerland.’
The structure of pseudo-geometric goal and source prepositions combines the derivational
principle of pseudo-geometric place prepositions discussed in Section 5.4.1.2, namely that
their Root position is empty, with the idea that goal and source prepositions are derived
5.4. Lexical prepositional structure 239
by the light preposition Q above P, which is discussed in Section 5.4.2.1. Considering the
toponymic goal preposition in (‘to, into’) in (400) we can thus assume the structure in (401).
(401) QP
PP
DPP○[LOC, uD]
P○[LOC, uD]∅
Q○[+TO, uP]
Considering the LF-instructions for P formulated in (370) and for Q formulated in (395),
the structure in (401) is interpreted as depicted in (402). The QP is compositionally interpreted
as denoting a func-region r′ of the state of Switzerland x′ that is entered via an anticipated
spatial path w in an anticipated event e. Note that toponymic source prepositions involving
Q[−TO] derive accordingly.
(402) QP
r′ x′
func(r′, x′) enter(w, r′, e)
State-of-Switzerland(x′)
PP
r′ x′
func(r′, x′)
State-of-Switzerland(x′)
DP
x′
State-of-Switzerland(x′)
P○[LOC]
r′
func(r′, x)
Q○[+TO]
enter(w, r, e)
Let us now look at the PF-realization of the structure (401). As in the case of toponymic
place prepositions discussed in Section 5.4.1.2, we can assume that the DP Schweiz (‘Switzer-
land’), which refers to a state, contains the abstract Content feature [ℵ]. This feature is
copied to the P○-node at PF. This yields the intermediate PF-representation in (403a). Then,
240 5. Spatial prepositions at the interfaces
the morphological operations of P-to-Q-Lowering and subsequent P/Q-Fusion take place,
as proposed in (397). This yields P/Q[LOC,ℵPF,+TO] as given in (403b). According the
PF-instructions for P as formulated in (398), this is pronounced as /In/, i.e. in.
(403) a. QP
PP
DP
[©SWITZERLAND,ℵ]
P○[LOC,ℵPF]
Q○[+TO]
b. QP
PP
DPP○/Q○[LOC,ℵPF,+TO]
/In/
So far, the system proposed here straightforwardly derives the (pseudo)-geometric goal
and source prepositions in (‘into, to’), an (‘onto, to’), auf (‘up onto, to’), aus (‘out of, from’),
von an (‘from on, from’), von auf (‘from upon, from’), von in (‘from in, from’), and the non-
geometric source preposition von (‘from’). However, there is a special pseudo-geometric goal
preposition that occurs in the context of determinerless toponyms. Consider the use of nach
(‘to’) in the examples (404). In all these examples, the toponymic place preposition cannot be
used as a toponymic goal preposition, in the way that was possible in the example in (400).
That is, the dative/accusative alternation (or place/goal alternation) seems to fail in this case.
(404) a. Hans
Hans
segelte
sailed
nach/*auf
to/up onto
Hispaniola.
Hispaniola
‘Hans sailed to Hispaniola.’
b. Hans
Hans
flog
flew
nach/*in
to/into
Haiti.
Haiti
‘Hans flew to Haiti.’
c. Hans
Hans
reiste
traveled
nach/*in/*auf
to/into/up onto
Kuba.
Cuba
‘Hans traveled to Cuba.’
5.4. Lexical prepositional structure 241
d. Hans
Hans
fuhr
drove
nach/*in
to/into
Österreich
Austria
‘Hans drove to Austria.’
Let us contrast the examples in (404) with the examples in (405). All toponyms in (405)
are – unlike the ones in (404) – feminine or masculine or plural and hence they cannot occur
determinerless. In these cases, nach (‘to’) is ungrammatical and ‘regular’ pseudo-geometric
goal preposition with accusative is required.
(405) a. Hans
Hans
reiste
traveled
in/*nach
into/to
die
the.FEM.SG.ACC
Türkei.
Turkey
‘Hans traveled to Turkey.’
b. Hans
Hans
ging
went
in/*nach
into/to
den
the.MASC.SG.ACC
Iran.
Iran
‘Hans went to Iran.’
c. Hans
Hans
fuhr
drove
in/*nach
into/to
die
the.PL.ACC
Niederlande.
Netherlands
‘Hans drove to the Netherlands.’
d. Hans
Hans
schwamm
swam
auf/*nach
up onto/to
die
the.FEM.SG.ACC
Pfaueninsel.
Pfaueninsel
‘Hans swam to Pfaueninsel.’
e. Hans
Hans
segelte
sailed
auf/*nach
up onto/to
den
the.MASC.SG.ACC
Darß.
Darß
‘Hans sailed to Darß.’
f. Hans
Hans
zog
moved
auf/*nach
up onto/to
die
the.PL.ACC
Lofoten.
Lofoten
‘Hans moved to Lofoten.’
As illustrated in (406), toponyms that are neuter and singular are typically used determin-
erless,120 while toponyms that are non-neuter (i.e. feminine as in (406b) or masculine as in
(406c)) or non-singular (i.e. plural as in (406d)) are used with a determiner.121
(406) a. (*das)
the.NEUT.SG
Frankreich/Argentinien/Schottland
France/Argentina/Scotland
b. *(die)
the.FEM.SG
Türkei/Schweiz/Mongolei
Turkey/Switzerland/Mongolia
120Interestingly, many neuter and singular toponyms, especially those that name regions in Germany, Aus-
tria, Switzerland, France, and Italy are not determinerless, *(das) Sauerland (‘Sauerland’), *(das) Allgäu (‘All-
gäu’), *(das) Oderbruch (‘Oderbruch’), *(das) Rhinluch (‘Rhinluch’), *(das) Marchfeld (‘Marchfeld’), *(das) Salzkam-
mergut (‘Salzkammergut’), *(das) Tessin (‘Ticino’), *(das) Wallis (‘Valais’), *(das) Elsass (‘Alsace’), *(das) Limousin
(‘Limousin’), *(das) Languedoc (‘Languedoc’), *(das) Latium (‘Lazio’), *(das) Piemont (‘Piedmont’), ?(das) Friaul
(‘Friuli’), etc.
121Concerning the determiner, the toponym Kosovo is particularly interesting because it can either be masculine
or neuter der/(das) Kosovo. It is obligatorily used with a determiner if it is masculine, while it can be used with or
without a determiner if it is neuter. Only since Kosovo has been frequently mentioned in the media – due to the
Yugoslav Wars and especially since its independence in 2008 – there seems to be the tendency away from the
uses as masculine with a determiner towards the uses as neuter without a determiner.
242 5. Spatial prepositions at the interfaces
c. *(der)
the.MASC.SG
Iran/Libanon/Jemen
Iran/Lebanon/Yemen
d. *(die)
the.PL
Niederlande/Lofoten/Kanaren
Netherlands/Lofoten/Canaries
If, however, neuter/singular toponyms are subject to modification, then they necessarily
co-occur with a determiner, as (407).
(407) a. *(das)
the.NEUT.SG
Frankreich
France
des
the.GEN
18.
18th
Jahrhundert-s
century-GEN
‘the France of the 18th century’
b. *(das)
the.NEUT.SG
Argentinien,
Argentina
das
that
er
he
aus
from
seiner
his
Jugend
youth
kennt
knows
‘the Argentina that he knows from his youth’
c. *(das)
the.NEUT.SG
regnerische
rainy
Schottland
Scotland
‘the rainy Scotland’
As soon as neuter/singular toponyms co-occur with a determiner, nach is ungrammatical
and a straightforward toponymic goal preposition must be used (i.e. in, auf, or an). This is
illustrated in (408).
(408) a. Hans
Hans
segelte
sailed
auf/*nach
up onto/to
das
the.NEUT.SG.ACC
tropische
topical
Hispaniola.
Hispaniola
‘Hans sailed to the tropical Hispaniola.’
b. Hans
Hans
flog
flew
in/*nach
to/into
das
the.NEUT.SG.ACC
von
by
einem
an
Erbeben
earthquake
betroffene
affected
Haiti.
Haiti
‘Hans flew to Haiti, that is affected by an earthquake.’
c. Hans
Hans
reiste
traveled
in/auf/*nach
into/up onto/to
das
the.NEUT.SG.ACC
Kuba
Cuba
der
the.GEN
Nachkriegszeit.
post-war era
‘Hans traveled to post-war Cuba.’
d. Hans
Hans
fuhr
drove
in/*nach
into/to
das
the.NEUT.SG.ACC
bergige
mountainous
Österreich
Austria
‘Hans drove to the mountainous Austria.’
We observe that the availability of the special toponymic goal preposition nach depends
on the absence of a determiner. If a toponym occurs without a determiner, then nach is
required as the goal preposition; if, however, a toponym occurs with a determiner, then
nach is ungrammatical as the goal preposition. As for the syntacticosemantic identity of
determinerless toponyms, I follow Matushansky (2015, 2016) and assume that they lack
5.4. Lexical prepositional structure 243
φ-features, i.e. person/number/gender features. This means that determinerless toponyms
can be identified by the absence of φ-features on their D○-head. I represent this as D[¬∃φ].
In order to illustrate the derivation, consider the example with nach in (409a) and the
example with auf in (409b).
(409) a. Hans
Hans
ging
went
nach/*auf
to/up onto
Hispaniola.
Hispaniola
‘Hans went to Hispaniola.’
b. Hans
Hans
ging
went
auf/*nach
up onto/to
das
the.NEUT.SG.ACC
tropische
tropical
Hispaniola.
Hispaniola
‘Hans went to the tropical Hispaniola.’
After PF-copying the abstract Content feature [ℷ] from within the NP to P○ and after Q-to-P-
Lowering and subsequent P/Q-Fusion has taken place, the QP in (409a) can be represented
at PF as given in (410a) and the QP in (409b) can be represented at PF as given in (410b).
(410) a. QP
PP
DP
NP
[©HISPANIOLA, ℷ]
D○[¬∃φ]
P○/Q○[LOC, ℷPF,+TO]
244 5. Spatial prepositions at the interfaces
b. QP
PP
DP
NP
NP
[©HISPANIOLA, ℷ]
AP
D○[φ]
P○/Q○[LOC, ℷPF,+TO]
In both cases, the P○/Q○-node has the feature specification, viz. [LOC, ℷPF,+TO]. The difference
is on the D○-node; it hosts φ-features in (410b), while it does not in (410a). I propose that we
can exploit this difference for the formulation of the PF-instruction for P. In order to account
for the toponymic goal preposition nach (‘to’), we can expand the PF-instructions for P by the
rule in (411a). As the context in (411a) is the most specific one, this rule outranks the other
rules.
(411) PF-instructions for P (fourth version):
a. P ↔ /na:x/ / [ _ [LOC,+TO] ... D[¬∃φ]]
b. ↔ /au<s/ / _ [LOC,ℵ,−TO]
c. ↔ /fOn/ / _ [−TO]
d. ↔ /In/ / _ [LOC,ℵ]
e. ↔ /an/ / _ [LOC,ℶ]
f. ↔ /au<f/ / _ [LOC, ℷ]
g. ↔ /bai</ / _ [AT]
5.4.2.3 Non-geometric prepositions
This section derives the non-geometric goal and source prepositions zu (‘to’) and von (‘from’),
respectively. In line with Noonan (2010), I assume that they are the directional counterparts of
the place peposition bei (‘at’). A prototypical example of the non-geometric goal preposition
zu is given in (412).
(412) Hans
Hans
rannte
ran
zu
to
einem
a.DAT
Wald.
forest
‘Hans ran to a forest.’
5.4. Lexical prepositional structure 245
I propose that the lexical structure of the non-geometric goal preposition zu (‘to’) in (412)
looks as in (413). The light preposition Q above P[AT] can host the synsem feature [+TO]
and thereby derives the non-geometric goal preposition zu. Note at this point that the non-
geometric source preposition von (‘from’) is derived analogously. In that case, Q hosts the
synsem feature [−TO].
(413) QP
PP
DPP○[AT, uD]
P○[AT, uD]∅
Q○[+TO, uP]
Let us now look at the interpretation of this structure at LF. Up to the level of PP, the
interpretation is parallel to the interpretation of the non-geometric place preposition bei (‘at’)
given in (369). The higher P○-node is subject to interpretation at LF. It hosts the synsem feature[AT], which is interpreted as specifying an at-region r′ of an anticipated material object x. In
this example, the DP is interpreted as specifying a forest-entity x′, which instantiates x. That
is, the PP is compositionally interpreted to the effect that r′ is an at-region of the forest x′. At
the next level, the light preposition Q hosts the synsem feature [+TO], whose interpretation
introduces the three-place predicate to(w, r, e); see the definition of the predicate to in (390b).
An anticipated spatial path w, which is a non-transitional spatial path that is conceptualized
as extended, leads to an anticipated region r in an anticipated event e. The discourse referent
r′ is the referential argument of the PP. It instatiates the anticipated region of Q. That is, QP
is compositionally interpreted as denoting an at-region r′ of the forest x′; and an anticipated
spatial path w leads to r′ in an anticipated event e. The LF-representation is given in (414).
246 5. Spatial prepositions at the interfaces
(414) QP
r′ x′
at(r′, x′) to(w, r′, e)
forest(x′)
PP
r′ x′
at(r′, x′)
forest(x′)
DP
x′
forest(x′)
P○[AT]
r′
at(r′, x)
Q○[+TO]
to(w, r, e)
In order to account for the interpretation of Q, we can expand the LF-instructions for
Q by the rules in (415c) and (415d). I assume that Q[±TO] above P[AT] is the less specific
case, as compared to the case when Q[±TO] occurs above P[LOC]. That is, the contexts of
non-geometric goal and source prepositions are less specifc than those of (pseudo)-geometric
goal and source prepositions. As a result, the rules in (415a) and (415b) rank higher than the
rules in (415c) and (415d). Note furthermore that the LF-instructions for P as formulated in
(370) apply straightforwardly and do not need to be extended here.
(415) LF-instructions for Q (second version, final):
a. Q ↔
enter(w, r, e) / [ _ [+TO] ... P[LOC]]
b. ↔
leave(w, r, e) / [ _ [−TO] ... P[LOC]]
c. ↔
to(w, r, e) / _ [+TO]
d. ↔
from(w, r, e) / _ [−TO]
Let us now look at the PF-realization of the structure in (413). As usual, Q lowers to and
subsequently fuses with P at PF. Thus, the non-geometric goal preposition zu (‘to’) involves
the complex morpheme P/Q[AT,+TO], which is realized with the exponent /ts<u:/, i.e. zu; see
(416).
5.4. Lexical prepositional structure 247
(416) QP
PP
DPP○/Q○[AT,+TO]
/ts<u:/
We already have a rule in the PF-instructions for P that accounts for the non-geometric
source preposition von, i.e. /fOn/. The rule In (417c), which was introduced in Section 5.4.2.1,
is underspecified to the effect that it covers both (pseudo)-geometric and non-geometric
source prepositions. So, we need to add only the rule in (417g) in order to account for the
non-geometric goal preposition zu. This rule must rank lower than the rules involving the
synsem feature [LOC], but higher than the rule involving the synsem feature [AT].
(417) PF-instructions for P (fifth version):
a. P ↔ /na:x/ / [ _ [LOC,+TO] ... D[¬∃φ]]
b. ↔ /au<s/ / _ [LOC,ℵ,−TO]
c. ↔ /fOn/ / _ [−TO]
d. ↔ /In/ / _ [LOC,ℵ]
e. ↔ /an/ / _ [LOC,ℶ]
f. ↔ /au<f/ / _ [LOC, ℷ]
g. ↔ /ts<u:/ / _ [+TO]
h. ↔ /bai</ / _ [AT]
5.4.3 Route prepositions
This section discusses the German route prepositions durch (‘through’), um (‘around’), and
über (‘over, across’). Prototypical examples of them are given in (418).
(418) a. Hans
Hans
joggte
jogged
durch
through
einen
a.ACC
Wald.
forest
‘Hans jogged through a forest.’
b. Hans
Hans
ritt
rode
um
around
einen
a.ACC
Wald.
forest
‘Hans rode around a forest.’
c. Hans
Hans
flog
flew
über
over
einen
a.ACC
Wald.
forest
‘Hans flew over a forest.’
Intuitively, the route prepositions durch, um, and über correspond to the place and goal
prepositions in (‘in, into’), an (‘on, onto’), and auf (‘upon, up onto’), respectively. In fact, I will
248 5. Spatial prepositions at the interfaces
claim that the same abstract Content features that give rise to topological geometric place
and goal (and source) prepositions give also rise to route prepositions, but in another synsem
feature context. In the Root position of a locative preposition, the abstract Content feature[ℵ], which relates to interiority, gives rise to the locative prepositions in and aus (‘out of’); in
the Root position of a route preposition, it gives rise to the route preposition durch (‘through’).
In the Root position of a locative preposition, the abstract Content feature [ℶ], which relates
to contiguity, gives rise to the locative preposition an (‘on, onto’); in the Root position of a
route preposition, it gives rise to the route preposition um (‘around’). In the Root position of
a locative preposition, the abstract Content feature [ℷ], which relates to verticality, gives rise
to the locative preposition auf (‘upon, up onto’); in the Root position of a route preposition, it
gives rise to the route preposition über (‘over, across’).
After the discussion in the previous sections on (pseudo)-geometric and non-geometric
prepositions, it should be clear that P[LOC] and P[AT] are characteristic of locative preposi-
tions. But now the question arises of what is characteristic of route prepositions. In a nutshell,
I propose that a third synsem feature is characteristic of route prepositions; I will label this
feature [±NINF], for positive/negative non-initial, non-final paths.
In order to motivate and explicate the synsem feature [±NINF] characteristic of route
prepositions, I should like to draw the reader’s attention to the typology in Figure 35 estab-
lished in Section 5.1.1: goal (and source) prepositions – which are derived from locative place
prepositions – denote directed spatial paths, while route prepositions denote undirected
spatial paths (Jackendoff 1991, Piñón 1993, Kracht 2002, 2008, Zwarts 2005b, Pantcheva 2011).
That is, route prepositions are undirected path prepositions, and, therefore, I model them
in terms of Krifka’s (1998: 203) plain path structure H. In this respect, route prepositions
contrast with goal and source prepositions, which are directed path prepositions. For the
latter, a modeling in terms of Krifka’s (1998: 205) directed path structure D is required; cf.
(259) on page 150, as well as the LF-predicates enter and leave which are based on a directed
path structure (cf. (388) on page 231). Let us look at three properties of route prepositions:
(i) route prepositions are systematically ambiguous with regard to lexical aspect; (ii) route
prepositions do not commit to direction; and (iii) route prepositions do not entail a result
state.
First, all the route prepositions this thesis focuses on are systematically ambiguous be-
tween a bounded and an unbounded interpretation. As discussed in Section 5.1.3, most route
prepositions give rise to a telic (bounded) and an atelic (unbounded) interpretation, when
combined, for instance, with a motion verb; cf. Piñón’s (1993: 298) English examples given in
(312) on page 192; they are repeated here as (419).
(419) a. The insect crawled through the tube {for two hours, in two hours}.
b. The procession walked by the church {for 45 minutes, in 45 minutes}.
c. Mary limped across the bridge {for ten minutes, in ten minutes}.
(Piñón 1993: 298)
5.4. Lexical prepositional structure 249
Consider the German data in (420), too.
(420) a. Hans
Hans
lief
ran
in/für
in/for
30
30
Minuten
minutes
durch
through
den
the
Wald.
.ACC forest
‘Hans ran through the forest in/for 30 minutes.’
b. Hans
Hans
rannte
ran
in/für
in/for
5
5
Minuten
minutes
um
around
den
the.ACC
Turm.
tower
‘Hans ran around the tower in/for 5 minutes.’
c. Hans
Hans
flog
flew
in/für
in/for
3
3
Minuten
minutes
über
over
den
the.ACC
Platz.
square
‘Hans flew over the square in/for 3 minutes.’
Second, route prepositions do not commit to direction, something I already argued for in
Section 4.3, where I also drew attention to the fact that in this respect they differ from goal (and
source) prepositions, which do commit to direction. PPs headed by route prepositions serve
as felicitous modifiers of underived nominals, such as wall or fence that are not conceptualized
as having an inherent direction. PPs headed by goal (or source) prepositions are odd as
modifiers of these nouns; see the examples (210) on page 121 and (211) on page 121. The
example (210a) is repeated here as (421) and the example (211a) as (422). A further example
of a route preposition is (423); further examples of goal and source prepositions are given in
(424) and (425).
(421) [ Die
the
Mauer
wall
durch
through
die
the.ACC
Stadt
city
] wurde
was
niedergerissen.
torn down
‘The wall through the city has been torn down.’
(422) [ Die
the
Mauer
wall
??in
into
die
the.ACC
Stadt
city
] wurde
was
niedergerissen.
torn down
??‘The wall into the city has been torn down.’
(423) Demonstranten
protesters
zerstörten
destroyed
[ den
the
Zaun
fence
um
around
das
the.ACC
Gebäude
building
].
‘Protesters destroyed the fence around the building.’
(424) Demonstranten
protesters
zerstörten
destroyed
[ den
the
Zaun
fence
??an
onto
das
the.ACC
Gebäude
building
].
??‘Protesters destroyed the to around the building.’
(425) [ Die
the
Hecke
hedge
??aus
out of
dem
the
Garten
garden
] hatte
had
Mehltau.
powdery mildew
??‘The hedge out of the garden had powdery mildew.’
I take these data as evidence that Krifka’s (1998: 203) plain path structure H is sufficient for
the modeling of spatial paths denoted by route prepositions.
Third, route prepositions do not entail a result state. Indicating repetition, wieder (‘again’)
can generally give rise to two readings (von Stechow 1996, Beck and Johnson 2004): (i) a
repetitive reading, where a event is repeated, and (ii) a restitutive reading, where a (result)
250 5. Spatial prepositions at the interfaces
state is restored. Ramchand (2012) observes that route prepositions give only rise to a
repetitive reading in the scope of wieder (‘again’), while goal and source prepositions give rise
to a repetitive and restitutive reading in the scope of wieder. Consider the goal and source
prepositions in (426), where both restitutive and repetitive readings are available; and the
route prepositions in (427), where only repetitive readings are available.
(426) a. Hans
Hans
rannte
ran
wieder
again
in
in
den
the.ACC
Wald.
forest
‘Hans ran into the forest again.’
b. Hans
Hans
rannte
ran
wieder
again
aus
out of
dem
the.DAT
Wald.
forest
‘Hans ran out of the forest again.’
(427) a. Hans
Hans
rannte
ran
wieder
again
durch
through
den
the.ACC
Wald.
forest
‘Hans ran through the forest again.’
b. Hans
Hans
rannte
ran
wieder
again
um
around
das
the.ACC
Haus.
house
‘Hans ran around the house again.’
c. Hans
Hans
rannte
ran
wieder
again
über
over
den
the.ACC
Platz.
square
‘Hans ran across the square again.’
I interpret this as follows. The motion verbs in (426) and (427) denote events and thus
repetitive readings are always available here. Goal and source prepositions denote regions,
which can be targeted by result state predications. Thus, they give rise to restitutive readings.
In contrast, route prepositions do not denote regions, which can be targeted by result state
predications. Thus, restitutive readings are not available.
The hypothesis that the semantics of route prepositions does not involve regions is
corroborated by the observation that route prepositions do not provide regions for anaphoric
binding. The goal preposition in (‘into’) in (428a) refers to an in-region of the park at the end
of a spatial path; this region is then available for anaphoric binding by the locative pronoun
dort (‘there’). In contrast, the route preposition durch (‘through’) in (428b) does not refer to an
in-region of the park at the end of a spatial path; and thus dort is infelicitous.
(428) a. Hans
Hans
rannte
ran
in
into
den
the.ACC
Park
park
und
and
blieb
stayed
dort
there
für
for
5
5
Minuten.
minutes
‘Hans ran into the park and stayed there for 5 minutes.’
b. Hans
Hans
rannte
ran
durch
through
den
the.ACC
Park
park
??und
and
blieb
stayed
dort
there
für
for
5
5
Minuten.
minutes
??‘Hans ran through the park and stayed there for 5 minutes.’
I take the view that these semantic differences between goal and source prepositions, on
the one hand, and route prepositions, on the other, serve as indication that the synsem feature[LOC] is absent in the context of route prepositions. If [LOC] was present in the context of
5.4. Lexical prepositional structure 251
route prepositions, this would lead to a semantics involving regions, which then could be
targeted (i) by wieder (‘again’), giving rise to restitutive readings, or (ii) by dort (‘there’) for
anaphoric binding. This means that the synsem feature [LOC], which correlates to regions at
LF, is absent in the structure of route prepositions. Instead, another synsem feature, which I
label [±NINF] (for non-initial, non-final spatial paths), is characteristic of route prepositions.
Below, I justify the feature [±NINF] semantically.
I argue that route prepositions denote route paths that have a tripartite structure. In
particular, a route path w consists of a non-initial, non-final subpath v, the NINF-path, and
two peripheral subpaths z′, z′′, the tail paths. The route path w is the mereological sum of the
NINF-path v and the two tail paths z′z,′′; and both tail paths are adjacent to the NINF-path,
one at each side. This can be illustrated as in (429).
(429) Tripartite structure of route paths w
consisting of a NINF-path v and two peripheral tail paths z′, z′′:
w
tail path
z′
Non-Initial, Non-Final
(NINF) path
v
tail path
z′′
I propose that NINF-paths and route paths figure at LF; tail paths do not. In particular, I
propose that NINF-paths are subject to geometric predication at LF; and route paths are SPs
denoted by route PPs. In Section 5.3, I have defined the LF-predicates durch-bar, um-bar, and
ueber-bar; these predicates geometrically relate line segments to material objects. I propose
that NINF-paths, qua line segments, can be predicated over by these predicates.
Let us now define NINF-paths of route paths in terms of mereological structure. As
mentioned above, I take the view that a route path w has a tripartite structure to the effect
that it consists of a NINF-path v and two tail paths z′, z′′. Recall that I assume that NINF-paths
can be arguments of the LF-predicates durch-bar, um-bar, and ueber-bar. However, the tail
paths z′, z′′ are not completely unaffected by the geometric predication. The definitions of
the LF-predicates durch-bar, um-bar, and ueber-bar in Section 5.3 each consists of a boundary
condition and a configurational condition. That is, when a NINF-path v serves as an argument
of one of the three LF-predicates above, then v also obeys a certain boundary condition B.
I claim that the two tail paths z′, z′′ of a NINF-path v are indistinguishable to the effect that
they either both obey the boundary condition B, or else neither obeys the boundary condition
B. I will discuss this in more detail below. To control for the indistinguishability of z′ and z′′
with regard to the boundary condition B, I use the meta-variable α, which can take either a
positive or negative value.122 Depending on whether the value of α is positive or negative
122That is, if α is positive then ‘αB(v, x)’ = ‘B(v, x)’, and when α is negative then ‘αB(v, x)’ = ‘¬B(v, x)’.
252 5. Spatial prepositions at the interfaces
we can speak of a positive or negative NINF-path. In particular, if α is positive, we speak of
a positive NINF-path v, and the tail paths z′, z′′ obey the same boundary condition B as the
NINF-path v; if α is negative, we speak of a negative NINF-path v, and the tail paths z′, z′′
do not obey the boundary condition B. These considerations give rise to the definition of
a positive/negative NINF-path v of a route path w relative to a material object x as given in
(430).
(430) ∀v, w, x [ninfα(v, w, x)↔
“v is a positive/negative NINF-path of route path w relative to material object x iff”
a. v < w ∧ obj(x)∧ B(v, x)
“v is a proper subpath of w, and v is an internal/external line segment of the
material object x (boundary condition B)”
b. ∧ ∃!z′∃!z′′[z′ < w ∧ z′′ < w
“and there are exactly two paths z′, z′′ (tail paths) that are proper subpaths of
w”
c. ∧ w = z′ ⊕ v⊕ z′′ ∧ z′∞ v∞ z′′
“and w is the mereological sum of z′, v, z′′, and v is adjacent to z′ and to z′′”
d. ∧ αB(z′, x)∧ αB(z′′, x)]]
“and z′, z′′ are indistinguishable with respect to the predicate B.”
We can diagram the two cases for the meta-variable α as in (431) below; the paths that obey
the boundary condition B relating to x are shaded gray.
(431) a. Route path w containing a negative NINF-path v
and two tail paths z′, z′′, i.e. ninf−(v, w, x):
w
z′ v z′′
b. Route path w containing a positive NINF-path v
and two tail paths z′, z′′, i.e. ninf+(v, w, x):
w
z′ v z′′
With this, we can account for the fact that route PPs are systematically ambiguous between
a bounded and an unbounded reading: (i) route PPs denoting route paths containing negative
NINF-paths have bounded reference, while (ii) route PPs denoting route paths containing
positive NINF-paths have unbounded reference. The proofs in Appendix B show that negative
5.4. Lexical prepositional structure 253
NINF-paths give rise to bounded PPs, and that positive NINF-paths give rise to unbounded
PPs.
The semantic considerations concerning route paths above motivate the bivalent synsem
feature [±NINF], which I consider to be characteristic of route prepositions. In fact, I take
the view that route prepositions involve the category P hosting [±NINF], instead of [LOC] or[AT]. The relation between the synsem feature [±NINF] and positive/negative NINF-paths is
straightforward: [+NINF] corresponds to positive NINF-paths, while [−NINF] corresponds to
negative NINF-paths.
Let us now look at the derivation of route PPs. A prototypical example of the route
prepositions durch (‘through’) is given in (432).
(432) Hans
Hans
rannte
ran
durch
through
einen
a.ACC
Wald.
forest
‘Hans ran through a forest.’
The lexical structure of the PP in (432) is depicted in (433). The category P hosts the synsem
feature [±NINF], which is characteristic of route prepositions, and a u-prefixed D-feature
triggering Merge with a DP-complement; the feature [+NINF] yields positive NINF-paths
and thus unbounded route PPs, and the feature [−NINF] yields negative NINF-paths and
thus bounded route PPs. Once P has merged with its DP-complement, it projects a PP and
the u-prefixed D-feature deletes. At the outset of the derivation, P[±NINF, uD] undergoes
Primary Merge and thereby generates a prepositional Root position; cf. Section 2.3. At
Spell-Out, this prepositional Root position serves as the insertion site for abstract Content
features. In the case of the route preposition durch, it is the abstract Content feature [ℵ]
relating to interiority that enters the structure at the Root position of P[±NINF].
(433) PP
DPP○[±NINF,ℵ, uD]
P○[±NINF, uD]√durch[ℵ]
Now, a terminological note is in order. In Section 2.3, I have argued that the notion of
Root is derivational in the sense that a Root is what is inserted into a Root position, i.e. sister
and daughter of a minimal projection; cf. (88) on page 56 and (90) on page 56. With regard to
the abstract Content features characteristic of the spatial preposition discussed in this thesis,
this means that (I) the abstract Content feature [ℵ] is interpreted (I-i) as the Root √durch in
the Root position of P[±NINF] and (I-ii) as the Root √in in the Root position of P[LOC]; (II)
the abstract Content feature [ℶ] is interpreted (II-i) as the Root √um in the Root position of
254 5. Spatial prepositions at the interfaces
P[±NINF] and (II-ii) as the Root √an in the Root position of P[LOC]; and (III) the abstract
Content feature [ℷ] is interpreted (III-i) as the Root √über in the Root position of P[±NINF]
and (III-ii) as the Root
√
auf in the Root position of P[LOC].
Let us look at the semantic interpretation of the structure in (433) at LF. The higher P○-node
is subject to interpretation at LF. It hosts the synsem feature [±NINF] for (positive/negative)
non-initial, non-final SPs,123 and the abstract Content feature [ℵ] relating to interiority. I
propose that P[±NINF,ℵ] is interpreted as specifying a SP v′ that is (i) a durch-bar-path of an
anticipated material object x and (ii) a ninf±-path of an anticipated route path w. The discourse
referent v′ serves as the referential argument of P○. In this example, the DP is interpreted as
specifying a forest-entity x′. The discourse referent x′ serves as the referential argument of the
DP and instantiates the anticipated discourse referent x. The PP is interpreted to the effect
that v′ is a durch-bar-path of the forest x′. The discourse referent v′ is the referential argument
of the PP. The semantic interpretation of the structure in (433) at LF is depicted in (434).
(434) PP
v′ x′
durch-bar(v′, x′) ninf±(v′, w, x′)
forest(x′)
DP
x′
forest(x′)
P○[±NINF,ℵ]
v′
durch-bar(v′, x)
ninf±(v′, w, x)
At this point, it is important to note that nothing in the syntactic module prevents the light
preposition Q from merging with a PP the head of which hosts the synsem feature [±NINF]
for route prepositions. However, such a derivation would crash at LF because Q[+TO], e.g.,
would be interpreted at LF as contributing the three-place predicate to characteristic of goal
paths. Consider (435) where Q[+NINF] merges with a route PP. The interpretation of the PP
involves an anticipated path w1, and the interpretation of Q○ involves an anticipated path
w2. Principally, they could unify with one another. Alternatively, the referential argument of
the PP v′ could unify with w2. However – and this is the crucial point – there is and there
will be no region available in the derivation of the fully-fledged PP that can unify with the
anticipated region r stemming from Q○.
123Note that the distinction between positive and negative NINF-paths is not crucial here. Therefore, I subsume
them under ‘±’ (positive/negative).
5.4. Lexical prepositional structure 255
(435) #QP
v′ x′
durch-bar(v′, x′) ninf±(v′, w1, x′)
to(w2, r, e) forest(x′)
PP
v′ x′
durch-bar(v′, x′) ninf±(v′, w1, x′)
forest(x′)
DP
x′
forest(x′)
P○[±NINF,ℵ]
v′
durch-bar(v′, x)
ninf±(v′, w1, x)
Q○[+TO]
to(w2, r, e)
In Section 5.5.2, I will introduce the LF-operation Dx-Adjustment, which adjusts the deictic
node Dx○ such that it fits the semantic contribution of its complement. In fact, the situation is
quite parallel to the situation here. The node Dx○ anticipates a region which might not be
filled by the referential argument of its complement. The complement of Dx○, which is AspP
in that case, can sometimes only provide a path. In that case, Dx-Adjustment adjusts the
interpretation of Dx○ such that a path can serve as the semantic input (cf. (465) on page 271).
A crucial difference with Dx-Adjustment is, however, that, here, no morphophonological
justification for such an operation is given. While Dx-Adjustment corresponds to the overt
realization of the node Dx○ as hin- (‘thither’) or her- (‘hither’), no such realizations of Q○ exist.
The derivations of the two other route prepositions um (‘around’) and über (‘over, across’)
differ from the derivation of durch (‘through’) in the choice of the abstract Content feature.
While durch comprises [ℵ] relating to interiority, um comprises [ℶ] relating to contiguity,
and über comprises [ℷ] relating to verticality. In order to account for the interpretations of
these three route prepositions, we can expand the LF-instructions for P by the rules in (436a),
(436b), and (436c), respectively. When [±NINF] pairs with the abstract Content feature [ℵ], P
is interpreted as specifying a SP v′ that is (i) a durch-bar-path of an anticipated material object
x and (ii) a ninf±-path of an anticipated route path w relative to an anticipated material object
x; when [±NINF] pairs with the abstract Content feature [ℶ], P is interpreted as specifying
a SP v′ that is (i) an um-bar-path of an anticipated material object x and (ii) a ninf±-path
of an anticipated route path w relative to an anticipated material object x; when [±NINF]
pairs with the abstract Content feature [ℷ], P is interpreted as specifying a SP v′ that is (i) an
ueber-bar-path of an anticipated material object x and (ii) a ninf±-path of an anticipated route
256 5. Spatial prepositions at the interfaces
path w relative to an anticipated material object x. Note that the rules in (436a), (436b), and
(436c) are more specific than the other rules for P, and thus they rank higher.
(436) LF-instructions for P (fourth version, final):
a. P ↔ v′
durch-bar(v′, x)
ninf±(v′, w, x)
/ _ [±NINF,ℵ]
b. ↔ v′
um-bar(v′, x)
ninf±(v′, w, x)
/ _ [±NINF,ℶ]
c. ↔ v′
ueber-bar(v′, x)
ninf±(v′, w, x)
/ _ [±NINF, ℷ]
d. ↔ r′
in(r′, x) / _ [LOC,ℵ]
e. ↔ r′
an(r′, x) / _ [LOC,ℶ]
f. ↔ r′
auf(r′, x) / _ [LOC, ℷ]
g. ↔ r′
func(r′, x) / _ [LOC]
h. ↔ r′
at(r′, x) / _ [AT]
At this point, we should address the question of how the DRSs assigned to P in the NINF-
contexts are interpreted model-theoretically. In Section 5.3, I have defined the LF-predicates
durch-bar, um-bar, and ueber-bar. These predicates geometrically relate line segments to
material objects. Each of these three LF-predicates impose one boundary condition (intlis
or extlis) and one configurational condition (spear-like, L-shaped, or plumb-square) on a line
segment v with regard to a material object x. In the case of durch-bar, the line segment must be
an internal and spear-like line segment of the material object; cf. (330) on page 204. In the case
of um-bar, the line segment must be an external line segment of the material object, and an
L-shaped line segment; cf. (332) on page 205. In the case of ueber-bar, the line segment must
be an external and plumb-square line segment of the material object; cf. (335) on page 208.
This is summarized in Table 11.
durch-bar(v, x) um-bar(v, x) ueber-bar(v, x)
boundary condition intlis(v, x) extlis(v, x) extlis(v, x)
configurational condition spear-like(v, x) L-shaped(x) plumb-square(v, x)
Table 11: Model-theoretic decomposition of durch-bar, um-bar, and ueber-bar
5.4. Lexical prepositional structure 257
Earlier in this section, I have defined the LF-predicate ninf± for positive and negative
NINF-paths. Positive NINF-paths underlie unbounded route paths, while negative NINF-paths
underlie bounded route paths. According to the definition of ninf±-paths, route paths w have
a tripartite structure, consisting of a NINF-path v and two peripheral tail paths z′ and z′′. At
LF, the NINF-path v is argument to one of the predicates durch-bar, um-bar, and ueber-bar. The
tail paths z′, z′′ are not visible at LF; however, the definition of the predicate ninf± imposes
the boundary condition relative to the material object x also on the tail paths. In the case of
ninf+, the tail paths z′, z′′ must obey the boundary condition; in the case of ninf−, the tail paths
z′, z′′ must not obey the boundary condition. Let us map the LF-predicates ninf−(v, w, x) and
ninf+(v, w, x) to the LF-predicates durch-bar(v, x), um-bar(v, x), and ueber-bar(v, x); where v is
the NINF-path; w is the route path, z′, z′′ are the tail paths, and x is a material object. This
yields the model-theoretic spell out of the route predicates as depicted in Table 12.
durch-bar(v, x) um-bar(v, x) ueber-bar(v, x)
ninf−(v, w, x) x
vz′ z′′ x vz′
z′′ x
vz′ z′′
DOWN
NINF-path v:
intlis(v, x)∧ spear-like(v, x)
tail paths z′, z′′:¬ intlis(z′, x)∧¬ intlis(z′′, x)
NINF-path v:
extlis(v, x)∧ L-shaped(v)
tail paths z′, z′′:¬ extlis(z′, x)∧¬ extlis(z′′, x)
NINF-path v:
extlis(v, x)∧ plumb-square(v, x)
tail paths z′, z′′:¬ extlis(z′, x)∧¬ extlis(z′′, x)
ninf+(v, w, x) x
vz′ z′′ x vz′
z′′ x
vz′ z′′
DOWN
NINF-path v:
intlis(v, x)∧ spear-like(v, x)
tail paths z′, z′′:
intlis(z′, x)∧ intlis(z′′, x)
NINF-path v:
extlis(v, x)∧ L-shaped(v)
tail paths z′, z′′:
extlis(z′, x)∧ extlis(z′′, x)
NINF-path v:
extlis(v, x)∧ plumb-square(v, x)
tail paths z′, z′′:
extlis(z′, x)∧ extlis(z′′, x)
Table 12: Model-theoretic spell out of route predicates
Let us now turn to the morphophonological realizations of P[±NINF] at PF. I propose that
German provides a PF-instruction to the effect that P[±NINF,ℵ] in the prepositional structure
in (433) is realized as /dUrç/, i.e. durch; this is illustrated in (437).
(437) PP
DPP○[±NINF,ℵ]
/dUrç/
258 5. Spatial prepositions at the interfaces
In order to account for the morphophonological realizations for the route prepositions durch
(‘through’), um (‘around’), and über (‘over, across’), we can now expand the PF-instructions
for P by the rules in (438d), (438e), and (438f), respectively.
(438) PF-instructions for P (sixth version, final):
a. P ↔ /na:x/ / [ _ [LOC,+TO] ... D[¬∃φ]]
b. ↔ /au<s/ / _ [LOC,ℵ,−TO]
c. ↔ /fOn/ / _ [−TO]
d. ↔ /dUrç/ / _ [±NINF,ℵ]
e. ↔ /Um/ / _ [±NINF,ℶ]
f. ↔ /y:b5/ / _ [±NINF, ℷ]
g. ↔ /In/ / _ [LOC,ℵ]
h. ↔ /an/ / _ [LOC,ℶ]
i. ↔ /au<f/ / _ [LOC, ℷ]
j. ↔ /ts<u:/ / _ [+TO]
k. ↔ /bai</ / _ [AT]
Finally, let me note that route prepositions with a certain abstract Content feature receive the
same morphophonological realization, irrespective of the question of whether they denote
route paths containing positive or negative NINF-paths. That is, the difference between[+NINF] and [−NINF] does not figure at PF.
5.5 Functional prepositional structure
In line with Van Riemsdijk (1990), Koopman (2000, 2010), Den Dikken (2010), Noonan (2010),
Svenonius (2010), a.o., I assume that fully-fledged prepositions project functional structure.
Van Riemsdijk (1990) – who uses the term ‘little p’ for functional prepositional structure –
argues that, in German, elements like her-auf (‘hither-upon’) in (439) can be hosted in the
functional prepositional structure.
(439) a. (*her-auf)
hither-upon
auf
upon
den
the.ACC
Berg
mountain
her-auf
hither-upon
b. her-auf
hither-upon
auf
upon
den
the.ACC
Berg
mountain
(*her-auf)
hither-upon
In German, it is typically the case that the lexical preposition is linearized to the left of its DP
complement, while the functional prepositional structure is linearized to the right of the DP.
That is, (439a) shows the canonical position of the functional prepositional structure.124 Due
to this fact, I represent the functional structure of prepositions to the right, even though the
structural representation is independent from the ultimate linearization. The right-headed
124Concerning the canonical linearization of lexical and functional prepositional structure Van Riemsdijk
observes that Hungarian shows the mirror image of German. In particular, he (1990: 241) states that Hungarian
typically shows the linearization [ p○ [ DP P○ ] ], while German typically shows the linearization [ [ P○ DP ] p○ ].
5.5. Functional prepositional structure 259
structures I present here should thus be seen as a convenient anticipation of the typical
linearization. Note, however, that the functional structure can – under certain circumstances –
precede the lexical preposition. This is given in (439b).
With regard to functional prepositional structure, I adopt Den Dikken’s (2010) proposal
that each fully-fledged (spatial) PP projects (i) an aspectual layer (AspP), (ii) a deictic layer
(DxP), and (iii) a complementizer layer (CP). Den Dikken proposes the parallelism of func-
tional structures in (440) across lexical domains.
(440) Parallelism of functional structures across domains:
a. verbal domain
C[FORCE] > Dx[TENSE] > Asp[EVENT] > V
b. nominal domain
C[DEF] > Dx[PERSON] > Asp[NUM] > N
c. spatial prepositions
C[SPACE] > Dx[SPACE] > Asp[SPACE] > P
(Den Dikken 2010: 100, 104)
I assume that the functional categories can host syntacticosemantic (synsem) features,
which I briefly present in the following. A crucial question in the domain of spatial preposi-
tions is whether the preposition speaks of a stative or dynamic spatial configuration. The
former are typically descriptions of regions, while the latter are descriptions of spatial paths.
I thus assume that prepositional C can host the synsem feature [±MOTION]. Prepositional
C is addressed in Section 5.5.1. Concerning deixis, I assume that prepositional Dx can host
the synsem feature [±PROX] (for proximity). Prepositional Dx is addressed in Section 5.5.2.
Concerning aspect, I assume that prepositional Asp can host the synsem feature [±UNBD]
(for unbounded). Prepositional Asp is addressed in Section 5.5.3. These considerations give
rise to the functional prepositional structure in (441).125
(441) CP
C○[±MOTION]DxP
Dx○[±PROX]AspP
Asp○[±UNBD]PP/QP
125Note that I henceforth omit Den Dikken’s [SPACE].
260 5. Spatial prepositions at the interfaces
I assume that Head Movement (Matushansky 2006) derives a Complex Head (Embick and
Noyer 2007: 303–304). The Complex Head structure of the functional prepositional structure
is depicted in (442).
(442) C○
C○Dx○
Dx○Asp○
Two potential realization patterns of functional prepositional structure figure in this thesis.
First, echo extensions are postpositional elements that can co-occur with geometric preposi-
tions, either place or path. As noted earlier, the term echo extension has been adopted from
Abraham (2010). There is, however, some terminological variation. Inspired by Perlmutter’s
term shadow pronoun (Perlmutter 1972), Noonan (2010: 164) refers to echo extensions as shadow
Ps. Generally, echo extensions consist of a recurrence of the preposition that is preceded by
a deictic element. Recall the construction auf ... her-auf (lit.: upon ... hither-upon) in (439).
The first, unpaired, occurrence of auf (‘upon’) arguably corresponds to the lexical category
P. Hence, the complex element her-auf (lit.: hither-upon) must correspond somehow to the
sequence of functional categories Asp-Dx-C that derives from the Complex Head structure in
(442). The morpheme her (‘hither’) is a deictic element and thus corresponds to the functional
category Dx, which is addressed in Section 5.5.2. I assume that the second occurrence of auf,
i.e. the one that forms a unit with her, corresponds to the functional category C, which is
addressed in Section 5.5.1. Table 13 lists the potential German echo extensions of geometric
prepositions according to the abstract topological Content feature residing in the Root posi-
tion of P. Note that deictic elements that are underlined in Table 13 have become obsolescent
in Standard German but are in fact historically attested.126
The second construction where the functional structure of prepositions (morphophono-
logically) is manifest are unbounded non-geometric path prepositions. As presented in
Section 5.1.3, German has the two prepositional constructions von ... weg (‘away from’) and
auf ... zu (‘towards’) that both consist of a prepositional element (i.e. von and auf ) and a
postpositional element (i.e. weg and zu). These prepositional constructions are in fact cir-
cumpositions. Both von ... weg and auf ... zu are (i) unbounded and (ii) non-geometric path
prepositions. By assumption, they are the unbounded counterparts of the bounded non-
126See Grimm’s Deutsches Wörterbuch (‘German Dictionary’), which is accessible online:
hin-an: http://www.woerterbuchnetz.de/DWB?lemma=hinan,
dr-um: http://www.woerterbuchnetz.de/DWB?lemma=darum,
hin-um: http://www.woerterbuchnetz.de/DWB?lemma=hinum,
her-durch: http://www.woerterbuchnetz.de/DWB?lemma=herdurch
5.5. Functional prepositional structure 261
place prepositions path prepositions
P Dx-C P Dx-C[ℵ] in ... dr-in in ... her-/hin-ein
aus ... her-/hin-aus
durch ... her-/hin-durch[ℶ] an ... dr-an an ... her-/dr-/hin-an
um ... her-/dr-/hin-um[ℷ] auf ... dr-auf auf ... her-/dr-/hin-auf
über ... her-/dr-/hin-über
Table 13: Echo extensions of geometric prepositions
geometric path prepositions von (‘from’) and zu (‘to’). As illustrated in Table 14, I assume that
the prepositional elements of non-geometric path prepositions relate to the category P, while
the postpositional elements of the unbounded non-geometric path prepositions relate to the
functional category Asp; cf. Section 5.5.3.
bounded unbounded
P Asp P Asp
goal prepositions zu ... ∅ auf ... zu
source prepositions von ... ∅ von ... weg
Table 14: Bounded and unbounded non-geometric path prepositions
Before discussing the functional prepositional categories in the following sections, it is
worth mentioning three things concerning echo extensions of German geometric preposi-
tions. First, it is interesting that echo extensions are straightforwardly felicitous only with
topological prepositions and with those projective prepositions that relate to the vertical axis
(über ‘above’ and unter ‘under’). Other spatial prepositions involving geometric information
are typically considered to be marked (443).127 Note that in the case of projective path prepo-
sitions (443b), the optional usage of the bare deictic elements hin and her are grammatical.
However, no recurrence of the preposition is possible.
(443) a. Hans
Hans
saß
sat
vor
in front of
der
the.DAT
Hütte
hut
(??davor).
there.in front of
‘Hans sat in front of the hut.’
b. Hans
Hans
rannte
ran
hinter
behind
die
the.ACC
Scheune
barn
(her/hin-*hinter).
hither/thither-behind
‘Hans ran behind the barn.’
Second, echo extensions should be distinguished from verbal particles, which can arguably
occur in the same position as echo extensions. Consider (444) involving the particle verb
ein-marschieren (‘march in’). The path PP in das Stadion is an optional argument of the verb.
127Note that da- corresponds to dr-. It is the form that is used when a consonant follows.
262 5. Spatial prepositions at the interfaces
(444) Hans
Hans
marschierte
marched
(in
into
das
the.ACC
Stadion)
stadium
ein.
in
‘Hans marched into the stadium.’
This type of verbal particles is clearly related to the functional structure of prepositions. This
can be seen from the contrast in the examples (445). When the verb is bare as in (445a), echo
extensions are possible. However, when the verb is combined with a verbal particle as in
(445b), echo extensions are blocked.
(445) a. Hans
Hans
konnte
could
in
into
das
the.ACC
Stadion
stadium
(hinein)
thither.in
marschieren.
march
‘Hans could march into the stadium.’
b. Hans
Hans
konnte
could
in
into
das
the.ACC
Stadion
stadium
(*hinein)
thither.in
ein-marschieren.
in-march
‘Hans could march into the stadium.’
These data suggest that echo extensions and some types of verbal particles share the same
structural position, or put differently, that some types of verbal particles correlate to the
functional structure of prepositions. Nevertheless, there is a crucial difference between echo
extensions, on the one hand, and this kind of verbal particles, on the other. The availability of
echo extensions seems to be independent of the verb – as long as they obey the prepositional
requirements – (446a), while the availability of verbal particles also depends on the verb in
combination with its complement noun (446b).128
(446) a. Hans
Hans
rannte
ran
in
into
den
the.ACC
Wald
forest
(hin-ein).
thither-in
‘Hans ran into the forest.’
b. Hans
Hans
rannte
ran
(in
into
den
the.ACC
Wald)
forest
??ein.
in
That is, the analysis of verbal particles, in contrast to the analysis of echo extensions, must
focus also on the respective verbs. I have nothing more to say about verbal particles in this
thesis. For further discussion of verbal particles across languages and frameworks, I refer
the reader to the extensive body of literature on particle verbs: Stiebels and Wunderlich
(1994), Den Dikken (1995), Stiebels (1996, 1998), Svenonius (1996, 2003, 2004, 2007a), Zeller
(1997, 2001a,b), Olsen (1998), Wurmbrand (1998, 2000), Lüdeling (1999), McIntyre (2001,
2002, 2003, 2004, 2007), Dehé et al. (2002), and contributions therein, Müller (2002), Nicol
(2002), Ramchand and Svenonius (2002), Aktas¸ (2005), Kolehmainen (2005), Romanova (2006),
Basilico (2008), Kliche (2008), Mateu (2008), Lechler and Roßdeutscher (2009), Levin and
Sells (2009), Heine et al. (2010), Mateu and Rigau (2010), Biskup et al. (2011), Dewell (2011),
Haselbach (2011), Roßdeutscher (2011, 2012, 2013), Öhl and Falk (2011), Springorum (2011),
Punske (2012), Ramchand (2012), a.o.
128So far, the restrictions on verbal particles are not well-understood.
5.5. Functional prepositional structure 263
Third, echo extensions must also be distinguished from other kinds of postpositional
elements that can co-occur with spatial prepositions. Consider, for instance, the direction-
indicating postpositions in (447) and (448).
(447) Die
the
Schnecke
snail
kroch
crept
auf
upon
das
the.ACC
Dach
roof
hin-auf/hin-ab/hin-über.
up/down/across
‘The snail crept up/down/across onto the roof.’
(Van Riemsdijk 2007: 267)
(448) Sam
Sam
tauchte
dived
in
into
die
the.ACC
Dunkelheit
darkness
hin-ab.
thither-down
‘Sam descended into darkness.’
(Abraham 2010: 267)
These direction-indicating postpositions clearly share some superficial commonalities with
echo extensions, namely that they involve some deictic element followed by some prepo-
sitional element. In fact, I assume that the deictic element of both echo extensions and
direction-indicating postpositions, and their non-deictic elements relate to the same func-
tional categories – the deictic elements relate to the prepositional functional category Dx
and the non-deictic elements relate to the prepositional functional category C. However,
direction-indicating postpositions differ from echo extensions in several respects, which justi-
fies the assumption that additional direction-related features are involved in the derivation
of direction-indicating postpositions.
For one, while the echo extensions in (449a) and (449d) can contain one of the three deictic
elements hin- (‘thither’), her- (‘hither’), or dr- (‘there’), the direction-indicating postpositions
in (449b) and (449c) can only contain either hin- or her-, but not dr-.
(449) a. Hans
Hans
sprang
jumped
auf
up onto
das
the.ACC
Dach
roof
hin-/her-/dr-auf
thither-/hither-/there-upon
‘Hans jumped onto the roof.’
b. Hans
Hans
sprang
jumped
auf
up onto
das
the.ACC
Dach
roof
hin-/her-/*dr-ab
thither-/hither-/there-down
‘Hans jumped down onto the roof.’
c. Hans
Hans
sprang
jumped
auf
up onto
das
the.ACC
Dach
roof
hin-/her-/*dr-über
thither-/hither-/there-over
‘Hans jumped over onto the roof.’
d. Hans
Hans
sprang
jumped
über
over
das
the.ACC
Dach
roof
hin-/her-/dr-über
thither-/hither-/there-over
‘Hans jumped over onto the roof.’
Moreover, direction-indicating postpositions can typically co-occur with projective prepo-
sitions (450a), unlike echo extensions (450b).
264 5. Spatial prepositions at the interfaces
(450) a. Hans
Hans
lief
walked
vor
in front of
das
the.ACC
Haus
house
hin-über.
thither-over
‘Hans walked over in front of the house.’
b. Hans
Hans
lief
walked
vor
in front of
das
the.ACC
Haus
house
*hin-*vor.
thither-in front of
‘Hans walked in front of the house.’
In this context I want to draw attention to the constructions given in (451), consisting of
a place preposition triggering dative and some postpositional element indicating direction.
Note, however, that I do not dwell on these in this thesis.
(451) a. Hans
Hans
rannte
ran
unter
under
der
the.DAT
Brücke
bridge
(hin)-durch.
thither-through
‘Hans ran under the bridge.’
b. Hans
Hans
rannte
ran
an
at
der
the.DAT
Hütte
hut
vorbei.
past
‘Hans ran past our house.’
On a final note, I leave direction-indicating postpositions for further research and refer
the reader in particular to Van Riemsdijk (2007), Svenonius (2007a, 2010), Abraham (2010),
Noonan (2010) for an in-depth discussion concerning postpositions indicating direction.
5.5.1 C-features
Concerning the functional structure of prepositions, I assume, following Den Dikken (2010),
that C (for complementizer) is the highest functional category in the prepositional domain.
Prepositional C can host the syntacticosemantic (synsem) feature [±MOTION] that corre-
sponds to the distinction between place and path prepositions established in Section 5.1.1. In
particular, [−MOTION] is characteristic for place prepositions, while [+MOTION] is character-
istic for path prepositions. That is, C[−MOTION] is tantamount to Den Dikken’s (2010: 104)
C[PLACE] and C[+MOTION] to his (2010: 104) C[PATH].
Let us first look at the LF-instructions for prepositional C. I propose that the main function
of the prepositional C is to introduce the referential argument of spatial PPs. The referential
argument of place prepositions is a region and the referential argument of path prepositions is
a spatial path. Therefore, I propose the LF-instructions for prepositional C in (452). Consider
first the case of path PPs in (452a), i.e. C[+MOTION]. The spatial path w′, which serves as the
referential argument of a path PP, is an argument of an anticipated Figure/Path Relation RFPR
(Beavers 2012) that is to be contextually instantiated through unification. For instance, when
a path PP is combined with a verbal motion predicate, this motion predicate instantiates the
anticipated Figure/Path Relation. Consider now the case of place PPs in (452b). The region
r′, which serves as the referential argument of a place PP, is an argument of an anticipated
stative relation ROCC to the effect that an anticipated Figure y occupies the region r′. When
5.5. Functional prepositional structure 265
a place PP is integrated in a verbal stative predicate, this stative predicate instantiates the
anticipated relation.
(452) LF-instructions for C:
a. C ↔ w′
RFPR(y, w′, e) / _ [+MOTION]
b. ↔ r′
s ∶ ROCC(y, r′) / _ [−MOTION]
Let us now look at the PF-instructions for prepositional C that figure in the context of echo
extensions. Echo extensions necessarily consist of two parts, a deictic morpheme, which is
hosted in Dx (cf. Section 5.5.2), and a morpheme that is (nearly) equivalent to the respective
lexical P. I assume that the recurrence P is related to prepositional C. Table 15 lists the echo
extensions according to the abstract Content features that can be involved in P.129
geometric geometric
place prepositions path prepositions
P Dx-C P Dx-C[ℵ] in ... dr-in in ... her-/hin-ein
aus ... her-/hin-aus
durch ... her-/hin-durch[ℶ] an ... dr-an an ... her-/dr-/hin-an
um ... her-/dr-/hin-um[ℷ] auf ... dr-auf auf ... her-/dr-/hin-auf
über ... her-/dr-/hin-über
Table 15: Recurrence of geometric prepositions in echo extensions
At least two factors condition the pronunciation of C: (i) the question of whether Dx is
pronounced or not, and (ii) the phonological matrix of P. The example in (453a) shows that
echo extensions necessarily consist of two parts. Neither the deictic morpheme (453b), nor
the recurrence of P alone (453c) can occur alone.130
(453) a. Hans
Hans
rannte
ran
in
into
den
the.ACC
Wald
forest
hin-/her-ein.
thither-/hither-in
‘Hans ran into the forest.’
b. Hans
Hans
rannte
ran
in
into
den
the.ACC
Wald
forest
*hin/*her.
thither/hither
‘Hans ran into the forest.’
c. Hans
Hans
rannte
ran
in
into
den
the.ACC
Wald
forest
??ein.
in
‘Hans ran into the forest.’
129Note that in the case when in (‘in’) serves as a path preposition the respective recurring element is -ein,
which is obviously morphologically related to in.
130Note that the recurrence of P in (453c) could be understood as a verbal particle, which is not intended here.
266 5. Spatial prepositions at the interfaces
Crucially, only a copy of the phonological matrix of P is a licit part of an echo extension. This
is illustrated for place prepositions in (454) and for path prepositions in (455).
(454) a. Hans
Hans
lag
lay
in
in
der
the.DAT
Kiste
box
dr-in/*auf/*an.
there-in/upon/on
‘Hans lay in the box.’
b. Hans
Hans
stand
stood
an
on
der
the
Wand
wall
dr-an/*auf/*in
there-on/upon/in
‘Hans stood at the wall.’
c. Hans
Hans
saß
sat
auf
upon
dem
the.DAT
Tisch
table
dr-auf/*in/*an.
there-upon/in/on
‘Hans sat upon the table.’
(455) a. Hans
Hans
rannte
ran
in
in
den
the.ACC
Wald
forest
her-ein/*an/*aus/*durch/*...
hither-in/on/out/through/...
‘Hans ran into the forest.’
b. Hans
Hans
kam
came
aus
out
dem
the.DAT
Zimmer
room
her-aus/*ein/*durch/*um/*...
hither-out/in/through/around/...
‘Hans came out of the room.’
c. Hans
Hans
kroch
crawled
durch
through
die
the.ACC
Hecke
hedge
hin-durch/*ein/*um/*...
thither-through/into/around/...
‘Hans crawled through the hedge.’
d. Hans
Hans
schwamm
swam
über
over
den
the.ACC
Fluß
river
hin-über/*durch/*um/*...
thither-over/through/around/...
‘Hans swam across the river.’
The fact that the non-deictic element of an echo extension is (nearly) equivalent to the
morphological surface form of the respective preposition suggests a reduplication-type
of approach (Haugen 2008, 2011, Haugen and Harley 2013). In fact, I assume that the
phonological matrix of the lexical category P is reduplicated under certain conditions and
thereby determines the pronunciation of the functional category C. In fact, I propose PF-
instructions that take the phonological matrix of categories in the local context into account. In
particular, I propose the PF-instructions for prepositional C in (456). At PF, the phonological
matrix of P is assigned (copied) to C iff (i) the phonological matrix of Dx is not zero, and (ii)
the Root position of P is filled with one of the abstract topological Content features [ℵ], [ℶ],
or [ℷ].131 Otherwise, C is silent.132
(456) PF-instructions for prepositional C:
a. C ↔ ℘(P) / ℘(Dx) /= ∅ ∧ [ P[ℵ] ∨ P[ℶ] ∨ P[ℷ] ]
b. ↔ ∅ elsewhere
131I use ‘℘’ as function at PF that provides the phonological matrix of a terminal node. For instance,℘(P[LOC,ℶ]) = /an/; cf. the PF-instructions for P as given in (438) on page 258.
132Note that, in order to account for other types of postpositional elements, e.g. extensions indicating direction
or verbal particles, the set of PF-instructions for prepositional C must be more comprehensive than given in
(456). Nevertheless, for echo extensions, which are in the focus of this thesis, this set of PF-rules suffices.
5.5. Functional prepositional structure 267
This correctly predicts that echo extensions are illicit in the context of pseudo-geometric
and non-geometric prepositions, because they lack a filling of the Root position of P. Further,
it predicts the recurrence of a preposition as part of an echo extension. And lastly, it predicts
that echo extensions must involve a phonologically overt deictic element together with a
phonologically overt non-deictic element.
Note that copying the phonological matrix of P to prepositional C predicts for the path
preposition in (‘into’) the ungrammatical echo extensions her-/hin-*in, i.e. /In/, instead of
the grammatical echo extensions her-/hin-ein, i.e. /ai<n/. In order to achieve the proper
phonological matrix of C , I assume that a morphological Readjustment Rule (cf. Section 3.6)
is appropriate. In particular, I propose the Readjustment Rule in (457) that transforms the
phonological matrix of C from /In/ (-in) to /ai<n/ (-ein) in the context of a path preposition, i.e.
C[+MOTION].
(457) /In/ → /ai<n/ / ℘(C) = /In/ ∧ C[+MOTION]
5.5.2 Deictic features
This section focuses on the deictic elements that are found as parts of echo extensions in Stan-
dard German geometric prepositions including place, goal, source, and route prepositions.133
In particular, we find the three deictic elements dr- (short for dar-, ‘there’), her- (‘hither’),
and hin- (‘thither’). Taking the abstract Content features [ℵ], [ℶ], and [ℷ] into account, these
deictic elements are distributed across place and path prepositions as given in Table 16.
geometric geometric
place prepositions path prepositions
P Dx-C P Dx-C[ℵ] in ... dr-in in ... her-/*dr-/hin-ein
aus ... her-/*dr-/hin-aus
durch ... her-/*dr-/hin-durch[ℶ] an ... dr-an an ... her-/dr-/hin-an
um ... her-/dr-/hin-um[ℷ] auf ... dr-auf auf ... her-/dr-/hin-auf
über ... her-/dr-/hin-über
Table 16: Deictic elements in echo extensions
In the context of place prepositions, we only find the morpheme dr-. In contrast, in the
context of path prepositions, we find her-, hin-, and dr-, except for the case when the abstract
Content feature [ℵ] is present. Note in this regard that deictic elements that are underlined
in Table 16 became obsolescent in Standard German but are in fact historically attested, cf.
133Note that the deictic marking on postpositional elements is generally to a great extent subject to di-
alectal and regional variation. For a study concerning the regional differences of the element hin-/her-ein
(lit.: thither-/hither-in), see: http://www.philhist.uni-augsburg.de/lehrstuehle/germanistik/
sprachwissenschaft/ada/runde_2/f24a-b/
268 5. Spatial prepositions at the interfaces
Footnote 126 on page 260. I have nothing to say in this thesis concerning the question of why
these forms became obsolescent. I leave this question for future work.
In general, spatial deictic expressions denote locations that are interpreted relative to
location of the speaker of an utterance.134 In fact, I assume that the spatial deixis of the
echo extensions in German is best understood in terms of a relation between two regions, a
deictic reference region, which is the region denoted by the deictic expression, and a deictic
center (or origo, cf. Bühler 1934, Kaplan 1989), a region which is typically determined by the
speaker’s self-location at the time of utterance.
The speaker-dependent definition of the deictic center means that the deictic center can
constantly change between the interlocutors in a conversation. Consider the English spatial
adverb here denoting locations that are included in the deictic center. Assume the telephone
conversion in (458) between interlocutor A in Stuttgart and interlocutor B in New York. In
(458a), here denotes the location of interlocutor A, i.e. Stuttgart, while it denotes the location
of interlocutor B, i.e. New York, in (458b).
(458) a. Interlocutor A:
“Here in Stuttgart, the weather is nice. How is it in New York?”
b. Interlocutor B:
“Here in New York, we have bad weather.”
Further, the region that is conceptualized as the deictic center can vary with the construal
of the speech situation. In (459), the conceptualization of the deictic center varies considerably,
ranging from a rather small location in (459a) to a huge location in (459e).
(459) a. Here where I am.
b. Here in this room.
c. Here in Stuttgart.
d. Here in Germany.
e. Here on this planet.
(adapted from Diessel 2012: 2410)
Assuming a two-way deictic system, we can contrast proximal and distal deixis. In the
case of proximal deixis, the deictic reference region is included in the deictic center, while, in
the case of distal deixis, the deictic reference region must not overlap with the deictic center.
Considering the three possible deictic elements her- (‘hither’), dr- (‘there’), and hin-
(‘thither’) as parts of echo extensions of path prepositions and their adverbial cognates
hier (‘here’), da (‘there’), and dort (‘yonder, over there’), German seems to have a three-way de-
ictic system. However, I assume that her- and hier indicate proximal deixis, and that hin- and
dort indicate distal deixis, while dr- and da indicate neither proximal nor distal deixis but are
134For a general discussion on deixis, I refer to Lyons (1977), Ehrich (1982, 1992), Fillmore (1982, 1997), Cairns
(1991), Levinson (2004), Diessel (2012), Harbour (2015), a.o.
5.5. Functional prepositional structure 269
underspecified with respect to proximity.135 The correspondence between the postpositional
deictic elements and the spatial adverbs is given in Table 17.
proximal deixis distal deixis
postpositions her- (‘hither’) hin- (‘thither’)
dr- (‘there’)
adverbs hier (‘here’) dort (‘over there’)
da (‘there’)
Table 17: Proximal and distal deictic marking in German postpositions and adverbs
In fact, deictic expressions can be underspecified with respect to proximity. Consider
English that. When used contrastively with this as in (460), that has a distal interpretation.
(460) This one (here) is bigger than that one (over there).
(Diessel 2012: 2419)
However, when used in a neutral context as in (461), this and that are generally interchange-
able. That is, that can also express proximal deixis.
(461) I like this/that one better.
(Diessel 2012: 2419)
Following Levinson (2004), Diessel (2012: 2419) argues that “this always expresses some sense
of proximity, [while] that is only interpreted as a distal term if it is used in explicit contrast
to this; that is, that is semantically unmarked for distance, but is interpreted as a distal term
by pragmatic contrast via Grice’s maxim of quantity (‘Be as informative as circumstances
permit’).” In this sense, that is the unmarked deictic demonstrative, while this is explicitly
marked for proximity. I assume that spatial dr-/da in German behave similarly to English
that. That means that their distal interpretations arise in contrast to her-/hier and, the other
way round, their proximal interpretations arise in contrast to hin-/dort.
Consider in this connection also the data in (462) where geometric prepositions together
with echo extensions are combined with spatial adverbials. In the context of place prepo-
sitions, dr- is compatible both with the proximal deictic adverbial hier (462a) and with the
distal deictic adverbial dort (462b). Likewise, in the case of path prepositions, dr- is typically
compatible both with the proximal deictic adverbial hier (462c) and with the distal deictic
adverbial dort (462d). However, her- is compatible only with the proximal deictic adverbial
hier (462c), and hin- is compatible only with the distal deictic adverbial dort (462d)
(462) a. Hans
Hans
saß
sat
hier
here
auf
upon
dem
the.DAT
Tisch
table
dr-auf
there-upon
b. Hans
Hans
saß
sat
dort
yonder
auf
upon
dem
the.DAT
Tisch
table
dr-auf
there-upon
135For a thorough discussion of these adverbials, I refer to Ehrich (1992: 8–62).
270 5. Spatial prepositions at the interfaces
c. Hans
Hans
sprang
jumped
hier
here
auf
upon
den
the.ACC
Tisch
table
her-/dr-/*hin-auf
hither-/there-/thither-upon
d. Hans
Hans
sprang
jumped
dort
yonder
auf
upon
den
the.ACC
Tisch
table
*her-/dr-/hin-auf
hither-/there-/thither-upon
With regard to the functional structure of prepositions, I assume, following Den Dikken
(2010), a functional category Dx (for deixis) that can host the syntacticosemantic (synsem)[±PROX] (for proximity). Dx[+PROX] indicates proximal deixis, where the deictic reference
region is included in the deictic center, and Dx[−PROX] indicates distal deixis (e.g. Fillmore
1982, Cairns 1991, Den Dikken 2010), where the deictic reference region and the deictic center
must not overlap.
Let us now look at the LF-instructions for prepositional Dx as I propose them in (463). As
mentioned above, I assume that the spatial deixis appearing in echo extensions of geometric
prepositions is best understood in terms of a relation between a deictic reference region rd and
a region ri that is identified as the deictic center. Following Roßdeutscher (2009), I assume
that the deictic reference region rd is included in the deictic center ri in the case of proximal
deixis.136 In the case of distal deixis, the deictic reference region rd and the deictic center ri
must not overlap. In both proximal and distal deixis, the deictic center ri is presupposed
and the deictic reference region rd is anticipated to be instantiated through unification, i.e. rd.
Typically, the region that comes from the downstairs PP unifies with rd.
(463) LF-intructions for Dx:
a. Dx ↔ ⟨{ ri } , rd ⊆ ri ⟩ / _ [+PROX]
b. ↔ ⟨{ ri } , ¬ rd ⊗ ri ⟩ / _ [−PROX]
This analysis obviously faces a problem in the context of route prepositions. As shown in
(464), route prepositions are straightforwardly felicitous with echo extensions involving a
deictic element.
(464) Hans
Hans
rannte
ran
durch
through
den
the.ACC
Wald
forest
hin-durch.
thither-through
‘Hans ran through the forest.’
I proposed in Section 5.4.3 that the semantic representation of route prepositions does not
contain regions, but tripartite spatial paths of the form ‘tail-NINF-tail’. Thus, there is no region
available in a downstairs route PP that the anticipated deictic reference region rd could unify
136See also Roßdeutscher’s (2009) analysis of hin- (‘thither’), her- (‘hither’) and hin und her (‘back and forth’).
5.5. Functional prepositional structure 271
with. I propose that this triggers an operation at LF that adjusts the input of the pending
DRS-Merge to the effect that the DRSs from Dx○ and AspP can be straightforwardly merged.
In particular, I propose an adjustment of the Dx-interpretations given in (463) such that the
deictic reference region rd, which is anticipated in (463), is instantiated by the existentially
bound discourse referent r′. Furthermore, r′ is interpreted as a goal of an anticipated to-path
v.137 Thereby, an argument slot is created for the ninf-path v′ from the downstairs route PP.
Note that r′ does not serve as the referential argument of Dx○. Note also that the to-path
necessitates the presupposition of an event e0. Later at the level of VP, this presupposed
event can typically be resolved as a proper part of the event e′ contributed by the verb, i.e.
e0 < e′. Hence, I propose the LF-rule of Dx-Adjustment as given in (465). Dx-Adjustment is
available only if P hosts a negative feature P[−NINF].
(465) Dx-Adjustment at LF:
a. ⟨{ ri } , rd ⊆ ri ⟩ → ⟨{ ri , e0 } ,
r′
r′ ⊆ ri
to(v, r′, e0) ⟩ / P[−NINF]
b. ⟨{ ri } , ¬ rd ⊗ ri ⟩ → ⟨{ ri , e0 } ,
r′¬ r′ ⊗ ri
to(v, r′, e0) ⟩ / P[−NINF]
This type of analysis does not only impose a direction onto otherwise undirected ninf-paths,
but, at the same time, it necessarily leads to the configuration that one tail path of the route
path is included in the deictic reference region, while the other tail path is not. Figure 44
illustrates this situation. These considerations yield the LF-representation of the prepositional
CP durch den Wald hin-durch (‘through the forest’) given in (466). See also the examples (492)
on page 285 and (493) on page 287.
w
v′
e0
r′
θ
Figure 44: NINF-path v′ is a path to deictic reference region r′ in e0
137Assuming that the ninf-path v′ and the deictic reference region rd relate to each other in this way is insofar
reasonable as I hypothesize that motion along spatial paths is generally conceptualized as monotone.
272 5. Spatial prepositions at the interfaces
(466) LF-representation of prepositional CP durch den Wald hin-durch:
⟨{ ri , e0 } , w
′ r′ v′ x′
durch-bar(v′, x′) ninf−(v′, w′, x′)
to(v′, r′, e0) ¬ r′ ⊗ ri
garden(x′) RFPR(y, w′, e)
⟩
Route PPs with echo extensions necessarily lead to telic predicates. That is, they can
involve only negative ninf-paths; cf. (431a). The plain route prepositions durch (‘through’),
um (‘around’), and über (‘over, across’) without echo extensions are aspectually ambiguous to
the effect that they give rise to telic and atelic interpretations when combined with manner
of motion verbs such as in (467a). In contrast, when the route preposition co-occurs with an
echo extension including a deictic element as in (467b), the atelic reading, which involves
positive ninf-paths, is no longer available.
(467) a. Hans
Hans
rannte
ran
in/für
in/for
zwei
two
Stunden
hours
durch
through
den
the
Wald.
forest
b. Hans
Hans
rannte
ran
in/*für
in/for
zwei
two
Stunden
hours
durch
through
den
the
Wald
forest
hin-durch.
thither-through
This is because the set of spatial paths denoted by the prepositional CP durch den Wald
hin-durch is not cumulative and thus the prepositional CP is bounded, which leads to telic
aspect, cf. (292) on page 172. The rationale for this is reminiscent of why sets of transitional
enter-paths (and leave-paths) – see Section 5.4.2 – are not cumulative (Zwarts 2005b: 761). The
set of spatial paths denoted by the prepositional CP durch den Wald hin-durch contains no
paths that can be concatenated: the tail paths of the respective spatial paths are always in
different regions – one tail path is included in the deictic reference region r′, while the other
tail path is not. Note that this aspectual effect of the deictic elements hin (‘thither’) and her
(‘hither’) can also be observed in contexts without any preposition whatsoever. The plain use
of the manner of motion verb in (468a) typically gives rise to an atelic predicate. However,
when used in combination with one of the deictic elements as in (468b), the atelic reading
becomes unavailable and the predicate is telic.
(468) a. Hans
Hans
rannte
ran
?in/für
in/for
zwei
two
Stunden.
hours
b. Hans
Hans
rannte
ran
in/*für
in/for
zwei
two
Stunden
hours
hin/her.
thither/hither
Let us now look at the PF-instructions of prepositional Dx in the context of echo exten-
sions. As discussed above, her- (‘hither’) expresses proximal deixis, hin- (‘thither’) expresses
distal deixis, and dr- (‘there’) is underspecified for proximity. Furthermore, pronouncing
prepositional C (cf. Section 5.5.1) is a precondition for pronouncing the functional category
Dx. That is, if C is silent, then Dx is also silent. I capture this with the condition ‘℘(C) /= ∅’
which reads as ‘the phonological matrix of C is not zero’. In order to achieve the distribution
5.5. Functional prepositional structure 273
of deictic elements given in Table 16, we can straightforwardly formulate the PF-instructions
for Dx in (469).
(469) PF-instrunctions for Dx:
a. Dx ↔ /hEr/ / ℘(C) /= ∅ ∧ _ [+PROX]
b. ↔ /hIn/ / ℘(C) /= ∅ ∧ _ [−PROX]
c. ↔ /dr/ / ℘(C) /= ∅
d. ↔ ∅ elsewhere
However, the PF-instructions in (469) predict that not only path prepositions but also place
prepositions can co-occur with hin- and her-, which is ungrammatical. Place prepositions can
only co-occur with dr-.
(470) Hans
Hans
saß
sat
in
in
der
the.DAT
Kiste
box
*her-/*hin-/dr-in
hither-/thither-/there-in
‘Hans sat in the box.’
In order to account for this, I propose a morphological Impoverishment rule (cf. Section 3.4.1)
that can target the feature [±PROX] hosted by Dx. In particular, I propose the Proximity
Impoverishment rule in (471a), which states that the proximity feature [±PROX] hosted by Dx
is necessarily deleted in the context of place prepositions, i.e. in the context of C[−MOTION].
In order to account for the co-occurrence of dr- in the context of path prepositions, we
can formulate the optional Proximity Impoverishment rule in (471b). However, Proximity
Impoverishment may not apply if the abstract Content feature [ℵ] co-occurs with path
prepositions, i.e. C[+MOTION]. Note that I leave the principles that guide optional Proximity
Impoverishment for further research.
(471) Proximity Impoverishment:
a. Delete [±PROX] hosted by Dx in the context of C[−MOTION].
b. Optionally delete [±PROX] hosted by Dx in the context of C[+MOTION],
however do not delete [±PROX] if, in addition, P hosts [ℵ].
Let me close this section with a note on some speaker-dependent variation considering
the distribution of deictic elements. Note that the conditions concerning the phonological
matrix of C in the PF-instructions in (469) are, to some extent, subject to variation. For
instance, Noonan (2010) accepts a bare postpositional deictic element in the context of the
non-geometric goal preposition zu (‘to’) as given in (472) – which I consider marked, at least.
(472) Sie
she
ist
is
zum
to.the.DAT
Laden
store
(hin)
thither
gelaufen.
run
‘She ran to the store.’
(Noonan 2010: 172)
274 5. Spatial prepositions at the interfaces
The PF-instruction in (469b) principally excludes the deictic element in (472) as ungrammati-
cal. However, for speakers who accept (472), the rules in (469a) and (469b) might in fact be
more sophisticated. But note that pseudo-geometric path prepositions are never grammatical
with bare deictic postpositional elements (473).
(473) Hans
Hans
ist
is
auf
upon
die
the.ACC
Balearen
Balearics
(*hin/*hin-auf)
thither/thither-upon
geflogen.
flown
‘Hans flew to the Balearics.’
This might suggest a reformulation of the PF-instructions in (469a) and (469b) to the effect
that (i) the phonological matrix of C is not zero, or (ii) downstairs P hosts the synsem feature[AT], which is characteristic for non-geometric prepositions. However, I leave this for further
research.
5.5.3 Aspectual features
Following Den Dikken (2010), I assume that the functional structure of (spatial) prepositions
involves the category Asp (for aspect). Arguably, aspect relates to boundedness in one way
or another. Hence, I assume that Asp can host the syntacticosemantic (synsem) feature[±UNBD] (for unbounded). This section focuses in particular on the obligatory postpositional
elements of unbounded non-geometric path prepositions, which are – I claim – realizations of
Asp[+UNBD]. Consider the circumpositional prepositions auf ... zu (‘towards’) and von ... weg
(‘away from’) in (474).
(474) a. Hans
Hans
rannte
ran
auf
upon
den
the.ACC
Wald
forest
zu.
to
‘Hans ran towards the forest.’
b. Hans
Hans
rannte
ran
von
from
dem
the.DAT
Wald
forest
weg.
away
‘Hans ran away from the hut.’
In this thesis, I adopt Piñón’s (1993) basic idea that paths towards X are inital parts of
paths to X.138 That is, unbounded paths towards X are partitives of bounded paths to X. Piñón
follows Verkuyl and Zwarts (1992: 498) who take the view that a PP such as towards the store
denotes a set of parts of paths to the store to the effect that these parts have no fixed end points.
In particular, Piñón (1993: 301) proposes that the PP towards the library denotes a set of initial
subpaths of a path that extends between an implicit starting point and the location of ‘the
library’. That is, when you are on a path ‘towards the library’ you are basically on the initial
part of a path ‘to the library’.139 I adopt this view and define the three-place LF-predicate
towards in (475). I propose that w is a path towards r in e iff it is a proper subpath of a path w′
138Note that I focus on auf ... zu (‘towards’) in the following. I leave an semantic analysis of von ... weg (‘away
from’) for future work.
139Krifka (1998: 228) proposes a similar analysis of towards.
5.5. Functional prepositional structure 275
to r in e′ to the effect that e, which is θ-related to w, is an initial subpart of e′. Note that the
definitions of the LF-predicates towards in (475) and to in (390b) do not directly refer to each
other. Nevertheless, the two definitions overlap to a great extent. Figure 45 illustrates a path
w towards region r in e as defined in (475).
(475) If θ is a (Strict) Movement Relation for spatial path w and event e, then∀e, r, w[towards(w, r, e)↔ ¬w ⊆ r ∧ θ(w, e)∧∃e′, w′[e < e′ ∧ INI(e, e′)∧ non-mco(w′)∧w < w′ ∧ θ(w′, e′)∧∀e′′, w′′[w′′ ≤ w′ ∧ e′′ ≤ e′ ∧ θ(w′′, e′′)→ [[FIN(e′′, e′)→ w′′∞ r]∧ [¬FIN(e′′, e′)→ ¬w′′∞ r]]]]]
“w is a path towards r in e iff w is not contained in r; and there is an event e′ and a
path w′, which e and w are proper subparts of; and e is an initial part of e′; and all
subpaths w′′ ≤ w′ that are θ-related to final subevents e′′ ≤ e′ are adjacent to r”
r
e′
w′
e′′
w′′
e
w
θ θθ
Figure 45: “w is a path towards region r in e”
Let us now address the question of how the predicates to and towards relate to each other
at LF. In (415) on page 246, I proposed that the predicate to is the interpretation of the light
preposition Q above P, if Q hosts the synsem feature [+TO]. In order to arrive at the predicate
towards for auf ... zu, I assume reinterpretation rules at LF that can target the interpretation of
the light preposition Q.In fact, such reinterpretation rules are similar to Readjustment Rules
at PF (cf. Section 3.6). In particular, I propose that Asp[+UNBD] triggers a reinterpretation
of the light preposition Q at LF to the effect that, in the context of Q[+TO], ‘to’ changes into
‘towards’, and likewise, in the context of Q[−TO], ‘from’ changes into ‘away-from’.140
(476) Reinterpretation of Q[±TO] under Asp[+UNBD]:
a.
to(w, r, e) → towards(w, r, e) / Q[+TO] ∧ Asp[+UNBD]
b.
from(w, r, e) → away-from(w, r, e) / Q[−TO] ∧ Asp[+UNBD]
140In this thesis, I omit a discussion of ‘away from’. I leave it for future work.
276 5. Spatial prepositions at the interfaces
I should mention here that I assume that LF-instructions for prepositional Asp are not
needed in order to account for auf ... zu (‘towards’) and von ... weg (‘away from’). Instead, I
assume that prepositional Asp[+UNBD] can affect the interpretation of the downstairs light
preposition Q as proposed in (476).
However, there is a flaw in this analysis. Krifka (1998) points to the problem that this
analysis necessitates the assumption of the event e′ and the path w′. However, the existence of
a event e′ of X-ing to the Ground need not exist in the real world. Krifka (1998: 228) constructs
an instance of the imperfective paradox (Dowty 1979). Consider the sentence in (477) where
the existence of an event of walking to the capitol is implausible.
(477) Mary walked from the university towards the capitol when she was hit by a truck.
(Krifka 1998: 228)
Krifka concludes that a proper treatment of such cases has to be couched in a modal repre-
sentation. In the proposed solution the modal embedding should take place in the definition
of the LF-prediate towards.
Let us now look at the PF-instructions for Asp. In contrast to the treatment of Asp at LF,
its treatment at PF is straightforward. Consider the forms of the unbounded non-geometric
path prepositions in Table 18. In order to account for the postpositional element, I propose
the PF-instructions for Asp in (478).
unbounded non-geometric
path prepositions
P[AT] Asp[+UNBD]
goal Q[+TO] auf ... zu
source Q[−TO] von ... weg
Table 18: Unbounded non-geometric path prepositions
(478) PF-instructions for Asp:
a. Asp ↔ /ts<u:/ / _ [+UNBD] ∧ Q[+TO]
b. ↔ /vEk/ / _ [+UNBD] ∧ Q[−TO]
c. ↔ ∅ elsewhere
What about the realization of P[AT]? The PF-instruction for P in (417c) on page 247
correctly predicts /fOn/ (von) for the source-case Q[−TO]. However, the PF-instruction in
(417g) predicts /ts<u:/ (zu) for the goal-case Q[+TO], which is obviously wrong. In order
to arrive at the correct form /au<f/ (auf ), I propose the morphophonological Readjustment
Rule in (479). The phonological matrix of P is changed from /ts<u:/ to /au<f/ in the context of
Q[+TO] and Asp[+UNBD].
5.5. Functional prepositional structure 277
(479) Readjustment of P under Q[+TO] and Asp[+UNBD]:
/ts<u:/ → /au<f/ / Q[+TO] ∧ Asp[+UNBD]
A further peculiarity of auf ... zu is that it takes accusative complements. In Section 6.4,
I lay out a morphological case theory for (spatial) prepositions in German. In particular,
I propose that the category P inherently assigns dative to DPs in its complement position.
Accusative in PPs is achieved, I claim, by a morphological Impoverishment operation that
deletes oblique case features, i.e. the case feature that distinguishes accusative from dative.
This Impoverishment operation is triggered by certain contexts. One of these contexts is the
particular combination Q[+TO] plus Asp[+UNBD]. Accusative case in the context of auf ... zu
is addressed separately in Section 6.4.2.
For some native speakers of German, the circumposition auf ... zu (‘towards’) is marked
when used in instructions for getting somewhere. Imagine a situation where someone asks
for the way to the palace, and the instructions would be such that one must go 150 m towards
the train station, which is further away, and then turn left into the street leading to the
palace asked for. In such a situation, the directions in (480a) involving auf ... zu are slightly
dispreferred. A more natural way of giving direction is given in (480b), which involves
the prepositional construction in Richtung (‘in the direction of’), the meaning of which is
comparable to ‘towards’ here.
(480) a. (?)Geh
go
150
150
m
m
auf
upon
den
the.ACC
Bahnhof
train station
zu
to
und
and
biege
bend
dann
then
links
left
zum
to.the.DAT
Palast
palace
ab.
off
‘Go 150 m towards the train station and then turn left to the palace.’
b. Geh
go
150
150
m
m
in
in
Richtung
direction
des
the.GEN
Bahnhof-s
train station-GEN
und
and
biege
bend
dann
then
links
left
zum
to.the.DAT
Palast
palace
ab.
off
‘Go 150 m towards the train station and then turn left to the palace.’
The preference for in Richtung in (480b), as opposed to auf ... zu in (480a), might correspond
to the fact that auf ... zu is arguably derived from zu (‘to’) and therefore involves the at-region.
In Section 5.4.1.3, I argued that an at-region is special to the effect that it must be functionally
determined, and that it must be relevant for the Figure to be at an at-region; see, in this
regard, also the example in (366). With this in mind, it is clear why (480a), which involves
an at-region of the train station, can be odd for some speakers. Being at an at-region of the
train station is of no relevance for the Figure in the context of directions she is given. In
contrast, the prepositional construction in Richtung in (480b) does not carry any relevance
implication. In a way, in Richtung seems to be a workaround for a non-existing simplex
unbounded (pseudo)-geometric goal preposition.
278 5. Spatial prepositions at the interfaces
Let me close this section with a brief comment on an aspectual effect in the context of echo
extensions of route prepositions. Considering the data in (467), which are repeated here in
(481), it seems reasonable to assume that echo extensions of this type are somehow related to
the category Asp, e.g. that the recurring element is a realization of Asp[−UNBD].
(481) a. Hans
Hans
rannte
ran
in/für
in/for
zwei
two
Stunden
hours
durch
through
den
the
Wald.
forest
b. Hans
Hans
rannte
ran
in/*für
in/for
zwei
two
Stunden
hours
durch
through
den
the
Wald
forest
hin-durch.
thither-through
In Section 5.5.2, I sketched a potential analysis of the aspectual effect in (481b). In fact, I
argued that it is the deictic element of the echo extension rather than Asp[−UNBD] that causes
this aspectual effect. When combined with deictic elements such as hin (‘thither’) or her
(‘hither’), route prepositions denote spatial paths where one tail path is included in the
deictic reference region, while the other tail path is not. Sets of such spatial paths cannot be
cumulative because they contain no paths that can be concatenated whatsoever. Thus, the
resulting prepositional CP is bounded.
5.6 Spatial prepositions in verbal contexts
This section briefly sketches how prepositional CPs headed by spatial prepositions can be
integrated in various verbal contexts. In particular, I present how various verbal structures
containing a prepositional CP are interpreted at LF. Four cases are illustrated: Section 5.6.1
illustrates the geometric place preposition in (‘in’) when it heads a prepositional CP serving as
an argument of the stative posture verb stehen (‘stand’); Section 5.6.2 illustrates the geometric
goal preposition in (‘into’) when it heads a prepositional CP serving as an argument of the
unaccusative manner of motion verb rennen (‘run’); Section 5.6.3 illustrates the geometric
route preposition durch (‘through’) when it heads a prepositional CP serving as an argument
of the transitive motion verb schieben (‘push’); and Section 5.6.4 illustrates the geometric goal
preposition in (‘into’) when it heads a prepositional CP serving as an argument of the unerga-
tive verb pinkeln (‘pee’). As for both the unaccusative motion verb rennen and the transitive
motion verb schieben, I assume that they instantiate Figure/Path Relations in the sense of
Beavers (2012); cf. Section 4.4.2. As for the unergative verb pinkeln, which belongs to the class
of verbs of bodily emission of fluids (Harley 2005), I assume that such verbs instantiate an
abstract Figure/Path Relation (FPR) (Beavers 2012) dubbed ‘send’. Morphophonologically,
the nominal argument of the phonologically null verb conflates with the verb. Semantically,
the nominal argument serves as the Figure argument of the abstract FPR send.
As for the functional structure of the clauses, i.e. the structure above VP or VoiceP involv-
ing AspP and TP, I refer the reader to Section 4.1.3, where a potential LF-interpretation is
sketched.
5.6. Spatial prepositions in verbal contexts 279
5.6.1 Place preposition and stative posture verb
I assume that the clause in (482) instantiates the syntactic structure given in (483). In particular,
I assume that the posture verb stehen (‘stand’), which is used here in the past tense, takes two
arguments: (i) a region-denoting prepositional CP, i.e. a fully-fledged place PP, and (ii) a DP,
which is merged in the specifier of the VP.
(482) Hans
Hans
stand
stood
(dort)
there
in
in
einer
a.DAT
Hütte
hut
dr-in.
there-in
‘Hans stood in a hut (over there).’
(483) CP
TP
AspP
VP
V′
CP
in einer Hütte drin
V○
stand
DP
Hans
Asp○
T○[+PAST]
-∅
C○
At LF, the prepositional CP of (482) is interpreted as given in (484). P[LOC,ℵ] is interpreted
as referring to an in-region r′ of an anticipated material object x. The referential argument of
the DP x′ unifies with x at the level of PP. The referential argument of the PP is r′. In this
example, Asp○ does not host any synsem features, and thus it has a null interpretation. The
DRS of the PP is percolated up to AspP. In this example, Dx○ hosts one of the synsem features[+PROX] or [−PROX]. As a matter of fact, both [+PROX] and [−PROX] are pronounced as dr- in
the context of place prepositions. Hence, we cannot determine from the surface form in (482)
which one is present in Dx○. However, when the pronominal adverb dort (‘there’) indicating
distal deixis is present, we can assume that Dx○ hosts [−PROX]. For the sake of simplicity, I
do not represent dort here. Dx[−PROX] contributes the condition that the anticipated deictic
reference region rd must not overlap with the presupposed deictic center ri. The referential
argument of AspP r′ unifies with the anticipated deictic reference region rd at the level of
280 5. Spatial prepositions at the interfaces
DxP. C[−MOTION] is interpreted as an anticipated stative relation ROCC holding between an
anticipated Figure y and the region r′′, which is the referential argument of C○. At the level of
CP, r′′ unifies with r′.
(484) CP
⟨{ ri } , r′′ x′in(r′′, x′) ¬ r′′ ⊗ ri
hut(x′) s ∶ ROCC(y, r′′) ⟩
DxP
⟨{ ri } , r′ x′in(r′, x′) ¬ r′ ⊗ ri
hut(x′) ⟩
AspP
r′ x′
in(r′, x′) hut(x′)
PP
r′ x′
in(r′, x′) hut(x′)
DP
x′
hut(x′)
P○[LOC,ℵ]
r′
in(r′, x)
Asp○
Dx○[−PROX]⟨{ ri } , ¬ rd ⊗ ri ⟩
C○[−MOTION]
r′′
s ∶ ROCC(y, r′′)
At LF, the VP of (482) is interpreted as given (485). The prepositional CP serves as an
argument of the stative posture verb stehen (‘stand’). The referential argument of V○ is the
state s′ that can be characterized by the predicate stand relating an anticipated entity y with
an anticipated region r. The anticipated stative relation of the prepositional CP ROCC unifies
with the stative predicate stand at the level of V′. The referential argument of the prepositional
CP r′′ unifies with r at the level of V′. The referential argument of the DP y′ unifies with y at
the level of VP.
5.6. Spatial prepositions in verbal contexts 281
(485) VP
⟨{ ri } , s
′ r′′ x′ y′
s′ ∶ stand(y′, r′′)
in(r′′, x′) ¬ r′′ ⊗ ri
hut(x′) Hans(y′) ⟩
V′
⟨{ ri } , s
′ r′′ x′
s′ ∶ stand(y, r′′)
in(r′′, x′) ¬ r′′ ⊗ ri
hut(x′) ⟩
CP
⟨{ ri } , r′′ x′in(r′′, x′) ¬ r′′ ⊗ ri
hut(x′) s ∶ ROCC(y, r′′) ⟩
V○
s′
s′ ∶ stand(y, r)
DP
y′
Hans(y′)
5.6.2 Goal preposition and unaccusative motion verb
I assume that the clause in (486) instantiates the syntactic structure given in (487). In particular,
I assume that the unaccusative motion verb rennen (‘run’), which is used here in the past
tense, takes two arguments: (i) a path-denoting prepositional CP, i.e. a fully-fledged path PP,
and (ii) a DP, which is merged in the specifier of the VP.
(486) Hans
Hans
rannte
ran
in
in
ein
a.ACC
Haus
house
hin-ein.
thither-in
‘Hans ran into a house.’
282 5. Spatial prepositions at the interfaces
(487) CP
TP
AspP
VP
V′
CP
in ein Haus hinein
V○
rann
DP
Hans
Asp○
T○[+PAST]
-te
C○
At LF, the prepositional CP of (487) is interpreted as given in (488). P[LOC,ℵ] is interpreted
as referring to an in-region r′ of an anticipated material object x. The referential argument of
the DP x′ unifies with x at the level of PP. Q[+TO] is interpreted as contributing an anticipated
enter-path w of an anticipated region r in an anticipated event e. The referential argument of
the PP r′ unifies with r at the level of QP. In this example, Asp○ does not contain any synsem
features and thus it has a null interpretation. The DRS of the PP is percolated up to AspP.
Dx[−PROX] is interpreted as contributing the condition that the anticipated deictic reference
region rd must not overlap with the presupposed deictic center ri. The referential argument
of AspP r′ unifies with rd at the level of DxP. C[+MOTION] is interpreted as contributing an
anticipated Figure/Path Relation RFPR holding between an anticipated Figure y, the spatial
path w′, and an anticipated event e. The referential argument of C○ w′ unifies with w at the
level of CP.
5.6. Spatial prepositions in verbal contexts 283
(488) CP
⟨{ ri } , w
′ r′ x′
in(r′, x′) enter(w′, r′, e)¬ r′ ⊗ ri house(x′)
RFPR(y, w′, e)
⟩
DxP
⟨{ ri } , r′ x′in(r′, x′) enter(w, r′, e)¬ r′ ⊗ ri house(x′) ⟩
AspP
r′ x′
in(r′, x′) enter(w, r′, e)
house(x′)
QP
r′ x′
in(r′, x′) enter(w, r′, e)
house(x′)
PP
r′ x′
in(r′, x′)
house(x′)
DP
x′
house(x′)
P○[LOC,ℵ]
r′
in(r′, x)
Q○[+TO]
enter(w, r, e)
Asp○
Dx○[−PROX]⟨{ ri } , ¬ rd ⊗ ri ⟩
C○[+MOTION]
w′
RFPR(y, w′, e)
At LF, the VP of (487) is interpreted as given in (489). I assume that the unaccusative motion
verb rennen (‘run’) contributes the Figure/Path Relation run holding between an anticipated
Figure y, an anticipated path w, and the event e′. The latter is the referential argument of V○.
The anticipated Figure/Path Relation of the prepositional CP RFPR unifies with run at the
level of V′. The referential argument of the prepositional CP w′ unifies with w at the level of
V′. The referential argument of the DP y′ unifies with y at the level of VP.
284 5. Spatial prepositions at the interfaces
(489) VP
⟨{ ri } , e
′ r′ w′ x′ y′
run(y′, w′, e′)
in(r′, x′) enter(w′, r′, e′)¬ r′ ⊗ ri house(x′) Hans(y′) ⟩
V′
⟨{ ri } , e
′ r′ w′ x′
run(y, w′, e′)
in(r′, x′) enter(w′, r′, e′)¬ r′ ⊗ ri house(x′)
⟩
CP
⟨{ ri } , w
′ r′ x′
in(r′, x′) enter(w′, r′, e)¬ r′ ⊗ ri house(x′)
RFPR(y, w′, e)
⟩
V○
e′
run(y, w, e′)
DP
y′
Hans(y′)
5.6.3 Route preposition and transitive motion verb
I assume that the clause in (490) instantiates the syntactic structure given in (491). In particular,
I assume that the transitive motion verb schieben (‘push’), which is used in the past tense here,
takes two arguments: (i) a path-denoting prepositional CP, i.e. a fully-fledged path PP, and
(ii) a DP, which is merged in the specifier of the VP. In addition, Voice introduces the agent of
the event in its specifier.
(490) Hans
Hans
schob
pushed
eine
a
Karre
cart
durch
through
einen
a.ACC
Garten
garden
hin-durch
thither-through
‘Hans pushed a cart through a garden.’
5.6. Spatial prepositions in verbal contexts 285
(491) CP
TP
AspP
VoiceP
Voice′
VP
V′
CP
durch einen Garten hindurch
V○
schob
DP
eine Karre
Voice○
DP
Hans
Asp○
T○[+PAST]
-∅
C○
At LF, the prepositional CP of (491) is interpreted as given in (492). P[−NINF] is interpreted
as contributing a negative ninf-path v′ of an anticipated path w relative to an anticipated object
x. The NINF-path v′ is a durch-bar-path of an anticipated material object x. The referential
argument of the DP x′ unifies with x at the level of PP. In this example, Asp○ does not contain
any synsem features and thus it has a null interpretation. The DRS of the PP is percolated up
to AspP. Dx[−PROX] is interpreted as contributing the condition that the anticipated deictic
reference region rd must not overlap with the presupposed deictic center ri. However, the
complement of Dx○ does not provide a discourse referent that could unify with rd. Hence,
the LF-operation Dx-Adjustment is triggered. Dx-Adjustment adds the region r′ to the DRS
of Dx○. The region r′ is interpreted as the goal of an anticipated to-path v in a presupposed
event e0. Note that r′ is not the referential argument of Dx○. Now, the referential argument
of AspP, which is the NINF-path v′, can unify with v at the level of DxP. C[+MOTION] is
interpreted as contributing an anticipated Figure/Path Relation RFPR holding between an
anticipated Figure y, the spatial path w′, and an anticipated event e. The referential argument
of C○ w′ unifies with w at the level of CP.
286 5. Spatial prepositions at the interfaces
(492) CP
⟨{ ri , e0 } , w
′ r′ v′ x′
durch-bar(v′, x′) ninf−(v′, w′, x′)¬ r′ ⊗ ri to(v′, r′, e0)
garden(x′) RFPR(y, w′, e)
⟩
DxP
⟨{ ri , e0 } ,
v′ r′ x′
durch-bar(v′, x′)
ninf−(v′, w, x′)¬ r′ ⊗ ri to(v′, r′, e0)
garden(x′)
⟩
AspP
v′ x′
durch-bar(v′, x′)
ninf−(v′, w, x′)
garden(x′)
PP
v′ x′
durch-bar(v′, x′)
ninf−(v′, w, x′)
garden(x′)
DP
x′
garden(x′)
P○[−NINF,ℵ]
v′
durch-bar(v′, x)
ninf−(v′, w, x)
Asp○
Dx○
⟨{ ri , e0 } , r′¬ r′ ⊗ ri
to(v, r′, e0) ⟩
Dx○[−PROX]⟨{ ri } , ¬ rd ⊗ ri ⟩
Dx-Adjustment
C○[+MOTION]
w′
RFPR(y, w′, e)
At LF, the VoiceP of (491) is interpreted as given in (493). I assume that the transitive
motion verb schieben (‘push’) contributes the Figure/Path Relation push holding between
an anticipated Figure y, an anticipated path w, and the event e′. The latter is the referential
argument of V○. The anticipated Figure/Path Relation of the prepositional CP RFPR unifies
with run at the level of V′. The referential argument of the prepositional CP w′ unifies with
w at the level of V′. At this level, the presupposed event e0 is resolved as a proper part of
e′. The referential argument y′ of the DP in the specifier of the VP unifies with y at the level
5.6. Spatial prepositions in verbal contexts 287
of VP. Voice○ contributes the agent-relation holding between an anticipated entity z and an
anticipated event e. The referential argument of VP e′ unifies with e at the level of Voice′. The
referential argument of the DP in the specifier of the VoiceP z′ unifies with z at the level of
VoiceP.
(493)
VoiceP
⟨{ ri } ,
e′ e0 r′ v′ w′ x′ y′ z′
push(y′, w′, e′) agent(z′, e′)
durch-bar(v′, x′) ninf−(v′, w′, x′)¬ r′ ⊗ ri to(v′, r′, e0) e0 < e′
garden(x′) cart(y′) Hans(z′)
⟩
Voice′
⟨{ ri } ,
e′ e0 r′ v′ w′ x′ y′
push(y′, w′, e′) agent(z, e′)
durch-bar(v′, x′) ninf−(v′, w′, x′)¬ r′ ⊗ ri to(v′, r′, e0) e0 < e′
garden(x′) cart(y′)
⟩
VP
⟨{ ri } ,
e′ e0 r′ v′ w′ x′ y′
push(y′, w′, e′)
durch-bar(v′, x′) ninf−(v′, w′, x′)¬ r′ ⊗ ri to(v′, r′, e0) e0 < e′
garden(x′) cart(y′)
⟩
V′
⟨{ ri } ,
e′ e0 r′ v′ w′ x′
push(y, w′, e′)
durch-bar(v′, x′) ninf−(v′, w′, x′)¬ r′ ⊗ ri to(v′, r′, e0) e0 < e′
garden(x′)
⟩
CP
⟨{ ri , e0 } ,
w′ r′ v′ x′
durch-bar(v′, x′)
ninf−(v′, w′, x′)¬ r′ ⊗ ri to(v′, r′, e0)
garden(x′) RFPR(y, w′, e)
⟩
V○
e′
push(y, w, e′)
DP
y′
cart(y′)
Voice○
agent(z, e)
DP
z′
Hans(z′)
288 5. Spatial prepositions at the interfaces
5.6.4 Goal preposition and unergative verb
I assume that the clause in (494) instantiates the unergative structure given in (495). I assume
that the unergative verb pinkeln (‘pee’), which belongs to the class of verbs of bodily emission
of fluids, is derived from an initially phonologically null verb V○ that takes two arguments:
(i) a bare nominal complement, which conflates with the verb,141 and (ii) a path-denoting
prepositional CP. In addition, Voice introduces the agent of the event in its specifier.
(494) Paul
Paul
pinkelte
peed
in
in
einen
a.ACC
Pool.
pool
‘Paul peed into a pool.’
(495) CP
TP
AspP
VoiceP
Voice′
VP
V′
N○/NP
pinkel
V○
CP
in einen Pool
Voice○
DP
Paul
Asp○
T○[+PAST]
-te
C○
At LF, the prepositional CP of (495) is interpreted as given in (496). P[LOC,ℵ] is interpreted
as referring to an in-region r′ of an anticipated material object x. The referential argument of
the DP x′ unifies with x at the level of PP. Q[+TO] is interpreted as contributing an anticipated
enter-path w of an anticipated region r in an anticipated event e. The referential argument of
the PP r′ unifies with r at the level of QP. In this example, Asp○ does not contain any synsem
features and thus it has a null interpretation. The DRS of the PP is percolated up to AspP.
Likewise, Dx○ does not contain any synsem features and thus it has a null interpretation.
141For the notion of conflation, I refer the reader to Hale and Keyser (2002).
5.6. Spatial prepositions in verbal contexts 289
The DRS of the AspP is percolated up to DxP. C[+MOTION] is interpreted as contributing an
anticipated Figure/Path Relation RFPR holding between an anticipated Figure y, the spatial
path w′, and an anticipated event e. The referential argument of C○ w′ unifies with w at the
level of CP.
(496) CP
w′ r′ x′
in(r′, x′) enter(w′, r′, e)
pool(x′) RFPR(y, w′, e)
DxP
r′ x′
in(r′, x′) enter(w, r′, e)
pool(x′)
AspP
r′ x′
in(r′, x′) enter(w, r′, e)
pool(x′)
QP
r′ x′
in(r′, x′) enter(w, r′, e)
pool(x′)
PP
r′ x′
in(r′, x′)
pool(x′)
DP
x′
pool(x′)
P○[LOC,ℵ]
r′
in(r′, x)
Q○[+TO]
enter(w, r, e)
Asp○
Dx○
C○[+MOTION]
w′
RFPR(y, w′, e)
290 5. Spatial prepositions at the interfaces
At LF, the VoiceP of (495) is interpreted as given in (497). I assume that V○ contributes the
abstract Figure/Path Relation send holding between an anticipated Figure y, an anticipated
path w, and the event e′. The latter is the referential argument of V○. The referential argument
of N○/NP y′ unifies with y at the level of V′. The referential argument of the prepositional CP
w′ unifies with w at the level of VP. The anticipated Figure/Path Relation of the prepositional
CP RFPR unifies with send at the the level of VP. Voice○ contributes the agent-relation holding
between an anticipated entity z and an anticipated event e. The referential argument of VP e′
unifies with e at the level of Voice′. The referential argument of the DP z′ unifies with z at the
level of VoiceP.
(497) VoiceP
e′ r′ w′ x′ y′ z′
send(y′, w′, e′) agent(z′, e′)
in(r′, x′) enter(w′, r′, e′)
pool(x′) pee(y′) Paul(z′)
Voice′
e′ r′ w′ x′ y′
send(y′, w′, e′) agent(z, e′)
in(r′, x′) enter(w′, r′, e′)
pool(x′) pee(y′)
VP
e′ r′ w′ x′ y′
send(y′, w′, e′)
in(r′, x′) enter(w′, r′, e′)
pool(x′) pee(y′)
V′
e′ y′
send(y′, w, e′)
pee(y′)
N○/NP
y′
pee(y′)
V○
e′
send(y, w, e′)
CP
w′ r′ x′
in(r′, x′) enter(w′, r′, e)
pool(x′) RFPR(y, w′, e)
Voice○
agent(z, e)
DP
z′
Paul(z′)
5.7. Summary 291
5.7 Summary
This chapter spelled out the syntax, semantics, morphology of spatial prepositions in German.
This chapter is the core of this thesis because it illustrates how spatial prepositions could be
implemented
Section 5.1 classified spatial prepositions according to several criteria. Section 5.1.1
presented a widely accepted typology of spatial prepositions (e.g. Jackendoff 1983, Piñón
1993, Zwarts 2006, Gehrke 2008, Kracht 2008, Svenonius 2010, Pantcheva 2011). On the one
hand, place prepositions denote static locations (regions), while path prepositions, on the
other hand, denote dynamic locations (spatial paths). Path prepositions can be directed or
undirected. Directed path prepositions are either goal prepositions or source prepositions.
Undirected path prepositions are route prepositions. In Section 5.1.2, I introduced a geometry-
based classification of spatial prepositions, which is orthogonal to the place/path typology.
I propose that spatial prepositions can be (i) geometric prepositions, (ii) pseudo-geometric
prepositions, or (iii) non-geometric prepositions. Geometric prepositions refer to geometric
relations that can be spelled out, for instance, in a parsimonious, perception-driven model
of space (Kamp and Roßdeutscher 2005). Examples are in (‘in, into’), aus (‘out of’), durch
(‘through’). Pseudo-geometric prepositions look like geometric prepositions, but do not refer
to geometric relations. Instead, they express functional locative relations. The peculiar goal
preposition nach (‘to’), which is obligatorily used, e.g., with determinerless toponyms, turns
out to be a special instance of a pseudo-geometric preposition. Pseudo-geometric prepositions
behave differently from geometric prepositions in several ways. For example, they do not
license a postpositional recurrence of the preposition and the choice of a pseudo-geometric
preposition is heavily influenced by denotational properties of the noun it co-occurs with.
The non-geometric prepositions bei (‘at’), zu (‘to’), and von (‘from’) form a third class of
spatial prepositions. They do not only impose semantic selection restrictions distinct from
geometric and pseudo-geometric prepositions, but also behave differently with regard to
lexical aspect. Section 5.1.3 classified path prepositions into bounded and unbounded path
prepositions. This was done according to Kracht’s (2002, 2008) classification: bounded
source prepositions denote coinitial paths, bounded goal prepositions denote cofinal paths,
bounded route prepositions denote transitory paths, unbounded source prepositions denote
recessive paths, unbounded goal prepositions denote approximative paths, and unbounded
route prepositions denote static paths. Section 5.1.4 mapped these classifications to syntactic
structure. The lexical category P is characteristic of prepositions in general. It can host one
of the following synsem features: (i) [LOC], which is characteristic of (pseudo)-geometric
prepositions (except for route prepositions), (ii) [AT], which is characteristic of non-geometric
prepositions; or (iii) [±NINF], which is characteristic of route prepositions. The lexical category
P can be dominated by the light preposition Q, which derives goal and source prepositions
from place prepositions. Q can host the synsem features [+TO] for goal prepositions or [−TO]
for source prepositions. Following (Den Dikken 2010), I adopt the Parallelism Hypothesis,
292 5. Spatial prepositions at the interfaces
which states that the (functional) categories are structured in parallel across lexical domains,
and assume functional structure above the categories P and Q. The functional category
Asp dominates P or Q and can host the synsem features [+UNBD] for unbounded aspect or[−UNBD] for bounded aspect. The functional category Dx dominates Asp and can host the
synsem features [+PROX] for proximal deixis or [−PROX] for non-proximal (distal) deixis.
The functional category C dominates Dx and can host the synsem features [+MOTION] for
path prepositions or [−MOTION] for place prepositions.
Section 5.2 touched upon the cartographic decomposition of spatial prepositions. I briefly
presented Svenonius’ (2006, 2010) cartographic decomposition of place prepositions and
Pantcheva’s (2011) cartographic decomposition of path prepositions.
Section 5.3 introduced three abstract Content features that relate to geometric concepts and
that figure in the derivation of the geometric prepositions: (i) the place and goal preposition
in (‘in, into’), the source preposition aus (‘out of’), and the route preposition durch (‘through’)
share the abstract Content feature [ℵ] relating to interiority; (ii) the place and goal preposition
an (‘on, onto’) and the route preposition um (‘around’) share the abstract Content feature[ℶ] relating to contiguity; and (iii) the place and goal preposition auf (‘upon, up onto’)
and the route preposition über (‘over, across’) share the abstract Content feature [ℷ] relating
to verticality. Sections 5.3.1 to 5.3.3 discussed how the abstract Content features manifest
themselves semantically. Focusing on [ℵ] (interiority), Section 5.3.1 defined in-regions and
durch-bar-paths. Focusing on [ℶ] (contiguity), Section 5.3.2 defined an-regions and um-bar-
paths. Focusing on [ℷ] (verticality), Section 5.3.3 defined auf-regions and ueber-bar-paths.
Section 5.4 derived the lexical structure of spatial prepositions and spelled out PF-
instructions for their morphophonological realization and LF-instructions for their semantic
interpretation. Section 5.4.1 addressed place prepositions: geometric place prepositions
were the subject of Section 5.4.1.1, pseudo-geometric place prepositions were the subject
of Section 5.4.1.2, and non-geometric place prepositions were the subject of Section 5.4.1.3.
Section 5.4.2 addressed goal and source prepositions: geometric goal and source prepositions
were the subject of Section 5.4.2.1, pseudo-geometric goal and source prepositions were the
subject of Section 5.4.2.2, and non-geometric goal and source prepositions were the subject of
Section 5.4.2.3. Section 5.4.3 addressed route prepositions.
Section 5.5 derived the functional structure of spatial prepositions and spelled out PF-
instructions for their morphophonological realization and LF-instructions for their semantic
interpretation. Section 5.5.1 addressed C-features, Section 5.5.2 addressed deictic features,
and Section 5.5.3 addressed aspectual features.
Section 5.6 illustrated how a fully-fledged PP, i.e. a prepositional CP, headed by a spatial
preposition can be integrated in various verbal contexts.
Appendix A.1 provides a synopsis of the syntactic structures of the German spatial
prepositions at issue, their LF-instructions for semantic interpretation and PF-instructions for
morphophonological realization, and the necessary morphological and semantic operations.
Chapter 6
Prepositional case
Prepositions determine the case of their complement DP. This chapter will discuss preposi-
tional case in German. I will present (i) the case assignment properties of (spatial) prepositions
in German (Zwarts 2006); (ii) several previous approaches to prepositional case (Bierwisch
1988, Arsenijevic´ and Gehrke 2009, Caha 2010, Den Dikken 2010); and (iii) a morphological
case theory proposed for the verbal domain Marantz (1991), McFadden (2004). This will
pave the way for a proposal of a morphological case approach to spatial prepositions in
German that is based on the syntacticosemantic analyses of spatial prepositions presented in
Chapter 5.142
This chapter is structured as follows. Section 6.1 will present the case assignment proper-
ties of spatial prepositions in German. Section 6.2 will present four previous approaches to
prepositional case: Den Dikken (2010) in Section 6.2.1; Caha (2010) in Section 6.2.2; Arsenijevic´
and Gehrke (2009) in Section 6.2.3; and Bierwisch (1988) in Section 6.2.4. Section 6.3 will
motivate and outline the hypothesis that case is not a phenomenon of the syntax proper, but
of the morphological component of the grammar. This section will present a morphological
case approach spelled out for the verbal domain (Marantz 1997, McFadden 2007). Section 6.4
will lay out a morphological case theory for simplex spatial prepositions in German that
is based on the syntacticosemantic analysis of spatial prepositions presented in Chapter 5.
Section 6.5 will summarize this chapter.
6.1 Prepositional case in German
In German, three of four cases occur in the prepositional domain: (i) dative (dat), (ii)
accusative (acc), and (iii) genitive (gen). The fourth case, nominative (nom), never occurs as
the complement of a preposition. The main focus here is on dative and accusative because
142The morphological case approach to prepositions proposed by Haselbach and Pitteroff (2015) presents
an early stage of the morphological case theory developed in Section 6.4. The morphological case approach
presented in Haselbach and Pitteroff (2015) was jointly developed by Boris Haselbach and Marcel Pitteroff.
At that stage, however, the approach was syntacticosemantically not as elaborated as it is here. Moreover,
Sections 6.2 and 6.3 overlap with Haselbach and Pitteroff (2015), to some extent. For the most part, this work
was carried out by me.
293
294 6. Prepositional case
these two cases are mainly assigned by simplex spatial prepositions in German.143 We should
first narrow down the domain we are looking at. This thesis focuses on German morpho-
logically simplex prepositions conveying spatial meaning. As a starting point, let us look at
the 16 morphologically-simplex spatial prepositions in German, listed by Zwarts (2006: 94)
according to their case assignment properties.
(498) German morphologically-simplex spatial prepositions assigning ...
a. Dative:
aus (‘out of’), bei (‘at’), nach (‘to’), von (‘from’), zu (‘to’)
b. Accusative:
durch (‘through’), um (‘around’)
c. Dative or accusative:
an (‘on’), auf (‘upon’), hinter (‘behind’), in (‘in’), neben (‘next to’), über (‘above;
over, across’), unter (‘under’), vor (‘in front of’), zwischen (‘between’)
(cf. Zwarts 2006: 94)
Some prepositions like bei (‘at’) or aus (‘out of’) occur only with a dative complement, while
others occur only with an accusative complement; the latter are the route prepositions
durch (‘through’) and um (‘around’). Yet, other simplex spatial prepositions like an (‘on’) or
unter (‘under’) occur with either a dative or accusative complement. Along with this case
alternation on the complement, there comes a semantic alternation. These prepositions serve
as place prepositions with a dative complement, while they serve as goal (path) prepositions
with an accusative complement. From a case-perspective, the alternation is referred to as the
dative/accusative alternation; from a semantic point of view, it is referred to as the place/goal
alternation.
Let us first look at those prepositions that participate in this alternation. All of them
are geometric prepositions, as discussed in Section 5.1.2. The geometric prepositions split
into two groups. On the one hand, we can identify the topological prepositions an, auf,
and in, which this thesis focuses on. On the other hand, we can identify the so-called
projective prepositions. This term is due to the assumption that the semantics of these
prepositions involve a projection onto an axis of a perceptually-anchored coordinate system.
The projective prepositions in German are hinter (‘behind’), neben (‘next to’), über (‘above’),
unter (‘under’), and vor (‘in front of’). With regard to case, the projective prepositions, as
well as the preposition zwischen (‘between’), exhibit the same behavior as the topological
prepositions in German, viz. they participate in the dative/accusative alternation. In this
thesis, I do not discuss them any further.
At this point, a word on the preposition über is in order. On the one hand, über has the
meaning ‘above’. In this reading, it behaves as a projective preposition and thus participates
143Note at this point that I use the term ‘assign’ here in a rather pretheoretical sense, without a commitment
to a certain theory of case.
6.1. Prepositional case in German 295
in the dative/accusative alternation. In this sense, it is the counterpart of unter (‘under’).
On the other hand, über has the meaning ‘over, across’. In this reading, it serves as a route
preposition. In fact, when über means ‘over, across’, it behaves like durch (‘through’) and um
(‘around’), in that it co-occurs only with an accusative complement.
Let us consider the spatial usage of nach (‘to’). As discussed in Section 5.4.2.2, it is a
special goal preposition classified as a pseudo-geometric preposition – even though the term
is misleading here, as there is no genuine geometric counterpart preposition nach. Zwarts
(2005a, 2006) claims that, with the spatial reading, nach takes a dative complement. This,
however, is an assumption rather than an empirical datum. In fact, one condition of nach
is the absence of φ-features on the nominal complement. However, φ-features seem to be a
precondition for case marking. That is, due to absence of an overt determiner, which typically
expresses φ-features in German, the ‘true’ case of the complement of spatial (!) nach is never
discernible. In contrast to Zwarts, I thus claim that the case-assigning properties of spatial
nach are uncertain. Note at this point that temporal nach (‘after’) – which takes dative – must
not be confused with spatial nach. Clearly, these two prepositions share only the phonological
exponent; apart from that, they instantiate distinct structures.
Let us now reconsider the typology of spatial prepositions presented in Figure 35 (cf.
Section 5.1.1), which is repeated here as Figure 46.
spatial prepositions
place prepositions path prepositions
directed
source prepositions goal prepositions
undirected
route prepositions
Figure 46: Typology of spatial prepositions (repeated from Figure 35)
Additionally, take into account the divide between non-geometric prepositions, on the one
hand, and (pseudo)-geometric prepositions, on the other.144 If we continue by mapping the
prepositions listed in (498) to their case-assigning properties, we achieve Table 19. Note that
we can, in German, ignore the projective prepositions, because they behave qua geometric
prepositions like the topological prepositions with regard to case.
Ignoring genitive-assigning prepositions for the moment, we can make the generalizations
in (499) concerning the German spatial prepositions listed in Table 19.
144Henceforth, I will use the term ‘(pseudo)-geometric’ as a collective term for both geometric and pseudo-
geometric.
296 6. Prepositional case
with dative with accusative
place non-geometric bei (‘at’) –
(pseudo)-geometric an (‘on’),
auf (‘upon’),
in (‘in’)
–
path source non-geometric von (‘from’) –
(pseudo)-geometric aus (‘out of’) –
goal non-geometric zu (‘to’) –
(pseudo)-geometric – an (‘onto’),
auf (‘up onto’),
in (‘into’)
nach (‘to’)
route non-geometric – –
(pseudo)-geometric – durch (‘through’),
über (‘across, over’),
um (‘around’)
Table 19: Case assignment of spatial prepositions in German
(499) Case generalizations concerning simplex spatial prepositions in German:
a. When functioning as goal prepositions,
(pseudo)-geometric prepositions take an accusative complement.
b. Route prepositions always take an accusative complement.
c. All other prepositions take a dative complement.
The morphological case theory proposed in this thesis accounts for these generalizations
as follows. At PF, the lexical category P inherently assigns dative case features to a DP in
its complement position. Accusative case is achieved by morphological deletion of oblique
case features in two distinct contexts: (i) with the synsem feature bundle [LOC,+TO], i.e. the
feature bundle that is characteristic of (pseudo)-geometric goal prepositions; and (ii) with the
synsem feature [±NINF], i.e. the feature that is characteristic of route prepositions.
Let me close this section with a discussion concerning the role of genitive in the preposi-
tional domain. We can observe that genitive case can occur in at least two distinct preposi-
tional contexts.
First, genitive case can occur on the DP-complement of a preposition that apparently in-
corporates some nominal element. Typically, these prepositions are morphologically complex,
like innerhalb (‘inside, within’) or jenseits (‘beyond’). In fact, such prepositions often find a
morphologically-related counterpart in the nominal domain, as depicted in (500), although
there are semantic differences.145 The preposition innerhalb seems to incorporate the head
145Typically, there is a semantic difference between a complex preposition and its nominal counterpart. Let
me illustrate this with the PP innerhalb des Gartens (‘within the garden’) and the corresponding DP die innere
Hälfte des Gardens (‘the inner half of the garden’). In the PP-variant, the entire space is partitioned into two
halves: (i) the interior of the garden and (ii) the exterior of the garden. That is, the PP refers to entire interior of
the garden. In the DP, in contrast, the space of the garden is partitioned into two halves: (i) an inner half of the
garden and (ii) an outer half of the garden. That is, the DP refers only to the inner half of the garden.
6.1. Prepositional case in German 297
nominal Hälfte (‘half’) and the prenominal adjective innere (‘inner’), while the preposition
jenseits seems to incorporate the head nominal Seite (‘side’) and the determiner jene (‘yonder’).
(500) a. [P inner-halb
inner-half
] ∼ [DP die
the
innere
inner
Hälfte
half
]
b. [P jen-seits
yonder-side
] ∼ [DP jene
yonder
Seite
side
]
Ignoring the semantic differences between complex prepositions and their nominal coun-
terparts mentioned in footnote 145, we can observe that the complex prepositions regularly
pattern, regarding case assignment, with their nominal counterparts. In particular, they show
a semantically-neutral case alternation between genitive and dative. They either directly take
a DP complement marked with genitive case (501), which is like their nominal counterparts
(502); or they involve the morpheme von (‘of’) and then take a DP complement marked with
dative case (503), which is again like their nominal counterparts (504).
(501) a. inner-halb
inner-half
des
the.GEN
Garten-s
garden-GEN
‘within the garden’
b. jen-seits
yonder-side
des
the.GEN
Wald-s
forest-GEN
‘beyond the forest’
(502) a. die
the
innere
inner
Hälfte
half
des
the.GEN
Garten-s
garden-GEN
‘the inner half of the garden’
b. jene
that
Seite
side
des
the.GEN
Wald-s
forest-GEN
‘that side of the forest’
(503) a. inner-halb
inner-half
von
of
dem
the.DAT
Garten
garden
‘within the garden’
b. jen-seits
yonder-side
von
of
dem
the.DAT
Wald
forest
‘beyond the forest’
(504) a. die
the
innere
inner
Hälfte
half
von
of
dem
the.DAT
Garten
garden
‘the inner half of the garden’
b. jene
that
Seite
side
von
of
dem
the.DAT
Wald
forest
‘that side of the forest’
Due to this parallelism, I consider this type of genitive case assignment by these prepositions
to be regular. In particular, I assume that what explains genitive and von-plus-dative in
the nominal domain can also help to explain genitive and von-plus-dative in the domain
298 6. Prepositional case
of complex prepositions. Further examples of spatial prepositions that incorporate some
nominal element and trigger either genitive or von-plus-dative are listed in (505).146
(505) German spatial prepositions with genitive or von plus dative:
abseits (von) (‘beside’), außerhalb (von) (‘outside of’), diesseits (von) (‘on this side of’),
entlang (von) (‘along’), fern (von) (‘far [away] from’), gegenüber (von) (‘opposite’),
inmitten (von) (‘in the middle of, midst of’), innerhalb (von) (‘within, inside’), jenseits
(von) (‘on the other side of, beyond’), längs (von) (‘alongside, along’), links (von) (‘to
the left of’), nahe (von) (‘near to’), nördlich (von) (‘to the north of’), oberhalb (von)
(‘above’), östlich (von) (‘to the east of’), rechts (von) (‘to the right of’), seitlich (von) (‘at
the side of, beside’), südlich (von) (‘to the south of’), unterhalb (von) (‘below’), unweit
(von) (‘not far from’), vis-à-vis (von) (‘vis-à-vis’), westlich (von) (‘to the west of’)
With regard to case assignment in the nominal domain, I refer the reader to Grosz (2008),
who puts forth a proposal concerning the von-case marking of a nominal’s arguments.
Second, genitive case can occur on the DP-complement of (normally non-spatial) prepo-
sitions that do not correspond to some nominal element. Interestingly, no such preposition
is found in the spatial domain. Examples from other domains are wegen (‘due to’), trotz
(‘despite’), laut (‘according to’), or während (‘during’).
One crucial difference with the regular genitive distribution described above is that
these prepositions disallow von-plus-dative. Instead, these prepositions can take a bare
DP-complement with dative case, without any semantic shift. Consider the examples in (506)
and (507).
(506) a. trotz
despite
des
the.GEN
Sturm-s
storm-GEN
‘despite the storm’
b. trotz
despite
(*von)
of
dem
the.DAT
Sturm
storm
‘despite the storm’
(507) a. während
during
des
the.GEN
Konzert-s
concert-GEN
‘during the concert’
b. während
during
(*von)
of
dem
the.DAT
Konzert
concert
‘during the concert’
I assume that genitive case assignment by these prepositions is best understood as being
idiosyncratic. In Section 6.4.3, I will briefly sketch how the morphological case theory
proposed here would tackle idiosyncratic genitive case assignment by prepositions.
146Note that some of these prepositions are in fact simplex, like fern (von) (‘far [away] from’). Nevertheless, all
involve a nominal (and/or adjectival) element, which is why I assume that their structure is more complex than
the one of ‘simplex’ prepositions, such as in (‘in’) or durch (‘through’).
6.2. Previous approaches to prepositional case 299
6.2 Previous approaches to prepositional case
This section presents some previous approaches to the case-marking properties of simplex
spatial prepositions in German. In particular, I will discuss three syntactic approaches and one
lexical approach. However, as we will see in the course of the discussion, all four approaches
suffer from theoretical stipulations or make wrong empirical predictions.
6.2.1 Den Dikken (2010): Structural case
Den Dikken (2010) takes the view that prepositional case assignment is structural. Fol-
lowing Koopman (2000, 2010), Den Dikken assumes a syntactic decomposition of spatial
prepositions into an obligatory locative lexical category Ploc for place prepositions and an
optional directional lexical category Pdir, above Ploc, for path prepositions. Additionally,
each lexical category can project functional structure on top of it. Recall from Section 5.5
that in Den Dikken’s approach Ploc may extend to Asp[PLACE], Dx[PLACE], and C[PLACE]; and
likewise Pdir may extend to Asp[PATH], Dx[PATH], and C[PATH]. In Den Dikken’s approach,
structural case means that the functional, rather than the lexical categories, are involved
in the assignment of case. In particular, Den Dikken (2010: 115) identifies the functional
heads Asp[PLACE] and Asp[PATH] as being responsible for case assignment in the domain of
spatial prepositions. He (2010: 114) formulates the case-assignment rule in (508), stating that
Asp[PLACE] checks oblique case on the complement of Ploc; here, oblique case is dative case (cf.
his footnote 40). Furthermore, he claims that Asp[PATH] checks accusative case. Den Dikken
follows common approaches to case assignment in assuming that, once assigned, a particular
case value cannot be overwritten. This means that once dative is assigned/checked by the
downstairs Asp[PLACE], the accusative feature of the upstairs Asp[PATH] ceases.
(508) The DP complement of Ploc checks oblique case iff Asp[PLACE] is present in the
structure.
(Den Dikken 2010: 114)
In order to account for the case-assignment properties of spatial prepositions in German,
Den Dikken (2010) proposes the three structures given in (509).
(509) a. [AspP Asp[PLACE]
<DAT>
[PP Ploc DP<DAT/*ACC> ]]
b. [AspP Asp[PATH]
<ACC>
[PP Pdir [PP Ploc DP<ACC/*DAT> ]]]
c. [AspP Asp[PATH]
<ACC>
[PP Pdir [ ... [AspP Asp[PLACE]
<DAT>
[PP Ploc DP<DAT/*ACC> ]]]]]
(cf. Den Dikken 2010: 114)
300 6. Prepositional case
The structure in (509a) comprises the functional head Ploc, which takes a DP-complement and
projects functional structure involving Asp[PLACE], which is assumed to comprise a dative
feature. As a result, the DP complement receives dative case. The place prepositions with
dative case, i.e. an (‘on’), auf (‘upon’), bei (‘at’), in (‘in’), etc., instantiate the structure in (509a).
In the structure in (509b), the functional head Pdir takes a PP headed by Ploc as a complement.
While Pdir projects functional structure involving Asp[PATH] with an accusative feature, Ploc
does not project functional structure. Crucially, there is no Asp[PATH] with a dative feature in
the structure. As a consequence, the DP-complement of Ploc receives accusative case from
Asp[PATH]. The path prepositions with accusative case, i.e. the goal prepositions an (‘onto’),
auf (‘up onto’), in (‘into’), etc., and the route prepositions durch (‘trough’) and um (‘around’),
are argued to instantiate the structure in (509b). In the structure in (509c), the functional head
Pdir takes a fully-fledged locative PP as a complement. That is, the lower Ploc projects its
own functional structure between Ploc and Pdir. Crucially, this functional structure involves
Asp[PLACE], comprising a dative feature. Thus, the DP-complement of Ploc receives dative.
The path prepositions with dative, i.e. the source prepositions aus (‘out of’) and von (‘from’),
as well as the goal prepositions nach (‘to’) and zu (‘to’), are argued to instantiate the structure
(509c).
Considering the mere structures in (509), it is not clear why prepositions distribute over the
structures the way they are said to do. Relating the dative on the embedded DP to the presence
of the functional head Asp[PLACE] in the structure means that the derivation of an alternating
preposition involves Asp[PLACE] in the place version, while the derivation of an alternating
preposition may not involve Asp[PLACE] in the goal version. In fact, Den Dikken models the
place/goal alternation by assuming that a locative preposition, i.e. Ploc can either project
its own functional structure (yielding a place preposition) or be embedded by a directional
Pdir without projecting its own functional structure (yielding a goal preposition). However,
in the case of source prepositions, Ploc is also embedded by Pdir but necessarily projects its
own functional structure. Zwarts (2006) and Caha (2010) point out that it is not clear what
motivates the absence of Asp[PLACE] in (509b) and its presence in (509c), independently from
case assignment. It seems that there is no systematic difference that justifies the distribution
of Asp[PLACE].
6.2.2 Caha (2010): Peeling off case
Caha (2010) proposes a peeling approach to the dative/accusative alternation in German (in
his terminology: locative/directional alternation). First, building on Bayer et al. (2001), he
proposes that nominal arguments come with a hierarchically-layered shell structure for case
features on top of the DP-level. In particular, Caha assumes that accusative case corresponds
to the functional layer F above DP, as given in (510a), and that dative case corresponds to the
6.2. Previous approaches to prepositional case 301
functional layer K above FP, as given in (510b). This means that accusative case is structurally
‘contained’ within dative case.147
(510) a. Accusative: [ F [ DP ] ]
b. Dative: [ K [ F [ DP ] ] ]
(cf. Caha 2010: 205)
Second, Caha assumes that, when a DP moves, it can strand its case layers. This leads to a
change of one case into another. For place prepositions, which take a dative complement, Caha
proposes the following derivation. The prepositional head P-loc takes KP as its complement
(511a). The aspectual prepositional head Asp-loc takes P-locP as its complement and attracts
KP from within P-locP to its specifier (511b). Finally, P-locP undergoes remnant movement
to the specifier position of an XP, in order to derive the correct linear order (511c).
(511) a. [ P-loc KP ]
b. [ KP [ Asp-loc [ P-loc KP ] ] ]
c. [XP [ P-loc KP ] X [ KP [ Asp-loc P-locP ] ] ]
(cf. Caha 2010: 186, 208)
For goal prepositions with an accusative complement, Caha proposes that the functional
head Path merges with the XP from (511c) and sub-extracts FP from within KP to its specifier,
as given in (512a). In this way, the dative layer is peeled off, resulting in accusative case on
the DP. Finally, XP undergoes remnant movement to the specifier position of a YP, in order
to precede the DP, as illustrated in (512b).
(512) a. [ FP [ Path [XP [ P-loc KP ] ... [ [ K FP ] Asp-loc ... ] ] ] ]
b. [YP [XP [ P-loc KP ] ... [ [ K FP ] Asp-loc ... ] ] Y [ FP [ Path XP ] ] ]
(cf. Caha 2010: 187, 208)
In order to block accusative case with the source path preposition aus (‘out of’), Caha
assumes that aus lexicalizes Path and that the Doubly Filled Nothing principle (Starke 2004),
which states that no projection can have both its head-terminal and its specifier present at the
same time, blocks the derivation of an accusative nominal. That is, the peeling of FP out of a
downstairs KP into the specifier of Path cannot happen. Caha proposes that durch (‘through’),
which does not alternate but exclusively takes an accusative complement, can be accounted
for by means of its lexical specification.
One general issue with Caha’s case-peeling theory is his claim that case alternations
are tied to movement. In other words, the theory predicts that if the case marking on an
argument changes from, say, accusative to nominative, like with verbal passives, movement
147Note that this is, in principle, comparable to the feature decomposition of case that I discuss in Section
6.3.2. One crucial difference is, however, that I assume that structural case is determined post-syntactically, and
thus has no repercussions in the narrow syntax.
302 6. Prepositional case
of the argument must have taken place. This prediction, however, is wrong for German.
It is a well-known fact, at least since Den Besten (1982), that, in German, passive subjects
can remain in their VP-internal base-position (see also Haider 1993, 2010; Wurmbrand 2006
shows that the subject does not move covertly). The shift from accusative to nominative in
these cases is thus unexpected under Caha’s theory, being contingent on movement.
Even though they are implemented differently, the approaches by Den Dikken (2003)
and Caha (2010) are akin to one another in that they both relate case (directly or indirectly)
to functional heads in the extended projection of prepositions. Dative case is linked to a
functional head above the locative preposition (i.e. Asp[PLACE] in Den Dikken’s system and
Asp-loc in Caha’s system) and accusative case is linked to a functional head in the directional
domain (i.e. Asp[PATH] in Den Dikken’s system and Path in Caha’s system).
6.2.3 Arsenijevic´ and Gehrke (2009): External accusative
Arsenijevic´ and Gehrke (2009) propose another syntactic account to the case distribution in
the domain of spatial prepositions. Leaving prepositions that assign only one case aside,
Arsenijevic´ and Gehrke discuss only those prepositions that appear with two different cases,
accompanied by a semantic shift. In particular, they focus on place/goal alternation (in
Serbo-Croatian and German), where the goal variant of a preposition surfaces with accusative
case, while its place variant surfaces with some other (oblique) case, i.e. instrumental case or
locative case in Serbo-Croatian and dative case in German. Arsenijevic´ and Gehrke claim
that the case shift to accusative with goal prepositions is not due to preposition-internal
structure, as claimed by Den Dikken 2010 or Caha 2010, for instance. Instead, they (2009: 2)
argue that “accusative case results from the embedding of the PP in the overall context, and
thus that it is part of the PP-external syntax.” In fact, they claim that the verbal case domain
can extend to a PP under certain conditions. In particular, they suggest that if a PP is in the
complement position of a verb, the case domain of the verb is extended and accusative case –
if available in the verbal domain for the direct object – is then also available in the PP. This
approach seems to run into serious problems in cases where accusative case is not available
contextually. Examples of such contexts are passives, as illustrated in (513a); unaccusatives,
as illustrated in (513b); or nominal constructions, as illustrated in (513c).
(513) a. Der
the
Schatz
treasure
wurde
was
in
in
den
the.ACC
/
/
*dem
the.DAT
Wald
woods
gebracht.
brought
‘The treasure was brought into the woods.’
b. Trümmerteile
debris
fielen
fell
in
in
den
the.ACC
/
/
*dem
the.DAT
Wald.
woods
‘Debris fell into the woods.’
c. der
the
Weg
way
in
in
den
the.ACC
/
/
*dem
the.DAT
Wald
woods
‘the path into the woods’
6.2. Previous approaches to prepositional case 303
In these contexts, accusative case is not available in the verbal domain – if present at all – and
thus it is not clear where accusative case in the PP should come from. If dative case is the
default prepositional case applied in the absence of accusative case, these cases are expected
to surface with dative case on the DP, contrary to fact.
6.2.4 Bierwisch (1988): Case from the lexicon
In contrast to the syntactic approaches proposed by Den Dikken (2010), Caha (2010), Arsenije-
vic´ and Gehrke (2009), the lexicalist approach by Bierwisch (1988) makes the right predictions
with respect to prepositional case assignment and it does not face the issues that the syntactic
approaches do. Bierwisch accounts for the case assignment properties of prepositions by
means of lexical rules. Consider the lexical entries for the prepositions in (‘in, into’) and an
(‘on, onto’) in (514), which both participate in the dative/accusative alternation. The entries
consist of a surface form, a set of morphosyntactic features in square brackets, and a semantic
form part with two variables that are linked into syntax.148 Ignoring the body of the semantic
part for the moment, we can see that the case feature [±OBL], which corresponds to dative
case, is tied to the internal argument, i.e. the complement of the preposition. Its value is
inversely connected to the value of the morphosyntactic directionality feature [±DIR], via the
variable α that ranges over the values ‘+’ and ‘−’. If the morphosyntactic feature for direction
has a positive value [+DIR], the oblique case feature has a negative value [−OBL]. As a result,
the internal argument will surface with accusative case. If the directional feature is specified
as negative [−DIR], this leads to a positive oblique case feature [+OBL] and thus to dative
case. In addition, the variable α conditions the occurrence of the function FIN in the body of
the semantic form. If α is positive, FIN contributes the directional (goal) semantics, while, if α
is negative, FIN is absent, leading to stationary semantics.
(514) a. /in/, [−V,−N,αDIR], λy[−αOBL] λx [ (αFIN) [LOC x] ⊂ LOC y ]
b. /an/, [−V,−N,αDIR], λy[−αOBL] λx [(αFIN) [LOC x] AT LOC y ]
(cf. Bierwisch 1988: 37)
For path prepositions like aus (‘out of’) that are exclusively directional and that only take
a dative complement, Bierwisch provides a lexical entry, like that in (515). Here, both the
morphosyntactic directional feature [+DIR] and the oblique case feature [+OBL] are specified
positively in the lexicon. Note that this specification is in a way hard-wired in the lexicon. In
the semantic form, the function INIT provides directional (source) semantics.
(515) /aus/, [−V,−N,+DIR], λy[+OBL] λx [ (αINIT) [LOC x] ⊂ LOC y ]
(cf. Bierwisch 1988: 35)
148Note that Bierwisch assumes a decomposition of the category feature P as [−V,−N].
304 6. Prepositional case
Even though Bierwisch does not provide a lexical entry for route prepositions like durch
(‘through’), we can assume that a corresponding lexical entry should look as sketched in
(516). Route prepositions are exclusively directional and exclusively take a complement with
accusative case. Ignoring the body of the semantic form, we can expect that the value of the
morphosyntactic directional feature is positive [+DIR], while the oblique case feature on the
internal argument must be negative [−OBL], in order to account for accusative case.
(516) /durch/, [−V,−N,+DIR], λy[−OBL] λx [...]
With respect to case assignment, the approach by Bierwisch seems to be superior to the
syntactic approaches presented above. However, it is conceptually unappealing to assume
that structural verbal case is calculated in the syntax or in the morphology, and that preposi-
tional case is determined (more or less arbitrarily) in another grammatical module, namely
the lexicon. Furthermore, word-syntactic frameworks, such as Distributed Morphology
(Halle and Marantz 1993), typically reject a separate lexical module preceding the syntactic
computation. Such frameworks cannot straightforwardly incorporate Bierwisch’s account;
they essentially require a (post)-syntactic approach to case.
6.3 Morphological case
This section motivates and outlines the hypothesis that case is not a phenomenon that
has repercussions in the syntax proper. Instead, it is argued that case is a morphological
phenomenon that builds on syntax. Furthermore, this section elaborates a decompositional
view on case to the effect that cases are the morphological realization of composite abstract
morphological features.
6.3.1 Abstract Case vs. morphological case
Traditional approaches in generative grammar allocate grammatical case to syntax.149 In
particular, case is considered to be related to nominal licensing via abstract Case. Pesetsky
and Torrego (2011) adduce data from Latin, illustrating that the complements of verbs (517)
and prepositions (518), but not of nouns (519) and adjectives (520), can show accusative
morphology. Instead, the complements of nouns and adjectives show other kinds of case
morphology (genitive/ablative) or are prepositional phrases (cf. in ‘into’, a ‘from’).
(517) [VP scripsit
wrote
libr-um
book-ACC
]
(518) [PP ad
to
Hispani-am
Spain-ACC
]
149Note that most of the discussion in this section is based on the introductory handbook article on case by
Pesetsky and Torrego (2011).
6.3. Morphological case 305
(519) a. [NP amor
love
libertat-is
liberty-GEN
]
‘love of liberty’
b. *[NP amor
love
libertat-em
liberty-ACC
]
c. [NP amor
love
[PP in
into
patriam
country
] ]
‘love for one’s country’
(520) a. urbs
city
[AP nuda
naked
praesidi-o
defense-ABL
]
‘a city deprived of defense’
b. *urbs
city
[AP nuda
naked
praesidi-um
defense-ACC
]
c. [AP liberi
free
[PP a
from
delici-is
luxuries
] ]
‘free from luxuries’
d. *[AP liberi
free
delici-as
luxuries-ACC
]
(Pesetsky and Torrego 2011: 53–54)
These observations lead to the assumption that (accusative) case assignment in languages
like Latin is subject to a grammatical rule which can be approximated as in (521).
(521) Accusative case in Latin-type languages
a. V and P assign accusative to an NP complement.
b. N and A do not assign accusative case (to an NP complement).
(Pesetsky and Torrego 2011: 54)
English, unlike Latin, does not have accusative case morphology. Nevertheless, the distri-
bution of complement NPs in English resembles the distribution of accusative NPs in Latin.
Nominal complements of verbs (522) and prepositions (523), but not of nouns (524) and
adjectives (525), are grammatical.
(522) [VP wrote the book ]
(523) [PP to Spain ]
(524) a. [NP love of liberty ]
b. *[NP love liberty ]
c. [NP love [PP for their country ] ]
(525) a. [AP free from luxuries ]
b. *[AP free luxuries ]
(Pesetsky and Torrego 2011: 54)
306 6. Prepositional case
Note that English is not completely free of case morphology. In the English pronominal
system, some case morphology has survived. This can easily be seen if the nominal arguments
without visible case morphology (526a) are replaced by personal pronouns (526b). The
internal argument of the verb attack is marked with accusative case, while the external
argument is marked with nominative.
(526) a. The butler attacked the robber.
b. He attacked him.
(Haegeman 1994: 155-156)
Relating nominal licensing to abstract Case (capitalized), it is assumed that English has a fully-
fledged system of abstract Case like Latin or German. But while Latin or German have more
or less rich systems of morphological case (not capitalized), English has a poor morphological
case system – except for the personal pronouns. That is, abstract Case (capitalized) relating to
nominal licensing is to be distinguished from morphological case (not capitalized) relating to
morphological realization.
With respect to abstract Case, the distribution of nominal arguments in (517)–(520) and
(522)–(525) can be captured with the so-called Case Filter (Vergnaud 1977, Chomsky 1981),
as formalized in (527).
(527) Case Filter:
Every overt NP must be assigned abstract Case.
(Haegeman 1994: 167)
In English, verbs and prepositions assign abstract accusative Case to nominal complements
which thus pass the Case Filter. Furthermore, it is assumed that English, unlike for instance
Latin, lacks other abstract Cases like genitive, which is supposed to be assigned by nouns, or
ablative, which is supposed to be assigned by adjectives. Hence, nominal complements of
nouns and adjectives are not licensed by abstract Case, and therefore they do not pass the
Case Filter. This explains the ungrammaticality of the respective examples.
The difference between English and Latin is (i) that Latin has a richer morphological case
system than English and (ii) that Latin has a wider range of abstract Cases. With respect to
(i), we can say that Latin has a complex inventory of morphological markers for cases, while
English has no case morphology (528a) except for the pronominal system. With respect to (ii),
it is assumed that English has only abstract accusative Case, while Latin has more abstract
Cases (528b).
(528) Differences between English and Latin:
a. Case morphology in English is phonologically zero.
6.3. Morphological case 307
b. English has accusative case, but does not have genitive, dative, ablative, etc., as
Latin does.
(Pesetsky and Torrego 2011: 55)
In this sense, the categories verbs, nouns, adjectives, and prepositions are split into two
groups: verbs and prepositions assign accusative Case to their complements, while nouns
and adjectives do not assign accusative Case to their complements (529).
(529) Accusative Case assignment:
α assigns accusative case to β only if:
a. α is V or P (not N or A); and
b. β is the complement of α.
(Pesetsky and Torrego 2011: 56)
This is, of course, not the whole story on accusative Case assignment. It is observed that a
verb cannot assign accusative Case if it lacks an external argument. For instance, the verb
arrive in (530) does not license an external argument, and also no accusative Case is assigned
to its complement, viz. the internal argument.
(530) *It arrived a man.
This condition, which has become known as Burzio’s Generalization (Burzio 1986), is given
in (531). Note that Burzio’s Generalization is a condition that explicitly relates accusative
Case assignment and nominal licensing.
(531) Burzio’s Generalization:
If a verb licenses accusative, it has an external argument.
(Pesetsky and Torrego 2011: 58)
Let us now look at the assignment of nominative Case. It is assumed that, at least in
English, tensed inflection, i.e. a finite T head, assigns nominative Case to a nominal in its
specifier position. Consider the data in (532).
(532) a. We were happy [ that Mary won the prize ].
b. *We were happy [ ∅ Mary to win the prize ].
c. We would be happy [ for Mary to win the prize ].
(Pesetsky and Torrego 2011: 56)
The subject of the embedded clause (Mary) receives nominative Case in a finite clause (532a).
It cannot not receive nominative Case in an infinite clause (532b). Thus it does not pass the
Case Filter. For a subject of an infinite clause to be licit, it must be licensed, for example, by a
PP as in (532c). This leads to the generalization in (533).
308 6. Prepositional case
(533) Nominative Case assignment:
Finite T assigns nominative Case to its specifier.
(Pesetsky and Torrego 2011: 57)
The Case theory outlined so far not only explains nominal licensing facts, but it also
accounts for displacement phenomena encountered in passives (534a),(534b) or unaccusatives
(534c). In all these constructions, the verb is unable to assign accusative to the base position
of the internal argument, which is indicated here by an underscore. In order to pass the
Case Filter, the respective arguments move from their base positions to the specifier of finite
T, where they can receive nominative Case. Similarly, non-finite T in (534d) cannot assign
nominative to its subject, which thus moves (raises) to the specifier of finite T in the matrix
clause.
(534) a. The book was put __ [PP under the desk].
b. Mary was persuaded __ [CP that we should leave tomorrow].
c. The door opened __ suddenly.
d. Mary seemed [ __ to have written the letter].
(Pesetsky and Torrego 2011: 57)
The Case theory relates nominative Case to T, and accusative Case to V and P. But what
about languages like Icelandic that show more case morphology than just accusative and
nominative? Consider the Icelandic examples in (535) and (536), which are originally from
Andrews (1982). In (535a), the complement of the verb is marked with dative and in (535b) it
is marked with genitive.
(535) a. Ðeir
they
luku
finished
kirkjunni.
the-church.DAT
b. Við
we
vitjuðum
visited
Olafs.
Olaf.GEN
(Pesetsky and Torrego 2011: 61)
Likewise, the subjects of the passive clauses in (536a) and (536b) are marked with dative
and genitive, respectively. Note that Zaenen et al. (1985) show that the nominal arguments
marked with dative and genitive in (536) are true subjects.
(536) a. Kirkjunni
the-church.DAT
var
was
lokið
finished
(af Jóni).
b. Olafs
Olaf.GEN
var
was
vitjadh
visited
(af Jóni).
(Pesetsky and Torrego 2011: 61)
The question is now whether dative and genitive in (535) and (536) are the result of different
abstract Cases in Icelandic (i.e. abstract dative Case and abstract genitive Case), or whether
6.3. Morphological case 309
they show deviating morphology, obscuring underlying abstract accusative Case in (535) or
underlying abstract nominative Case in (536).
It can be shown that, in Icelandic, the dative and genitive arguments discussed above
are licensed by abstract accusative Case and abstract nominative Case, like in English, and
that the deviating morphological case realizations are simply “paint” that obscures abstract
accusative and nominative Case. Such morphological “paint” that is imposed by a verb on
its argument(s) is called quirky case (Andrews 1982). The relevant piece of evidence for
quirky case comes from (537b). While the dative subject in (537a) is licensed by finite T, i.e.
abstract nominative Case that is covered with quirky dative case, the subject of the embedded
infinitival clause in (537b) is not licensed, because there is no finite T. This shows that “quirky
case morphology is not sufficient to license a nominal in a language like Icelandic” (Pesetsky
and Torrego 2011: 61).
(537) a. Mér
me.DAT
býður
is-nauseated
við
at
setningafræði.
syntax
b. *Hún
he
reyndist
tried
mér
me.DAT
bjóða
to-be-nauseated
við
at
setningafræði.
syntax
(Pesetsky and Torrego 2011: 61–62)
In contrast, languages like Russian and Latin have more abstract Cases than just nomina-
tive and accusative. Consider the Russian examples in (538), where it is assumed that the
verbs actually assign abstract dative Case (538a) and abstract instrumental Case (538b).
(538) a. Ivan
Ivan
pomog
helped
studentam.
students.DAT.PL
b. Maša
Masha
upravljaet
manage
zavodom
factory.INSTR.SG
(Pesetsky and Torrego 2011: 62)
If the verbs in these examples are passivized, the internal arguments do not move to the
subject position to receive abstract nominative Case, because they are already licensed by
an inherent Case assigned from the verb (Chomsky 1986). The derivations in (539) crash,
because nominative Case assignment fails.150
(539) a. *Bylo
was
pomoženo
helped
studentam.
students.DAT.PL
b. *Bylo
was
upravleno
managed
zavodom.
factory.INSTR.SG
(Pesetsky and Torrego 2011: 62)
While nominative and accusative are considered to be structural abstract Cases, other ab-
stract Cases such as dative or instrumental are considered to be inherent abstract Cases. This
150In (538), the EPP requirement, stating that every clause needs a subject, is violated.
310 6. Prepositional case
terminology reflects the fact that the former are related to structural conditions. In particular,
nominative relates to finite T, and accusative relates to verbs licensing an external argument.
Inherent abstract Cases relate to conditions that are inherent to particular verbs or other lexical
categories.
As mentioned above, there are subjects in Icelandic that bear case morphology other
than nominative (e.g. Andrews 1976, Þráinsson 1979, Zaenen et al. 1985, Jónsson 1996,
Bobaljik 2008). These subjects are, in fact, assumed to be licensed by abstract nominative
Case. However, they surface with quirky case, i.e. morphological “paint”, which is why they
are referred to as quirky subjects. Consider (540), where the subjects bear quirky dative case.
(540) a. Jóni
Jon.DAT
líkuðu
like.PL
þessir
these
sokkar.
socks.NOM
‘Jon likes these socks.’
b. Það
EXPL
líkuðu
liked.PL
einhverjum
someone.DAT
þessir
these
sokkar.
socks.NOM
‘Someone liked these socks.’
(Jónsson 1996: 143, 153)
Zaenen et al. (1985) provide several diagnostics for subjecthood in Icelandic. In the
following, I will briefly present three of them. The first subject diagnostic relates to raising.
In Icelandic, only subjects can raise. Consider the verb sakna (‘miss’) in (541a) taking a
nominative and a genitive argument. In (541b), the embedded subject (Guðrún) moves to
the object position of the matrix clause, where it receives accusative. The occurrence of the
adverbial í barnaskam mínum (‘in my foolishness’), as being between the matrix object and
the embedded clause, corroborates the assumption that displacement took place (Þráinsson
1979: 389–393). The nominative argument and the genitive argument of the verb sakna can
also permute, as illustrated in (541c). Nevertheless, the embedded object (Harald) cannot raise
to the matrix object position with either case marking configuration, as illustrated in (541d).
(541) a. Guðrún
Gudrun.NOM
saknar
misses
Haraldar.
Harold.GEN
b. Ég
I
taldi
believed
Guðrúnu
Gudrun.ACC
í
in
barnaskap
foolishness
mínum
my
sakna
to-miss
Haraldar.
Harold.GEN
c. Haraldar
Harold.GEN
saknar
misses
Guðrún.
Gudrun.NOM
d. *Ég
I
taldi
believed
{
{
Haraldar,
Harold.GEN,
Harald
Harold.ACC
}
}
sakna
to-miss
{
{
Guðrún,
Gurdun.NOM,
Gudrúnu
Gudrun.ACC
}
}
(Zaenen et al. 1985: 448)
However, the quirky dative argument of the embedded verb hjálpa (‘help’) raises to the matrix
clause, indicating its subjecthood.
6.3. Morphological case 311
(542) Ég
I
tel
believe
þeim
them.DAT
hafa
to-have
verið
been
hjálpað
helped
í
in
prófinu.
the-exam
(Zaenen et al. 1985: 455)
The second diagnostic for subjecthood relates to subject-verb inversion. If a constituent
other than the subject is fronted to the sentence-initial position, then the subject appears
immediately after the finite verb. The accusative object in (543a) is fronted to the sentence-
initial position, and the verb occurs in the second position immediately followed by the
subject. In contrast, (543b), where a prepositional adverbial is fronted, is ungrammatical.
This is because the accusative object intervenes between the finite verb and the subject.
(543) a. Refinn
the-fox.ACC
skaut
shot
Ólafur
Olaf.NOM
með
with
þessari
this
byssu.
shotgun
b. *Með
with
þessari
this
byssu
shotgun
skaut
shot
refinn
the-fox.ACC
Ólafur
Olaf.NOM
(Zaenen et al. 1985: 450)
Again, the quirky dative argument of the verb hjálpað in (544) occurs immediately after the
finite verb, corroborating the assumption that it is, in fact, a subject.
(544) Í
in
prófinu
the-exam
var
was
honum
him.DAT
víst
apparently
hjálpað.
helped
(Zaenen et al. 1985: 456)
The third – and last subject diagnostic that I present here – relates to control constructions.
Only subjects can be understood as anaphorically-controlled PROs in Icelandic. For example,
in (545) the speaker hopes that they can go home.
(545) Ég
I
vonast
hope
til
for
að
to
fara
go
heim.
home
(Zaenen et al. 1985: 454)
The verb vanta (‘lack’) takes an accusative subject and an accusative object (546a). As shown
in (546b), subjects with quirky accusative case can also be PRO subjects of infinitives.
(546) a. Mig
me.ACC
vantar
lacks
peninga.
money.ACC
b. Ég
I
vonast
hope
til
for PRO.ACC
að
to
vanta
lack
ekki
not
peninga.
money.ACC
(Zaenen et al. 1985: 454)
Again, the quirky dative argument of the verb hjálpað in (547) can be targeted by a control
construction. This further suggests that the dative argument serves as a subject here.
312 6. Prepositional case
(547) Ég
I
vonast
hope
til
for PRO.DAT
að
to
verða
be
hjálpað.
helped
(Zaenen et al. 1985: 457)
These quirky subjects pose a problem for abstract Case. In particular, the problem is that
if subjecthood is a structural property associated with a particular syntactic position, i.e. the
specifier of TP, quirky Icelandic subjects must also be assumed to move to this position. This,
however, conflicts with a theory that motivates movement by means of the Case Filter, as
outlined above.
Consider the examples in (548). In (548a), the double object verb óska (‘wish’) triggers
quirky dative case and quirky genitive case on its objects. The object with quirky dative is
optional. If the verb is passivized, and the argument with quirky dative is left out, as in
(548b), the argument with quirky genitive serves as the subject. In fact, the argument is not
licensed as an object by abstract Case. If, however, the argument with quirky dative is present
in the passive, as in (548c), then the argument with quirky genitive is licensed as an object by
abstract Case, even though no external argument is present (against Burzio’s Generalization).
So, the question is, how can it be that a passive verb can assign abstract Case to an argument
in object position if only a dative argument – which is not an external argument – is present?
(548) a. María
Mary.NOM
óskaði
wished
(Ólafi)
Olaf.DAT
alls
everything.GEN
goðs.
good.GEN
b. Þess
this.GEN
var
was
óskað.
wished
c. Henni
her.DAT
var
was
óskað
wished
þess.
this.GEN
(Marantz 1991: 241)
The example in (548c) presents an instance of a nominal that receives quirky case even
though it is not licensed by abstract Case. In (549), we encounter the opposite situation. Here,
the external argument of the verb þykja (‘think, find’) is a quirky subject with dative case.
Besides, the internal argument bears nominative case. As seen in (540), there are indeed
nominative objects in Icelandic that also agree with the verb. “But if tensed inflection with
agreement is the source of nominative case on the objects of dative subject verbs, we would
expect the object to lose its nominative in an infinitive, because infinitive inflection does not
assign nominative” (Marantz 1991: 241–242). However, and although there is no finite T in
the embedded clause in (549), the object still bears nominative.
(549) Eg
I
tel
believe
[ henni
her.DAT
hafa
to-have
alltaf
always
þótt
thought
Olafur
Olaf.NOM
leiðinlegur
boring.NOM
]
‘I believe she always thought Olaf to be boring.’
(Marantz 1991: 242)
6.3. Morphological case 313
Based on these data, Marantz (1991) suggests dissociating nominal licensing (i.e. the
assignment of abstract Case) from case morphology. In fact, he claims that abstract Case
does not exist at all. In this sense, case morphology never reflects nominal licensing. Instead,
Marantz proposes that case is purely a phenomenon of the morphological component of
the grammar, hence the name morphological case theory. In particular, Marantz claims
that the calculation of case morphology for a given nominal is sensitive to the syntactic
environment in which the nominal is embedded. A crucial difference between abstract Case
theories and morphological case theories concerns the treatment of accusative case on direct
objects. Particularly in morphological case theories, accusative case is not related to the
licensing of an external argument. However, accusative case is considered to be the marked
structural case available in a case domain if there is another argument in the same case
domain receiving unmarked structural case, which is nominative case. Before Section 6.3.3
outlines the morphological case theory adopted in this thesis, Section 6.3.2 will present the
decomposition of case into composite abstract morphological features.
6.3.2 Feature decomposition of case
In this thesis, I assume that case is the morphological realization of composite abstract
morphological features. I do not assume that the morphological realizations of case (i.e.
nominative, accusative, dative, and genitive in German) are primitives (as implemented for
instance by Adger 2003), but I assume that these realizations are built on composite features
(Hjelmslev 1935, Jakobson 1936, Bierwisch 1967, Halle 1997, Halle and Vaux 1997, Calabrese
1998, Blevins 2000, Wunderlich 2003, Müller 2004, McFadden 2004, Wiese 2004, Alexiadou
and Müller 2008, Harley 2008, a.o.). To capture the four cases of German, I will adopt the
trichotomy of abstract case features proposed by McFadden (2004, 2007, 2008). The three
binary case features that I assume in this thesis are [±INF] for inferior, [±OBL] for oblique,
and [±GEN] for genitive. The decompositional view on case imposes a specificity hierarchy
on the morphological case realizations. Nominative is the least specified case, having no
feature specification. Accusative is more specific, being [+INF]. Dative is more specific,
being [+INF,+OBL]. Genitive is the most specific case in German, being [+INF,+OBL,+GEN].
Table 20 maps the three case features to the four German cases. Note that positive valuation
of a case feature is an explicit condition for a certain case to apply. For accusative case, e.g.,
this means that it applies if and only if the inferior case feature [+INF] is positive and the
other case features are not positive. In particular, these other features can be negative or
absent. This is indicated by the parenthesized minus in Table 20.
Before discussing these case features individually, let me first present two arguments in
favor of modeling case by means of composite features. The first argument for composite
case features is that they allow one to generalize over case-assignment patterns, that is,
over nominative/accusative-assignment and absolutive/ergative-assignment patterns. For
example, we can state that both nominative and absolutive (the unmarked structural cases)
314 6. Prepositional case
nominative accusative dative genitive[±INF] (−) + + +[±OBL] (−) (−) + +[±GEN] (−) (−) (−) +
Table 20: Composite morphological case features
require no feature specification, while accusative and ergative (the marked structural cases)
require the feature specification [+INF]. Both patterns then differ only with respect to the
assignment algorithm for the feature [+INF]. In anticipation of the precise assignment
algorithm of case features, we can assume that accusative is the result of assigning [+INF] to
the structurally lower argument in a configuration with two structural arguments that do not
already bear some case specification, while ergative is the result of assigning [+INF] to the
structurally higher argument in a comparable structural configuration.151
The second argument in favor of composite case features is that a decomposition of case
categories into abstract case features can account for syncretisms more economically. The
following example from Alexiadou and Müller (2008) illustrates this. Modern Greek has
three major cases:152 nominative, accusative, and genitive, which Alexiadou and Müller
(2008) model with the features [±GOV(erned)] and [±OBL(ique)].153 Alexiadou and Müller
consider nominative to be [−GOV,−OBL], accusative to be [+GOV,−OBL], and genitive to be[+GOV,+OBL]. Note that Alexiadou and Müller discuss a feature decomposition of inflection
classes and that a thorough presentation of their analysis would make an illustrative example
way too complex. This is why I ignore the inflection classes here and focus on the distribution
of nominal suffixes for number and case within only one inflection class – namely, Alexiadou
and Müller’s inflection class II, which the noun maxit(i)- (‘fighter’) in (550) belongs to. The
declension of maxit(i)- involves two syncretisms. First, the accusative and genitive forms in
the singular are identical (both maxiti) and, second, the nominative and the accusative forms
in the plural are identical (both maxites).
151The view that both accusative and ergative are the marked cases with a feature specification [+INF] is
challenged by a phenomenon called split ergativity. In languages with split ergativity, such as Hindi (Mohanan
1994, Keine 2007), a situation may arise where ergative and accusative are not in complementary distribution,
i.e. they can occur in the very same clause. This can easily be captured by assuming a further case feature
reflecting the subjecthood property of arguments that are marked with ergative case, and of those that are
marked with accusative case. While the former can serve as the subject, the latter normally cannot. The use of
the feature [±SUBJ(ect)] (Wiese 2004, Alexiadou and Müller 2008) could then further sub-distinguish the marked
structural (i.e. dependent) cases as ergative and accusative. Ergative would then be specified as [+INF,+SUBJ]
and accusative as [+INF,−SUBJ].
152Vocative case is ignored here.
153Note that Alexiadou and Müller use a slightly different set of composite case features. Nevertheless,
this difference is not crucial for the general motivation of feature decomposition of case. The feature [±GOV]
is, although conceptually different, comparable to [±INF], and Alexiadou and Müller’s feature [±OBL] is
comparable to the feature [±GEN] used here.
6.3. Morphological case 315
(550) Declension of Greek maxit(i) (‘fighter’):
singular plural
nominative maxiti-s maxit-es
accusative maxiti-∅ maxit-es
genitive maxiti-∅ maxit-on
(Alexiadou and Müller 2008: 17)
Using a non-decompositional feature system with privative case features, the suffixes for
the declesion in (550) could be stated as (551). The six different entries could, of course, be
reduced to four entries using disjunctive statements such as [ACC ∨ GEN]. Nevertheless, a
privative feature system requires six different (disjunctive) specifications.
(551) Suffixes for Greek inflection class II with privative case features:
a. -s ↔ [NOM]
b. ∅ ↔ [ACC]
c. ∅ ↔ [GEN]
d. -es ↔ [NOM,+PL]
e. -es ↔ [ACC,+PL]
f. -on ↔ [GEN,+PL]
Using a decompositional case feature system, these facts can be stated more economically.
Reconsider the declension of the Greek noun maxit(i), which I repeat in (552), with the
respective decompositional feature specifications.
(552)
singular plural
nominative maxiti-s maxit-es
[−GOV,−OBL] [−GOV,−OBL,+PL]
accusative maxiti-∅ maxit-es
[+GOV,−OBL] [+GOV,−OBL,+PL]
genitive maxiti-∅ maxit-on
[+GOV,+OBL] [+GOV,+OBL,+PL]
Based on the feature distribution, the specifications of the Greek inflection class II suffixes
can be stated as in (553).
(553) Suffixes for Greek inflection class II with decompositional case features
a. -on ↔ [+GOV,+OBL,+PL]
b. -es ↔ [−OBL,+PL]
c. -s ↔ [−GOV,−OBL]
d. ∅ ↔ [ ]
While the specifications for the suffixes -on and -s precisely match the respective case features,
the suffix -es and the zero exponent ∅ are underspecified. The suffix -es requires only the
316 6. Prepositional case
feature specification [−OBL,+PL] for insertion. No specification for the feature [±GOV] is made,
the distinctive feature for nominative case and accusative. Formulated in this underspecified
way, the suffix -es is a suitable match for nominative and accusative plural. Likewise, the zero
exponent is underspecified for both case and number features, which is why it is a suitable
match for both accusative and genitive singular, in contrast to the nominative singular suffix
-s, which is respectively specified.154
Let us now go back to the feature system assumed in this thesis and look at the case
features [±INF], [±OBL], and [±GEN] in more detail. I adopt the view of McFadden (2004: 211–
212) that the primary purpose of the feature [+INF] is to distinguish the marked from the
unmarked structural case. While the unmarked structural case (i.e. nominative case in
German) is [−INF] or underspecified with respect to this feature, the marked structural case
(i.e. accusative case in German) is specified as [+INF]. The feature [±INF] is distributionally
similar, though not equal, to the features [±GOVERNED] (Bierwisch 1967, Alexiadou and
Müller 2008), [±SUPERIOR] (Halle 1997, Halle and Vaux 1997), or [±OBJ] (Wiese 2004). The
difference, however, is that [±INF] can be defined in purely morphological terms without
recurring to syntactic notions, such as government (McFadden 2004: 212). The feature [+OBL]
is assigned to arguments by certain functional heads (McFadden 2004: 213). It is the char-
acteristic feature for dative case. In fact, I argue in Section 6.4.1 that prepositions – the
category P, to be precise – assign dative case features to a DP in their complement position.
At a first glance, the use of the feature [±GEN] seems to be redundant, because one could
formally model the four case categories in German by means of two binary features. Using
the features [±INF] and [±OBL], we could account for nominative case with [−INF,−OBL], for
accusative case with [+INF,−OBL], for dative case with [+INF,+OBL], and for genitive case
with [−INF,−OBL]. However, this specification of genitive case seems to miss some empirical
generalizations. Consider Bierwisch’s (1967) arguments, among others, in favor of a distinct
feature [±GEN]. One way in which genitive case is special is that it “is the only case for which
there is predominantly an overt marking in the singular of non-feminine nouns” (Bierwisch
1967: 247). Consider the German noun Lehrer (‘teacher’). While the nominative, accusative,
and dative forms all equal the base form Lehrer, the genitive form is marked with special
morphology, viz. Lehrer-s. Besides, Bierwisch notes that genitive case behaves differently
in the pronominal domain. While the nominative, accusative, and dative forms of the pro-
nouns are usually monosyllabic in German, the genitive forms are polysyllabic. Consider
the declension for the first person pronouns in German: ich (1.SG.NOM), mich (1.SG.ACC),
mir (1.SG.DAT), mein-er (1.SG.GEN), wir (1.PL.NOM), uns (1.PL.ACC, 1.PL.DAT), and un-ser
(1.PL.GEN). Bierwisch further points out that genitive can often be substituted by a PP. In fact,
a PP headed by von (‘of’) often serves as genitive suppletion (cf. Section 6.1). A similar regular
suppletion for other cases is not attested in German. Furthermore, genitive case is often
154Considering only this snippet of the Greek declension, one could of course specify the zero exponent ∅ as[+GOV] in order to account for accusative and genitive singular of inflection class II. However, in order to also
account for other inflection classes, where the zero exponent is also found, it is necessary to specify it as in (553).
6.3. Morphological case 317
involved when one expresses possession. For instance, many languages derive possessive
adjectives from genitive pronouns (Greenberg 1966: 100). Considering these arguments, I will
follow McFadden (2004: 213–214) and assume that the feature [±GEN] is what distinguishes
genitive from other cases.
6.3.3 Morphological case assignment
In morphological case theories, case features are typically assumed to figure only in the
morphological component of the grammar. With regard to Distributed Morphology, case fea-
tures are dissociated features, because they are assumed to be added to a DP under specified
conditions at PF (Embick and Noyer 2007: 309); see Section 3.3. This section illustrates how
such conditions at PF are specified.
An important distinction in (morphological) case theory in general is the one between
structural cases and non-structural cases. Structural cases are typically sensitive to structural
alternations, while non-structural cases are typically insensitive to structural alternations.
One of the most common case alternations is the alternation between active and passive
voice in the verbal domain. Consider the active clause in (554a), where the external argument
bears nominative case, and the internal argument bears accusative case. If the verb is
passivized, as in (554b), the external argument is demoted and the internal argument no
longer bears accusative case. Instead, it now bears nominative case. That is, nominative case
and accusative case are sensitive to the voice of the verb. They are thus considered to be
structural cases.
(554) a. dass
that
sie
she.NOM
einen
a.ACC
Mantel
coat
gekauft
bought
hat
has
‘that she bought a coat’
b. dass
that
ein
a.NOM
Mantel
coat
gekauft
bought
worden
become
ist
is
‘that a coat was bought’
(McFadden 2004: 188)
Structural case is computed in argument-structural terms. As observed by Yip et al.
(1987), Marantz (1991), Bittner and Hale (1996), McFadden (2004), a.o., there is a distinction
between the structural cases. Usually, one of the structural cases is the unmarked case,
because it behaves as the basic case. In fact, the unmarked case normally appears on the sole
argument of verbs that only have one argument (intransitive verbs) or on one argument of
verbs that have more than one argument (transitive or ditransitive verbs). This contrasts
with the marked case, which normally shows up on one argument of verbs that have another
argument already bearing the unmarked case. Following this line of reasoning, it is reasonable
to see the marked structural case as that case that depends on (the presence of) the unmarked
structural case. The fact that the marked case depends on the unmarked case is exactly what
is the core of most morphological case theories; a reason why these theories are sometimes
318 6. Prepositional case
referred to as ‘dependent case theories’. In fact, the marked structural case is often referred to
as the dependent case (Marantz 1991).
Generally, languages split in two groups: (i) accusative languages and (ii) ergative lan-
guages.155 In accusative languages (e.g. English, Icelandic, Latin, German), nominative is
the unmarked case and accusative is the marked case.156 In ergative languages (e.g. Basque,
Georgian, Tibetan), absolutive is the unmarked case and ergative is the marked case. The
contrast between accusative languages and ergative languages is essentially the distribution
of the respective structural cases over the structural arguments. In both accusative and
ergative languages, the sole argument of intransitive verbs bears the respective unmarked
case; i.e. nominative in accusative languages, and absolutive in ergative languages.157 The
patterns are the opposite for transitive verbs. In the accusative languages, on the one hand,
the external argument bears the unmarked case (nominative), while the internal argument
bears the marked case (accusative). In ergative languages, on the other hand, the external
argument bears the marked case (ergative), while the internal argument bears the unmarked
case (absolutive). Table 21 contrasts the nominative/accusative case-assignment pattern
of accusative languages with the absolutive/ergative case-assignment pattern of ergative
languages.
accusative languages ergative languages
intransitive verbs external arg. unmarked (NOM) unmarked (ABS)internal arg.
transitive verbs external arg. unmarked (NOM) marked (ERG)
internal arg. marked (ACC) unmarked (ABS)
Table 21: Accusative languages vs. ergative languages
Non-structural case is assigned to arguments in fixed structural positions. This contrasts
with structural case, which is computed in argument-structural terms. Non-structural case is
normally not sensitive to structural case alternations, such as the passive diathesis. Let us
add a benefactive argument with dative case to the clause in (554). We see that the dative
case marking does not change with respect to the voice of the verb. In both the active
(555a) and the passive (555b) clause, the benefactive argument bears dative case. Dative qua
non-structural case does not figure in the case alternation under passivization.
(555) a. dass
that
sie
she.NOM
ihm
him.DAT
einen
a.ACC
Mantel
coat
gekauft
bought
hat
has
‘that she bought him a coat’
155Let us ignore, for the moment, languages that show split-ergativity, i.e. languages with both ergative and
accusative case-assignment properties.
156English does, in fact, have accusative case. However, this is visible only in the pronominal system. English
does not have the morphological means to mark other nominal elements with accusative case.
157Intransitive verbs are defined as verbs with only one argument. Those with only an external argument are
normally called unergative verbs. Examples from English are laugh, dance, or run. Intransitive verbs with only
an internal argument are normally called unaccusative verbs. Typical English examples are arrive, die, or come.
See Perlmutter (1978) for one of the first discussions of the unaccusative-unergative distinction.
6.3. Morphological case 319
b. dass
that
ihm
him.DAT
ein
a.NOM
Mantel
coat
gekauft
bought
worden
become
ist
is
‘that a coat was bought for him’
(McFadden 2004: 188)
While structural case is assigned post-syntactically to DPs relative to the argument struc-
ture, non-structural case is assumed to be assigned to DPs in certain syntactic positions. For
example, the benefactive argument bearing dative in (555) can be identified on independent
grounds as being base-generated in the specifier position of an applicative phrase. We can
thus assume that DPs in the specifier position of applicatives receive non-structural dative
case.
Let us now look at two different types of non-structural case. Woolford (2006) argues
for two types of non-structural case: (i) lexical case and (ii) inherent case.158 Woolford
addresses the observation that some instances of non-structural case are more or less regular
and predictable on thematic grounds (inherent case), while other instances of non-structural
case seem to be arbitrary (lexical case). In fact, she (2006: 126) characterizes the difference
between lexical case and inherent case as follows. Lexical case is “lexically selected by
particular verbs [and] licensed by V inside the VP proper [...]”, while inherent case is a
“relatively predictable non-structural [c]ase licensed by little/light v heads above the VP
proper [...].” Furthermore, she (2006: 114) adduces the Icelandic data in (556) as instances of
lexical case. In particular, the quirky case markings on the subject arguments, i.e. dative in
(556a), accusative in (556b), and genitive in (556c), are assumed to be lexically conditioned
by the respective verbs. One crucial property of lexical case is that it is not predictable
on thematic grounds, i.e. there is no discernible syntactic or semantic reason why these
arguments should be excluded from structural case assignment.
(556) a. Bátnum
boat.DAT
hvolfdi.
capsized
‘The boat capsized.’
(Levin and Simpson 1981: (1b))
b. Bátinn
boat.ACC
rak
drifted
á
to
land.
shore
‘The boat drifted to the shore.’
(Jónsson 2003: 156)
c. Jóns
John.GEN
nýtur
enjoys
ekki
not
lengur
longer
við
at
‘John is no longer available.’
(Jónsson 2003: 130)
158Note that Woolford (2006) assumes abstract Case. Concerning this argument, this is not in opposition with
the assumptions made here.
320 6. Prepositional case
In German, only a few verbs trigger this kind of non-structural case marking. Looking at
simplex verbs, we find verbs like zeihen (‘accuse’) as in (557a) or harren (‘await’) as in (557b)
as instances of verbs that trigger lexical genitive on an internal argument.159
(557) a. Ich
I
bin
am
als
as
Lutheraner
Lutheran
aufgewachsen;
grown up
rechtfertigt
justifies
mich
me
das,
this
meine
my
katholischen
Catholic
und
and
jüdischen
Jewish
Mitschüler,
schoolmates
die
the
Hindus
Hindus
und
and
Buddhisten
Buddhists
Asiens,
from Asia
die
the
Atheisten
atheists
in
in
Marxismus
Marxism
und
and
Naturwissenschaft
natural science
des
the.GEN
Irrtums
fallacy
zu
to
zeihen?
accuse
‘I grew up as Lutheran; does this justify me to accuse my Catholic and Jewish
schoolmates, the Hindus and Buddhists from Asia, and the atheists in Marxism
and natural sciences of fallacy?’
b. Wir
we
alle
all
harren
await
deiner.
you.GEN
‘We all wait for you.’
In contrast, Woolford observes that instances of inherent case are, more or less, regularly
predictable on thematic grounds. In particular, she argues that this type of case is inherently
associated with θ-marking. Let’s look at Icelandic again. Dative case in (558) is predictable in
so far as benefactives in Icelandic often bear dative case. The picture is similar in German,
where benefactives can also show up with dative, as already illustrated in (555).
(558) Þeir
they.NOM
gáfu
gave
konunginum
king-the.DAT
ambáttina.
slave-girl-the.ACC
‘They gave the king the slave girl.’
(Maling 2002: 58, Woolford 2006: 112)
In contrast to Woolford (2006), I do not assume abstract Case in this thesis. Nevertheless, I
distinguish between inherent case and idiosyncratic case, which comes close to Woolford’s
lexical case. I recast Woolford’s typology of non-structural case in the following way. Both
inherent and idiosyncratic case are assigned post-syntactically to DPs in certain syntactic
positions. An example of inherent case is typically oblique case assignment to the specifier
position of applicatives, viz. marking the applied object with dative case in German. While
inherent assignment is independent of idiosyncratic contextual material, idiosyncratic case
assignment additionally depends on idiosyncratic contextual material. In particular, I assume
that the presence of certain Roots (i.e. certain Content features in certain Root positions) can
trigger idiosyncratic case assignment. For instance, I assume that the Root
√
harr corresponds
to the verb harren (‘await’). The presence of this Root triggers genitive case on the DP-
159Both the example in (557a) and the example in (557b) are excerpts from Von Weizsäcker (1988: 254).
6.3. Morphological case 321
complement of the verb; cf. (557b). Note that this does not mean that the respective Roots
assign case. It is only their presence that triggers idiosyncratic case assignment at PF.
Let’s take stock. I distinguish structural case from non-structural case. The former is
further subdivided into unmarked case and marked (or dependent) case, while the latter is
further subdivided into inherent case and idiosyncratic case. Consider the classification in
(559).
(559) (morphological)
case
structural case
unmarked case marked case
non-structural case
inherent case idiosyncratic case
Let us now see how the case features for a given DP-argument are calculated within a
given syntactic structure, and how they are then assigned to the respective DP-argument at
PF, i.e. in the morphological component of the grammar. Marantz (1991) proposes that the
assignment of morphological case proceeds along the Case Realization Disjunctive Hierarchy
in (560), which orders the morphological case types according to their specificity.
(560) Case Realization Disjunctive Hierarchy:
a. lexically-governed case
b. dependent case (accusative and ergative)
c. unmarked case (environment-sensitive)
d. default case
(Marantz 1991: 247)
Lexically-governed case, i.e. non-structural case, precedes the two structural case types:
dependent and unmarked case. The dependent (or marked) case, being the more specific one,
precedes the unmarked case. Default case, which is supposed to be the least specific case,
comes last; it is supposed to be the most general, domain-independent case that applies in
contexts where other case cannot apply. Note that I will not discuss default case here any
further; instead, I refer the reader to Schütze (2001). As I assume two types of non-structural
case, I will refine the Case Realization Disjunctive Hierarchy in (561), such that idiosyncratic
case, as the most specific case applying only in very specific contexts, precedes inherent case.
Marked (or dependent) case, unmarked case, and default case follow in this order.
322 6. Prepositional case
(561) Case Realization Disjunctive Hierarchy (refined):
a. idiosyncratic case
b. inherent case
c. marked case
d. unmarked case
e. default case
In what follows, I will illustrate the post-syntactic calculation and assignment of the morpho-
logical case types of the hierarchy in (561) in their respective order.
Let us first look at the post-syntactic assignment of idiosyncratic case. As mentioned
above, idiosyncratic case is assigned to DPs in certain syntactic positions. Additionally, the
assignment is conditioned by certain Content material in the respective syntactic head, i.e. in
the Root position of the verb. Consider the sentence in (562) with the verb harren (‘await’),
which takes a genitive complement.
(562) Wir
we
harrten
awaited
deiner.
you.GEN
‘We awaited you.’
For the sake of illustration, let us assume the simplified structure (563) to be underlying
the clause (562). Note that it is also assumed that Roots (or Content features) are generally
present at the point when case is calculated, i.e. at PF, which is after Spell-Out.
(563)
VoiceP
Voice’
VP
DP
deiner
V○
V○√harr
Voice○
DP
wir
In order to account for idiosyncratic case assignment to the internal argument of verbs like
harren (‘await’) or zeihen (‘accuse’), we can formulate the post-syntactic, viz. morphological,
case rule in (564), which lists the Roots conditioning idiosyncratic case.
(564) Idiosyncratic case assignment:
Assign [+INF,+OBL,+GEN] to a DP in the complement of V○ that contains one of the
following Roots:
√
harr,
√
zeih, ...
6.3. Morphological case 323
Admittedly, it is unattractive to list case assignment properties in this way. However, there are
only a few Roots that condition idiosyncratic case assignment. Only a few morphologically
simplex German verbs take an internal argument with genitive case. Examples are freuen
(‘rejoice over sth.’), harren (‘await sb./sth.’), schämen (‘be ashamed of sb./sth.’), zeihen (‘accuse
sb. of sth.’). Examples of morphologically complex verbs with a genitive argument are
bedienen (‘avail oneself of sth.’), bezichtigen ( ‘accuse sb. of sth.’), gedenken (‘commemorate’),
verdächtigen (‘suspect sb. of sth.’).
Haider (2010: 261) argues that the few ditransitive verbs in German where the accusative
argument precedes the dative argument in the base order are instances where dative is
assigned idiosyncratically (i.e. lexically, in Woolford’s system). This is unlike McFadden (2004)
and Meinunger (2000), for instance, who argue in favor of some verb-internal prepositional
structure with a phonologically zero preposition that inherently assigns dative. Examples of
this type of ditransitive verbs are aussetzen (‘expose’), unterziehen (‘subject’), zuführen (‘submit
to’), and entziehen (‘withdraw/extract from’).
(565) Er
he
setzte
put
die
the.ACC
Probe
sample
tiefen
low.DAT
Temperaturen
temperatures
aus.
out
‘He exposed the sample to low temperatures.’
(Haider 2010: 261)
For a thorough discussion of this type of verbs, I refer the reader to Cook (2006).160 What is
nevertheless interesting is that many verbs that presumably assign idiosyncratic case, may it
be genitive or dative, are morphologically complex. Instead of simply assuming that these
verbs condition idiosyncratic case, a fine-grained syntactic analysis, potentially involving
some prepositional element as proposed by Meinunger (2000) and McFadden (2004), and
taking their morphological complexity into account may shed light on the case-assigning
properties of these verbs. However, I refrain from analyzing these verbs here.
160In fact, the verbs zuführen and entziehen occur with both the ‘regular’ dative-accusative base word order
(566a) and the ‘exceptional’ accusative-dative (566b) base word order.
(566) a. Dann
then
habe
have
ich
I
dem
the.DAT
Wasser
water
die
the.ACC
Giftstoffe
poisons
entzogen.
stripped
‘Then I stripped the water of poisonous substances.’
b. Es
it
hat
has
die
the
Beschuldigte
accused
das
the.ACC
Tier
animal
der
the.DAT
öffentlichen
public
Beobachtung
view
entzogen.
withdrawn
‘The accused withdrew the animal from public view.’
(Cook 2006: 152, 154)
Assuming LFG’s Lexical Mapping Theory (Bresnan 2001), Cook (2006) convincingly argues that this difference
is related to a difference in conceptual structure. The verb entziehen in (566a) (‘strip of’) assigns the grammatical
functions OBJθ and OBJ, which map to the semantic roles BENEFICIARY and THEME, respectively, while entziehen
in (566b) (‘withdraw’) assigns the grammatical functions OBJ and OBL, which map to the semantic roles THEME
and LOCATION, respectively. Assuming that grammatical functions are hierarchically ordered (i.e. OBJθ > OBJ >
OBL) – reflected in the base word order – and that, in German, both OBJθ and OBL are marked with dative case,
while OBJ receives structural case (i.e. accusative in the transitive frame), Cook (2006) correctly accounts for this
difference.
324 6. Prepositional case
Consider now the active and passive clauses in (567) involving the ditransitive verb
schenken (‘give’). I will illustrate the assignment of inherent case and the two types of
structural case with this example.
(567) a. Die
the.NOM
Ulrike
Ulrike
schenkte
gave
dem
the.DAT
Sepp
Sepp
einen
a.ACC
Tirolerhut
Tyrolean hat
‘Ulrike gave Sepp a Tyrolean hat.’
b. Dem
the.DAT
Sepp
Sepp
wurde
became
ein
a.NOM
Tirolerhut
Tyrolean hat
geschenkt
given
‘Sepp was given a Tyrolean hat.’
(McFadden 2004: 30)
The active clause in (567a) contains three nominal arguments: an external argument marked
with nominative case, an internal argument marked with accusative, and an applied argument
(benefactive) marked with dative. In the corresponding passive clause in (567b), the external
argument is demoted. The applied argument is still marked with dative, but now the internal
argument is marked with nominative, not accusative. Adopting Kratzer’s (1996) Voice
analysis and Pylkkänen’s (2000, 2002) analysis of applicatives, we can assume the structures
in (568) for the two clauses in (567).
(568) a. VoiceaP
Voice′a
VP
ApplP
Appl′
DP
einen Tirolerhut
Appl○
DP
dem Sepp
V○
schenk
Voice○a
DP
Ulrike
b. VoicepP
VP
ApplP
Appl′
DP
ein Tirolerhut
Appl○
DP
dem Sepp
V○
schenk
Voice○p
The structures are identical up to the level of VP. The verb embeds a low applicative construc-
tion (Pylkkänen 2000, 2002) that relates two arguments, an applied argument (benefactive) in
6.3. Morphological case 325
the specifier position of the applicative and an internal argument in its complement position.
The two clauses differ in their voice. Let us assume, for the sake of argument, that active and
passive voice corresponds to two distinct voice heads, Voice○a for active voice, and Voice○p
for passive voice. While the active voice head Voice○a in (568a) projects a specifier position
for an external argument, the passive voice head Voice○p in (568b) does not project a specifier
position (Kratzer 1996).
Let us first look at inherent case assignment, i.e. the dative case of the applied argument.
It is typically assumed that inherent case is assigned to a DP in a certain syntactic position.
Among others, McFadden (2004) and McIntyre (2009) propose that the specifier of an applica-
tive is an inherent case position and receives dative case features in German. Assuming that
dative case is construed by the case features [+INF,+OBL] (cf. Section 6.3.2), we can formulate
the post-syntactic rule of inherent case assignment in (569).
(569) Inherent case assignment:
Assign [+INF,+OBL] to a DP in the specifier of Appl○.
(adapted from McFadden 2004: 225)
Let us now look at the assignment of the structural case, i.e. nominative and accusative
in (567). Having provided the applied argument with dative case features, two arguments
remain in the active structure in (568a), and one argument remains in the passive structure
in (568b). In the active clause, the external argument and the internal argument are eligible
for structural case. The former, which receives nominative case, is the structurally higher
argument and the latter, which receives accusative case, is the structurally lower argument.
Recall that accusative case is considered to be the marked structural case in contrast to
nominative case, which is considered to be the unmarked structural case. That is, structural
accusative depends on nominative case. In the passive clause, the internal argument is the
single argument eligible for structural case. It thus receives unmarked nominative. Assuming
that nominative case is specified by the absence (or negative valuation) of case features, and
that accusative case is specified as [+INF], the case distribution on the structural arguments
can be accounted for with the post-syntactic rules for structural case assignment in (570).
(570) Structural case assignment:
Assign [+INF] to a DPi if and only if
a. there is a DPj within the same phase, and
b. DPj c-commands DPi, and
c. DPj does not bear a non-structural case.
(McFadden 2007: 9)
Let us finally take a brief look at how the case assignment algorithm described above
would work for the absolutive/ergative assignment pattern.161 Recall from the discussion
161Note that I am omitting a discussion on split ergativity.
326 6. Prepositional case
above that, in ergative languages, external arguments of transitive verbs receive the marked
structural case (ergative), while internal arguments of transitive verbs receive the unmarked
structural case (absolutive). Consider the example from Yup’ik (‘Western Eskimo’) in (571).
(571) a. Angute-m
man-ERG
qusngiq
reindeer.ABS
ner-aa.
eat-[+TRANS].3s
‘The man is eating (the) reindeer.’
b. Qusngiq
reindeer.ABS
ner’-uq.
eat-[−TRANS].3s
‘The reindeer is eating.’
(Bobaljik 1993: 48)
In (571a), on the one hand, the external argument of the transitive verb eat surfaces with
ergative case, while the internal argument surfaces with absolutive case. In (571b), on the
other hand, verb eat is used intransitively, such that the internal argument is omitted. It
only projects an external argument. Crucially, in the intransitive usage of the verb, the
external argument surfaces with absolutive case, unlike in the transitive usage, where the
external argument is marked with ergative case. For the sake of illustration, let us assume
the structures in (572a) and (572b) for the clauses in (571a) and (571b), respectively. In both
clauses, the external argument is projected in the specifier of VoiceP. The two structures differ
in that the transitive verb in (572a) takes a complement, while the intransitive verb in (572b)
does not.
(572) a. VoiceP
Voice′
VP
DP
qusngiq
V○
ner-
Voice○
DP
Angute-m
b. VoiceP
Voice′
VP/V○
ner’-
Voice○
DP
Qusngiq
In both structures, all arguments are eligible for structural case. In particular, no argument is
in a position where it receives non-structural case. By simply permuting the DP-indexes in
the structural case assignment rule formulated in (570b) can account for the observation that
the external argument receives ergative only if the internal argument is present (otherwise it
receives absolutive). This has the effect that the higher of the two arguments receives [+INF],
6.4. Morphological case assignment of prepositions 327
i.e. ergative as the marked structural case, only if the lower argument is present. Otherwise,
it surfaces with absolutive as the unmarked structural case.
6.4 Morphological case assignment of prepositions
This section lays out a morphological case theory for simplex spatial prepositions in German.
First, I will argue that the lexical category P triggers the inherent assignment of the dative
case features [+INF,+OBL] to a DP in its complement position. Then, I will argue that those
prepositions that assign accusative case are those that contain the synsem feature bundle[LOC,+TO], characteristic of (pseudo)-geometric goal prepositions, or the synsem feature[±NINF], characteristic of route prepositions. I propose that exactly those synsem features
trigger the deletion of the oblique case feature [+OBL], resulting in accusative case assignment.
Finally, I briefly look at German prepositions that assign genitive, and at how this approach
might be extended to other languages.
6.4.1 Prepositions assign inherent dative
In this section, I will argue that dative case features are inherently assigned to DP-complements
of prepositions in German. Generally, this is in line with those scholars who assume that
dative is the ‘default’ case in the prepositional domain (Zwarts 2005a, Van Riemsdijk 2007,
Abraham 2010). However, regarding morphological case theories, there is a terminological
and also theoretical drawback in referring to dative case in the prepositional domain as a
default case. In morphological case theories, the notion of default case is typically reserved
for a morphological case that applies independently of categorial domains in contexts where
no other morphological case is applicable (Schütze 2001). That is, default case is considered
to be some kind of last-resort case if all other cases fail to apply. I do not assume, however,
that dative is that kind of default case in the prepositional domain. In particular, dative is not
a last-resort case in the prepositional domain (Caha 2010). Instead, I argue that dative is a
non-structural case (as it is typically argued for when regarding the verbal domain) that is in-
herently assigned by prepositions to DPs in their complement position: very much like when
applicatives inherently assign dative case to DPs in their specifier position. Nevertheless, let
us first look at the argument in favor of dative as the ‘default’ case in PPs.
Van Riemsdijk (1983, 2007) argues that dative is the ‘default’ case in oblique domains
in general, and thus also in the prepositional domain. Van Riemsdijk adduces data that
contain a case mismatch within German PPs. Some prepositions such as ohne (‘without’)
take an accusative complement, but dative appositives to nominals that are marked with
accusative case by a preposition are acceptable (573a). This is unlike dative appositives to
nominals, which are marked with structural accusative case by a verb (573b). This suggests
(i) that dative case must be available inherently in the prepositional domain, and (ii) that the
328 6. Prepositional case
accusative assignment in the prepositional domain differs in a yet-to-be specified way from
the accusative assignment in the verbal domain.
(573) a. Der
the
König
king
kam
came
aber
however
[PP ohne
without
Krone
crown.ACC
und
and
Zepter,
scepter.ACC
den
the.DAT
wichtigsten
most important
Symbolen
symbols
seiner
of his
Macht
power
und
and
Würde
dignity
].
‘But the king arrived without crown and scepter, the most important symbols
of his power and dignity.’
b. Ich
I
besuchte
visited
dann
then
Herrn
Mr.ACC
Müller,
Müller
unseren
our.ACC
/ *unserem
our.DAT
Vertreter
representative
in
in
Pforzheim.
Pforzheim
‘I then visited Mr. Müller, our representative in Pforzheim.’
(Van Riemsdijk 2007: 278)
Interestingly, we can also find corpus evidence that dative case is available for appositives
in PPs headed by prepositions that participate in the place/goal alternation and are used in
their goal reading, i.e. with accusative case (574).
(574) Ägypten
Egypt
spielte
played
mit
with
dem
the
Gedanken,
thought
einen
a
Kanal
canal
vom
from.the
Mittelmeer
Mediterranean
über
over
70
70
Kilometer
kilometers
bis
up
[PP in
in
die
the.ACC
Qattara-Depression,
Qattara Depression
einer
a.DAT
[...] riesigen
giant
Wüstenniederung
desert depression
], zu
to
sprengen.
blast
‘Egypt thought about blasting a canal over 70 kilometers from the Mediterranean up
to the Qattara Depression, a giant desert depression [...].’
(Die Tageszeitung)162
Haider (2010) discusses similar data for prepositions that take an accusative complement,
e.g. für (‘for’) in (575a) and (575b), or a genitive complement, e.g. trotz (‘despite’) in (576a).
These prepositions allow an appositive nominal in their complement domain, which is
marked with dative case even though the respective prepositions do not assign dative case.
Crucially, in a context that is comparable to (575a), but where accusative case is not triggered
by a preposition but structurally by a verb, dative case is illicit (575b). Likewise, if the genitive
is not triggered by the preposition, but by DP-internal structure, an appositive surfaces with
nominative rather than with dative (576b).
(575) a. [PP für
for
eine
a.ACC
Weltregierung,
world government
als
as
das
the.ACC
/
/
dem
the.DAT
Endziel
ultimate goal
]
(Leirbukt 1978: 3)
162Part of a corpus containing articles from 01.07.1988 until 30.06.1994
6.4. Morphological case assignment of prepositions 329
b. [PP für
for
Österreich,
Austria.ACC
als
as
den
the.ACC
/
/
dem
the.DAT
schwächeren
weaker
Partner
partner
]
(Leirbukt 1978: 4)
c. Österreich,
Austria.ACC
als
as
den
the.ACC
/
/
*dem
the.DAT
schwächeren
weaker
Partner
partner
unterstützen
support
‘support Austria as the weaker partner’
(Haider 2010: 243)
(576) a. [PP trotz
despite
eines
a.GEN
wenig
little
begabten
gifted
Mann-es
man-GEN
als
as
politisch-em
political-DAT
Berater
adviser
]
(Lawrenz 1993: 114)
b. die
the
Charakterisierung
characterization
dieses
this.GEN
Mannes
man.GEN
als
as
ein
a.NOM
gefährliches
dangerous.NOM
Subjekt
fellow
‘the characterization of this man as a dangerous fellow’
(Haider 2010: 245)
Let me add further data corroborating the idea that dative is an inherent case in the
prepositional domain. In German, there are prepositions that weaken their idiosyncratic case
assignment without a semantic shift. Some prepositions that assign genitive case can also
occur with a dative complement, but never with an accusative or nominative complement.
For example, the preposition wegen (‘due to’) typically takes a genitive complement (577a).
However, one can also find dative instead of genitive case, but never accusative or nominative
case (577b).
(577) a. Der
the
Zug
train
fiel
fell
[PP wegen
due to
eines
a.GEN
Sturm-s
storm-GEN
] aus.
out
‘The train was canceled due to a storm.’
b. Der
the
Zug
train
fiel
fell
[PP wegen
due to
einem
a.DAT
/ *einen
a.ACC
/ *ein
a.NOM
Sturm
storm
] aus.
out
‘The train was canceled due to a storm.’
This semantically neutral alternation is not restricted to the preposition wegen, although
wegen appears to the most frequent case. The alternation occurs also with other prepositions
that typically assign idiosyncratic genitive case. Examples are außer (‘except for’), gemäß
(‘according to’), laut (‘according to’), statt (‘instead of’), trotz (‘despite’), and während (‘during’).
Interestingly, this alternation is not restricted to individual registers, styles, or historic stages
of German; it can occur within one and the same PP. In fact, we can find PPs in the SDeWaC-
Corpus (Faaß and Eckart 2013) that take a coordination of two DPs as their complement where
one of the DPs has ‘expected’ genitive case, while the other DP has ‘unexpected’ dative case.
Consider the examples in (578) involving the preposition wegen. The majority of examples
of this kind are such that the DP with genitive case precedes the DP with dative case (578a)–
(578c). However, the other order is also attested (578d). Furthermore, other prepositions,
such as trotz, are also attested (579). Note also that in all examples below, accusative or
nominative DPs – instead of the dative DPs within the PPs – would be unacceptable.
330 6. Prepositional case
(578) a. Ich
I
habe
have
mir
me
diese
this
Memorycard
memory card
[PP wegen
due to
des
the.GEN
Speicherplatz-es
memory space-GEN
und
and
dem
the.DAT
günstigen
cheap
Preis
price
] gekauft.
bought
‘I bought this memory card because of its memory space and its low price.’
(SDeWaC, Faaß and Eckart 2013)
b. Der
the
russische
Russian
Präsident
president
Boris
Boris
Jelzin
Yeltsin
hat
has
am
on
Mittwoch
Wednesday
mit
with
den
the
vier
four
Ministern
ministers
konferiert,
conferred
die
who
[PP wegen
due to
des
the.GEN
Tschetschenienkrieg-s
Chechnya war-GEN
und
and
dem
the.DAT
Geiseldrama
hostage crisis
in
in
Budjonnowsk
Budyonnovsk
] Zielscheiben
target
vehementer
vehement
Kritik
critic
in
in
der
the
Staatsduma
State Duma
geworden
become
sind.
are
‘On Wednesday, the Russian president Boris Yeltsin conferred with the four
ministers who became the target of vehement criticism in the State Duma, due
to the war in Chechnya and the hostage crisis in Budyonnovsk.’
(German section of the European Language News Corpus)163
c. Die
the
Mutter
mother
sorgte
worried
sich
REFL
natürlich
certainly
immer
always
noch
still
und
and
wollte
wanted
ihrem
her
Sohn,
son,
wenn
if
er
he
endlich
finally
käme,
came
bittere
bitter
Vorwürfe
reproaches
[PP wegen
due to
seines
his.GEN
langen
long
Schweigen-s
silence-GEN
und
and
seinem
his.DAT
herzlosen
cruel
Leichtsinn
recklessness
] machen.
make
‘Of course the mother still worried and she wanted to scold her son, if he finally
came, for his long silence and his cruel recklessness.’
(Gutenberg Corpus)164
d. Im
in.the
Alter
age
bleibt
stay
man
one
dann
then
meist
often
[PP wegen
due to
dem
the.DAT
Herz
heart
oder
or
eines
a.GEN
Karzinom-s
carcinoma-GEN
] auf
upon
der
the
Strecke.
way
‘When people get old, they often die of cardiac diseases or a carcinoma.’
(SDeWaC, Faaß and Eckart 2013)
(579) Der
the
Nachteil
disadvantage
des
of the
Bildes
picture
ist
is
aber,
but
[PP trotz
despite
des
the.GEN
guten
good
Kontrast-es
contrast-GEN
und
and
dem
the.DAT
starken
strong
Farbumfang
color gamut
], die
the
Softheit
softness
des
of the
Bildes
picture
[...].
‘However, the disadvantage of the picture is its softness, despite its good contrast
and the wide color gamut, [...].’
(SDeWaC, Faaß and Eckart 2013)
163URL: http://www.ldc.upenn.edu/Catalog/catalogEntry.jsp?catalogId=LDC95T11
(27.06.2017)
164URL: http://www.gutenberg.org/ (27.06.2017)
6.4. Morphological case assignment of prepositions 331
Note that this mismatch between genitive and dative case in coordination structures is not
attested for genitives that occur outside PPs, e.g. possessive genitives. Consider the example
in (580), where the second DP cannot surface with dative case, but necessarily bears genitive
case.
(580) die
the
Autos
cars
der
the.GEN
Lehrenden
teachers
und
and
der
the.GEN
/ *den
the.DAT
Studierenden
students
‘the cars of the teachers and of the students’
The data presented above indeed suggest that dative case is a kind of default case in
the prepositional domain; that is, a last-resort case if – for whatever reason – the actual
morphological case fails to apply. However, Caha (2010) adduces an argument that dative
cannot be the prepositional default case in the sense of a last-resort case. Consider the two
distinct usages of the temporal preposition vor (‘before, ago’) in (581).
(581) a. Die
the
Dinosaurier
dinosaurs
sind
are
vor
before
der
the.DAT
Eiszeit
ice age
ausgestorben.
died out
’The dinosaurs died out before the ice age.’
b. Thomas
Thomas
ist
is
vor
before
einem
a.DAT
Jahr
year
nach
to
Cambridge
Cambridge
gegangen.
went
’Thomas went to Cambridge a year ago.’
(Haspelmath 1997: 11)
In the anterior reading of vor (‘before’) in (581a), the PP denotes some point in time before the
ice age. This reading is typically considered to be the transparent one. In the distance-past
reading of vor (‘ago’) in (581b), vor seems to have a non-compositional meaning, because the
PP denotes a point in time located exactly one year before the utterance time, viz. it measures
a distance backwards in time.165
Caha (2010) proposes that the distance-past reading derives from the anterior reading.
He analyzes the surface complement of vor in the distance-past reading as a measure phrase
that measures the time backwards from some silent deictic element referring to the utterance
time (UT). This silent element arguably serves as the underlying complement of the preposi-
tion, which has the advantage that a unified anterior reading for vor can be assumed. The
underlying structure for the distance-past reading of vor (582) is sketched in (583). In particu-
lar, the measure phrase ein Monat (‘a month’) is arguably base-generated in some specifier
position of the PP.
(582) vor
before
einem
a.DAT
Monat
month
‘one month ago’
(Caha 2010: 191)
165Note that I adopt Haspelmath’s (1997) terms ‘anterior’ and ‘distance-past’ without a commitment to his
analysis.
332 6. Prepositional case
(583) [ a month [ before = vor [ UT ] ] ]
(Caha 2010: 192)
Disregarding Caha’s precise implementation concerning movement and word order, what is
crucial here is the fact that measure phrases normally have access to accusative case, which
is illustrated in (584). We can assume that (584), where vor exhibits the transparent anterior
reading, has a comparable underlying structure to (583), with the only difference being that
the overt DP dem Konzert (‘the concert’) occupies the complement position of the preposition,
instead of the silent element UT.
(584) einen
a.ACC
Monat
month
vor
before
dem
the.DAT
Konzert
concert
‘a month before the concert’
(Caha 2010: 193)
Considering the fact that measure phrases typically have access to accusative case, it is
not clear why vor in the distance-past reading takes a dative complement. If dative was
a last-resort default case in the prepositional domain, the complement DP of vor in the
distance-past reading should not bear dative case because, qua measure phrase, it already has
accusative case and does not need a last-resort case. In fact, dative case seems to ‘overwrite’
an underlying measure-phrase accusative case, which would not be expected if dative was a
default case. Thus, Caha reasonably concludes that dative in the prepositional domain cannot
be a default case in the sense of a last-resort case. Instead, he proposes that dative is assigned
in the specifier position of some functional projection above the underlying prepositional
structure to which the measure phrase raises (cf. ‘raising to dative’, Caha 2010: 190–194).
Note that I refrain from analyzing vor any further in this thesis.
Let us take stock. Dative case is systematically available in the prepositional domain
when other cases fail to apply. However, dative does not serve as a last-resort case. Hence,
I propose that dative is an inherent case post-syntactically assigned, but not only to the
specifier position of applicatives (McFadden 2004: 225), but also to the complement position
of prepositions. In particular, I formulate the morphological rule for Prepositional Case
Assignment (PCA) in (585).
(585) Prepositional Case Assignment (PCA):
Assign [+INF,+OBL] to a DP in the complement position of P○.
The morphological rule PCA alone predicts that all DP-complements of prepositions receive
dative case features. Assuming the morphological rule in (585) that inherently assigns
dative case features to a DP in the complement position of a preposition, we need a special
explanation for those prepositions with an accusative complement, i.e. (pseudo)-geometric
goal and route prepositions. Section 6.4.2 addresses these cases. In Section 6.4.3, I tentatively
sketch an analysis for some prepositions that idiosyncratically take a genitive complement.
6.4. Morphological case assignment of prepositions 333
6.4.2 Impoverishment to accusative
At the end of Section 6.4.1, I proposed the morphological rule for Prepositional Case Assign-
ment (PCA), stating that the lexical category P assigns inherent dative case features to its
complement, i.e. [+INF,+OBL]. Recall from Section 6.3.2 that I assume a decomposition of
case features, such that accusative case is specified as inferior, i.e. [+INF], while dative case is
specified as inferior and oblique, i.e. [+INF,+OBL]. That is, the difference between dative and
accusative case relates to the presence of the oblique case feature [+OBL]. Informally speaking,
we could also say that accusative case is ‘contained’ in dative case, which comes close to
Caha’s (2010) idea of case peeling.166 So, why do some prepositions apparently assign only
an inferior feature, instead of both an inferior feature and an oblique feature? The answer to
this question is, I propose, that in fact all prepositions assign an inferior case feature and an
oblique case feature to their complements (so, PCA always applies), but that certain synsem
contexts can trigger an additional morphological rule to the effect that oblique case features
are deleted. In particular, I propose a morphological Impoverishment rule (cf. Section 3.4.1)
that deletes the oblique case feature [+OBL], yielding the change from dative to accusative.
Now, the question is: Under which conditions does such an Impoverishment rule ap-
ply? In Section 6.1, we identified (i) (pseudo)-geometric goal prepositions and (ii) route
prepositions as those prepositions that take accusative complements, while all other sim-
plex spatial prepositions take dative complements; cf. Table 19. The respective structures of
(pseudo)-geometric goal prepositions and route prepositions are given in (586).167
(586) a. Structure of (pseudo)-geometric goal prepositions:
QP
PP
DPP○/Q○[LOC,+TO]
b. Structure of route prepositions:
PP
DPP○[±NINF]
166Note, however, that Caha (2010) assumes the a syntactic repercussion of case features to the effect that
they form a syntactic shell structure around DP. Opposed to that, I assume that case features are purely
morphological without any repercussion in syntax proper.
167(586a) is the structure at PF after Q-to-P-Lowering and subsequent P/Q-Fusion has taken place.
334 6. Prepositional case
The synsem feature bundle [LOC,+TO], hosted by P/Q, is characteristic of (pseudo)-geo-
metric goal prepositions, while the synsem feature [±NINF], hosted by P, is characteristic of
route prepositions. The negatively-valued synsem feature [−TO] is characteristic of source
prepositions, which all take dative complements. We can therefore assume that [−TO] is
irrelevant for morphological case assignment. Note that we can further assume that the
synsem feature [AT], which is characteristic of non-geometric spatial prepositions is also
irrelevant for morphological case assignment, because all non-geometric prepositions (bei ‘at’,
zu ‘to’, and von ‘from’) take a dative complement. As for route prepositions, we can identify
the synsem feature [±NINF] as their characteristic context, irrespective of whether the feature
is positive or negative.
Based on these considerations, I propose the Prepositional Case Impoverishment (PCI)
rule in (587) that deletes the oblique case feature [+OBL] if the structure of a preposition
contains the feature bundle [LOC,+TO], accounting for (pseudo)-geometric goal prepositions;
or the feature [±NINF], accounting for route prepositions.
(587) Prepositional Case Impoverishment (PCI):
Delete [+OBL] in the local context of P/Q[LOC,+TO] or P[±NINF].
At this point, it is important to mention that PCA precedes PCI at PF. This is in line with the
assumptions about the PF branch made in Chapter 3. In particular, I assume that PCA is an
instance of dissociated feature assignment (cf. Section 3.3) that precedes operations on nodes,
such as Impoverishment (cf. Section 3.4.1). In other words, PCA feeds PCI.
PCI predicts accusative case, not only for the (pseudo)-geometric goal prepositions an
(‘onto’), auf (‘up onto’), and in (‘into’); and for the route prepositions durch (‘through’), über
(‘over, across’), and um (‘around’) – it predicts accusative case also for the spatial usage of
nach (‘to’). This is clearly in contradiction to Zwarts (2005a, 2006), who claims that spatial
nach takes a dative complement. Note, however, that the morphological case of spatial nach
is never discernible. Spatial nach is illicit in all contexts where morphological case would
be visible, e.g. on a determiner, on an attributive adjective, or on a pronoun. Recall from
the discussion in Section 5.4.2.2 that one condition for the insertion of nach is the absence
of φ-features; cf. (411) on page 244. In fact, φ-features seem to be a precondition for the
realization of case morphology. As soon as case morphology is visible in a respective context,
another pseudo-geometric goal preposition (i.e. an, auf, or in) with accusative case is used.
(588) a. Hans
Hans
reiste
traveled
nach
to
Italien.
Italy
b. Hans
Hans
reiste
traveled
*nach
to
/
/
in
into
das
the.ACC
sonnige
sunny
Italien.
Italy
Note in this respect that the temporal usage of nach (‘after’), which takes a dative com-
plement, is different. Qua preposition, it involves the lexical category P, which correctly
predicts dative case, due to PCA. Furthermore, it should be clear that temporal nach has a
6.4. Morphological case assignment of prepositions 335
different structure than spatial nach. Crucially, it involves neither the synsem feature bundle[LOC,+TO], nor the synsem feature [±NINF], and its complements are thus not subject to PCI.
Note, however, that the synsem feature bundle [LOC,+TO] and the synsem feature[±NINF] are not necessarily the only contexts that may trigger PCI. In Section 5.1.3, I briefly
discussed that the non-geometric goal and source prepositions zu (‘to’) and from (‘from’),
which are bounded, have unbounded counterparts, unlike the (pseudo)-geometric goal and
source prepositions. In particular, I argued that the circumpositions auf ... zu (‘towards’) and
von ... weg (‘away from’) are the unbounded non-geometric goal and source prepositions. The
circumposition auf ... zu – which involves P/Q[AT,+TO] and Asp[+UNBD] – takes accusative
complements (589a), while the circumposition von ... weg – which involves PQ[AT,−TO] and
Asp[+UNBD] – takes dative complements (589b).
(589) a. Hans
Hans
rannte
ran
auf
upon
die
the.ACC
Hütte
hut
zu.
to
‘Hans ran towards the hut.’
b. Hans
Hans
rannte
ran
von
from
der
the.DAT
Hütte
away
weg.
‘Hans ran away from the hut.’
In order to account for accusative in (589a), I propose that the context P/Q[AT,+TO] plus
Asp[+UNBD] also triggers PCI. Note, however, that this feature context does not appear to be
a systematic PCI context, but an idiosyncratic one.
Furthermore, it is interesting that many functional usages of the prepositions an, auf, and
in selected by certain verbs also take accusative complements; consider (590).
(590) Hans
Hans
glaubt
believes
an
on
eine
a.ACC
/ *einer
a.DAT
bessere
better
Zukunft.
future
‘Hans believes in a better future.’
If one wants to assume that such PPs also involve a lexical category feature P triggering PCA,
one would then argue that such functional contexts also trigger PCI.
Let me close this section with a remark on the data in (573a), (574), and (575a), which
I adduced in favor of dative as the inherent prepositional case. These examples involve
accusative PPs containing appositive DPs with dative case. The respective PPs are repeated
here as (591), (592), and (593).
(591) ohne
without
Krone
crown.ACC
und
and
Zepter,
scepter.ACC
den
the.DAT
wichtigsten
most important
Symbolen
symbols
seiner
of his
Macht
power and dignity
(592) in
in
die
the.ACC
Qattara-Depression,
Qattara Depression
einer
a.DAT
[...] riesigen
giant
Wüstenniederung
desert depression
336 6. Prepositional case
(593) für
for
eine
a.ACC
Weltregierung,
world government
als
as
das
the.ACC
/ dem
the.DAT
Endziel
ultimate goal
Under the assumption that PCA is the general morphological rule that provides dative
case features to complements of prepositions, it is clear, in this kind of data, where the
underlying dative comes from. It is the lexical category P that triggers the assignment of
an inferior and oblique case feature [+INF,+OBL] to its complement domain. Furthermore,
we can assume that both the prepositions ohne (‘without’) and für (‘for’) contain respective
(synsem or Content) features that also trigger PCI. Interestingly, the appositive DPs seem
to be in a structural position that is not necessarily targeted by PCI, while the local context
of the preposition is of course targeted by PCI. In this way, we can account for the fact that
appositive DPs in non-dative PPs can surface with dative case. However, I will leave further
exploration of this phenomenon for future research.
6.4.3 Outlook for other cases and other languages
In order to account for the idiosyncratic genitive case assignment of prepositions like wegen
(‘due to’) and trotz (‘despite’) (cf. Section 6.1), we can formulate the Idiosyncratic Preposi-
tional Case Assignment (IPCA) rule in (594). It idiosyncratically assigns the genitive case
feature [+GEN] in addition to the inferior and oblique case features [+INF,+OBL], which are
regularly assigned by the lexical category P. The IPCA is formulated in such a way that it
applies only in certain exceptional contexts. In particular, the presence of certain Roots (or
synsem features) triggers the application of IPCA.
(594) Idiosyncratic Prepositional Case Assignment (IPCA):
Assign [+INF,+OBL,+GEN] to a DP in the complement position of P○ containing one
of the following Roots:
√
wegen,
√
trotz,
√
während, ...
In order to account for the phenomenon that prepositions like wegen and trotz can al-
ternatively take dative complements, instead of genitive complements, without a semantic
difference, we can assume that the application of IPCA fades. As IPCA is an idiosyncratic
rule, this is no surprise. Consider the PPs in (577), which are repeated here as (595).
(595) a. wegen
due to
eines
a.GEN
Sturm-s
storm-GEN
b. wegen
due to
einem
a.DAT
Sturm
storm
Consider also the PP in (578a), which is repeated here as (596). In PPs of this kind, we find
two different case markings on the coordinated DPs: genitive case on the first DP, and dative
case on the second DP. It seems that, in these examples IPCA, can only reach out to the closer
DP.
6.4. Morphological case assignment of prepositions 337
(596) wegen
due to
des
the.GEN
Speicherplatz-es
memory space-GEN
und
and
dem
the.DAT
günstigen
cheap
Preis
price
Adopting an asymmetric analysis of coordination à la Zhang (2010), i.e. where coordinated
phrases are assumed to be in a specifier-complement relation, we could analyze the PP in
(596) as given in (597). The non-application of IPCA on the second DP can then be understood
as a locality effect. Only the so-called external conjunct in the specifier position of D&P is
local enough for IPCA. As for the so-called internal conjunct in the complement position of
D&P, regular PCA applies.
(597)
PP
D&P
D′&
DPINT
dem günstigen Preis
D○&
und
DPEXT
des Speicherplatzes
P○
wegen
Let me close this section with some cross-linguistic remarks about the morphological case
theory for prepositions proposed in this thesis. The first remark concerns the PCA rule. Note
that PCA is claimed to be part of PF, i.e. of the morphological component of the grammar.
This component is language-specific and can vary from language to language. I do not claim
that PCA holds universally. And even if rules comparable to PCA were attested for other
languages, it may well be that other languages assign other inherent cases in the prepositional
domain. Nevertheless, it seems to be plausible to assume that other Germanic languages
with a case system comparable to German, e.g. Icelandic and Faroese, also have a PCA rule
involving dative case. With regard to non-Germanic languages it seems to be plausible to
assume that prepositions assign an oblique case inherently.
The second remark concerns the PCI rule. The place/goal alternation is attested not only
for German (dative/accusative alternation), but also for other Indo-European languages,
e.g. Ancient Greek (Smyth 1956), Classical Armenian (Schmitt 1981), Czech (Emonds 2007,
Biskup 2009, Caha 2010, 2013), Icelandic (Pétursson 1992, Svenonius 2002), Latin (Hale and
Buck 1903), Russian (Arsenijevic´ and Gehrke 2009), and Serbo-Croatian (Arsenijevic´ and
Gehrke 2009). Table 22 lists cross-linguistic examples of spatial prepositions participating
in the place/goal alternation. From a cross-linguistic perspective, it is interesting that the
languages show a certain variety concerning the case co-occurring with place prepositions,
but they show no variety concerning the case co-occurring with the respective goal path
338 6. Prepositional case
prepositions. On their goal-path reading, these prepositions always take accusative. That is,
several oblique cases figure with place prepositions, while it is the marked structural case,
not oblique, which figures with (derived) goal path prepositions. In fact, Caha (2010: 181)
formulates the so-called Law of the Locative-Directional Alternation in (598).
(598) The Law of the Locative-Directional Alternation:
For alternating adpositions, locative interpretation is associated with an oblique
case, directional interpretation with accusative.
(Caha 2010: 181)
If we generalized PCI to the extent that it targets all oblique cases and thereby impoverishes
the case features to the effect that only the minimally-marked case feature expressing in-
feriority, i.e. [+INF], remains, then one could claim that this generalized PCI is a common
morphological rule across Indo-European languages for marking the place/goal alternation
in the prepositional domain.
language adposition case with
place reading
case with
goal path reading
Ancient Greek para (‘at’) dative accusative
Classical Armenian i (‘in’) locative accusative
Czech na (‘on’) locative accusative
pod (‘under’) instrumental accusative
Icelandic í (‘in’) dative accusative
Latin in (‘in’) ablative accusative
Russian v (‘in’) locative accusative
pod (‘under’) instrumental accusative
Serbo-Croatian u (‘in’) locative accusative
pod (‘under’) instrumental accusative
Table 22: Cross-linguistic examples of alternating adpositions (cf. Caha 2010: 181)
My third and last cross-linguistic remark concerns the variety of oblique cases seen in
Table 22. Czech, Russian, and Serbo-Croatian, which generally have, qua Slavic languages,
a relatively rich system of morphological case, show a further interesting systematicity.
Topological place prepositions take complements with locative case, while projective place
prepositions take complements with instrumental case. This seems to suggest that topolog-
ical and projective prepositions involve different structures. This difference, which can be
understood in terms of different synsem features, can be held accountable for the respective
morphological case-assigning properties. With regard to Slavic prepositions, I refer the reader
to Caha (2010, 2013), and leave an implementation in terms of morphological case for further
research.
6.5. Summary 339
6.5 Summary
This chapter discussed prepositional case in German. I presented (i) the case assignment
properties of (spatial) prepositions in German (Zwarts 2006); (ii) several previous approaches
to prepositional case (Bierwisch 1988, Arsenijevic´ and Gehrke 2009, Caha 2010, Den Dikken
2010); and (iii) a morphological case theory proposed for the verbal domain Marantz (1991),
McFadden (2004). This paved the way for a proposal of a morphological case approach to
spatial prepositions in German.
Section 6.1 presented the case assignment properties of spatial prepositions in German.
It picked up the classification of spatial prepositions into (i) place prepositions and (ii)
path prepositions; the latter subdivide into (ii.a) directed prepositions (goal and source
prepositions) and (ii.b) undirected prepositions (route prepositions). This classification was
combined with the one proposed in Section 5.1.2, namely that spatial prepositions can be
(pseudo)-geometric prepositions or non-geometric prepositions. It turned out that (pseudo)-
geometric goal prepositions and route prepositions co-occur with accusative case, while
(pseudo)-geometric place and source prepositions and non-geometric prepositions co-occur
with dative case. In addition, Section 6.1 briefly presented the German spatial prepositions
that assign genitive case.
Section 6.2 presented four previous approaches to prepositional case: Section 6.2.1 pre-
sented Den Dikken’s (2010) structural approach where prepositional case assignment is linked
to functional heads in the extended projection of prepositions; Section 6.2.2 presented Caha’s
(2010) peeling approach where DPs are assumed to peel off their hierarchically structured case
layers under movement; Section 6.2.3 presented Arsenijevic´ and Gehrke’s (2009) approach
where it is argued that accusative case in spatial PPs stems from PP-external structure; and
Section 6.2.4 presented Bierwisch’s (1988) lexicalist approach where the case assignment
properties of spatial prepositions are assigned to their lexical entries. Some drawbacks of the
approaches were discussed, too.
Section 6.3 motivated and outlined the hypothesis that case is not a phenomenon of the
syntax proper, but of the morphological component of the grammar. Section 6.3.1 discussed
the notions of abstract Case and morphological case (Pesetsky and Torrego 2011). Abstract
Case is linked to nominal licensing, while morphological case is linked to the morphophono-
logical realization of case. Section 6.3.2 presented the feature decomposition of case. In
particular, this section laid out the idea that the case categories nominative, accusative, dative,
and genitive are not grammatical primes, but the result of composite case features: nomi-
native case corresponds to the absence of case features, accusative case corresponds to the
feature [+INF] (for inferior), dative case corresponds to the feature bundle [+INF,+OBL] (obl
for oblique), and genitive case corresponds to the feature bundle [+INF,+OBL,+GEN] (gen for
genitive); cf. Bierwisch (1967), McFadden (2004), a.o. Section 6.3.3 presented a commonly
assumed classification of morphological case into (i) structural case and (ii) non-structural
case; the former further subdivides into (i.a) unmarked case and (i.b) marked case, while the
340 6. Prepositional case
latter further subdivides into (ii.a) inherent case and (ii.b) idiosyncratic case. This section also
spelled out the principles of structural and non-structural morphological case assignment
proposed for the verbal domain (Marantz 1991, McFadden 2004, 2007).
Section 6.4 laid out a morphological case theory for simplex spatial prepositions in German.
Using corpus data, a.o., I argued in Section 6.4.1 that the lexical category P triggers the
inherent assignment of the dative case features [+INF,+OBL] to a DP in its complement
position; see the morphological rule for Prepositional Case Assignment (PCA) in (585) on
page 332. In Section 6.4.2, I argued that those prepositions that assign accusative case are those
that contain the synsem feature bundle [LOC,+TO], characteristic of (pseudo)-geometric goal
prepositions, or the synsem feature [±NINF], characteristic of route prepositions. I proposed
that exactly those synsem features trigger the deletion of the oblique case feature [+OBL],
resulting in accusative case assignment; see the rule of Prepositional Case Impoverishment
(PCI) in (587) on page 334. In Section 6.4.3, I briefly looked at German prepositions that assign
genitive, and at how this approach might be extended to other languages.
Appendix A.2 provides a synopsis of the morphological case approach to spatial preposi-
tions in German proposed in this thesis.
Chapter 7
Conclusions and prospect for future work
Conclusions
In this thesis, I spelled out the syntax, semantics, and morphology of spatial prepositions
in German. I did this by assuming the Y-model of grammar (Chomsky 1995, Marantz 1997,
Bobaljik 2002, 2008, Embick and Noyer 2007, Embick and Marantz 2008, Harley 2012, 2014,
a.o.), where Syntax is considered to be the only combinatorial engine (Marantz 1997, Bruening
2016). Syntactic structures on which no further syntactic operations are executed constitute
Spell-Out. Syntactic structures at Spell-Out interface with the Articulatory-Perceptual (A-P)
systems, on the one hand, and with the Conceptual-Intentional (C-I) systems, on the other.
The interface representation of the A-P systems is Phonological Form (PF). The operations
executed at PF constitute the Morphology. The interface representation of the C-I systems is
Logical Form (LF). The operations executed at LF constitute the Semantics. The Y-model of
grammar is depicted in Figure 47; cf. the beginning of Chapter 2 and in particular Figure 3 on
page 12.
The structure of this thesis reflects the Y-model of grammar. Chapter 2 addressed the
syntax, Chapter 3 addressed the morphology, and Chapter 4 addressed the semantics. Then,
Chapter 5 spelled out German spatial prepositions with regard to syntax, semantics and
morphology. Then, Chapter 6 laid out a morphological case approach to spatial prepositions
in German. Let us briefly revisit these chapters individually.
Chapter 2 laid out the syntactic module within the Y-model of grammar. In this thesis, I
adopted the tenets of the Minimalist Program (MP) (Chomsky 1995, Adger 2003).
Section 2.1 addressed the notion of ‘feature’; features are considered to be the core building
blocks of the grammatical theory adopted here. Section 2.1.1 presented the two types of
feature systems that are relevant in this thesis: (i) privative features, where features are
considered to be an attribute; and (ii) binary features, where features are considered to be
pairs consisting of an attribute and a value drawn form a binary domain. Focusing on
prepositions, Section 2.1.2 discussed category features. A general division into three types of
341
342 7. Conclusions and prospect for future work
Spell-Out
Phonological
Form (PF)
Articulatory-Perceptual
(A-P) systems
Morphology
Logical
Form (LF)
Conceptual-Intentional
(C-I) systems
Semantics
Syntax
Figure 47: The Y-model of grammar
category features was made: (i) the lexical categories V (verb), N (noun), A (adjective), and P
(preposition); (ii) the functional categories C (complementizer) > Dx (deixis) > Asp (aspect);
and (iii) light categories such as verbal Voice (Kratzer 1996) or Appl (applicative) (Pylkkänen
2002, McIntyre 2006) and prepositional ‘little p’ (Split P Hypothesis) (Svenonius 2003). The
functional categories dominate the lexical categories. Light categories are considered to
be in between functional and lexical categories. The Parallelism Hypothesis states that
the functional categories, which dominate the lexical categories, are structured in parallel
across the lexical domains; cf. Den Dikken (2010: 100 104). Section 2.1.3 briefly addressed
syntacticosemantic (synsem) features, i.e. those feature that are drawn from the universal
inventory of syntacticosemantic features (Embick 2015: 6). In Section 2.1.4, I introduced
Content features, which I consider to be language-specific, conceptually grounded, and
non-generative. They can affect the semantic interpretation at LF and the morphological
realization at PF. I identified two types of Content features: (i) idiosyncratic Content features,
which relate to the arbitrary differences between two grammatical entities, with all else being
equal (e.g. the difference between cat and dog); and (ii) abstract Content features, the function
of which is at least two-fold. On the one hand, they can relate to general perceptually-
grounded concepts like ‘interiority’ or ‘verticality’, while, on the other hand, they can bundle
with idiosyncratic Content features and thereby give rise to particular aspects of meaning
of the idiosyncratic Content features. This was illustrated with the toponym Kuba (‘Cuba’),
which can denote the island of Cuba or the state of Cuba. Depending on the abstract Content
343
feature the idiosyncratic Content feature bundles with, either of these interpretations is
promoted at LF.
Section 2.2 presented the principles according to which structure can be generated in the
Minimalist Program (MP) (Chomsky 1995). MP applies Bare Phrase Structure (BPS) as its
phrase structure module. Section 2.2.1 laid out the tree-structural relations and projection
principles of BPS; Section 2.2.2, the major operations of BPS. Section 2.2.3 derived the notions
complement, specifier, and adjunct. Then, that section also discussed the differences between
BPS and X-bar Theory (XbT), which is the phrase structure module of Government and
Binding (GB) (Chomsky 1981, Haegeman 1994, a.o.), MP’s predecessor.
Section 2.3 clarified the status of Roots in the approach proposed here. Adopting the
operation Primary Merge (De Belder and Van Craenenbroeck 2015), I defined a Root position
as the position that is a sister and a daughter of a minimal projection; cf. (88) on page 56.
Consequently, I defined a Root as what is inserted into a Root position; cf. (90) on page 56.
Section 2.4 summarized Chapter 2.
Chapter 3 explored the morphological branch of the Y-model of grammar, that is Phono-
logical Form (PF). In this thesis, I adopted the tenets of Distributed Morphology (DM)
(Halle and Marantz 1994, Embick 2015).
Section 3.1 presented the operation Vocabulary Insertion. In DM, morphophonological
exponents are inserted late, i.e. after the syntactic derivation, into the terminal nodes of
syntax, which are considered to be abstract morphemes. Vocabulary Insertion is controlled
by the Subset Principle (Halle 1997: 128); according to the Subset Principle, the phonological
exponent of a Vocabulary Item (VI) is inserted into a morpheme if the item matches all or a
subset of the grammatical features specified in the terminal node. Insertion does not take
place if the VI contains features that are not present in the morpheme. Where several VIs
meet the conditions for insertion, the item matching the greatest number of features specified
in the terminal node is chosen. Then, Section 3.2 discussed the Late Linearization Hypothesis
according to which the elements of a phrase marker are linearized at Vocabulary Insertion
(Embick and Noyer 2001: 562). In the Minimalist Program (MP), it is typically assumed
that syntax does not commit to a inherent serialization of the terminal nodes (Chomsky
1995, Embick and Noyer 2001, 2007, Hornstein et al. 2005, Bobaljik 2015). At PF, the two-
dimensional, hierarchical structure generated by syntax is flattened to a one-dimensional
string by the morphological operation Lin (linearization) (Embick and Noyer 2007: 294).
Section 3.3 discussed two instances of ornamental morphology (Embick and Noyer
2007: 305): (i) dissociated nodes, i.e. nodes that are added to a structure under specified
conditions at PF; and (ii) dissociated features, i.e. features that are added to a node under
specified conditions at PF.
Section 3.4 presented morphological operations on nodes. Section 3.4.1 presented the
operation Impoverishment, where certain features are deleted from a node under specified
conditions (Bonet 1991, Embick 2015). Section 3.4.2 presented two morphological operations
344 7. Conclusions and prospect for future work
with which one can account for syntax/morphology mismatches: (i) Fusion, where two
abstract morphemes fuse to one abstract morpheme, under specified conditions; and (ii)
Fission, where one abstract morpheme splits into two abstract morphemes, under specified
conditions.
Section 3.5 addressed morphological displacement operations generally referred to as
Morphological Merger (Marantz 1988: 261). Two such movement operations at PF, were
briefly presented: (i) Lowering, which takes place before Linearization (Embick and Noyer
2001: 561); and (ii) Local Dislocation, which takes place after Linearization (Embick and Noyer
2007: 319).
Section 3.6 presented Readjustment Rules with which one can account for (minor) changes
of morphophonological exponents in certain contexts (Embick 2015: 204).
Section 3.7 summarized Chapter 3.
Chapter 4 explored the semantic branch of the Y-model of grammar, that is Logical Form
(LF). In this thesis, I adopted the tenets of Discourse Representation Theory (DRT) (Kamp
and Reyle 1993, 2011, Kamp et al. 2011) to model LF. As for the model of space, I followed
Kamp and Roßdeutscher (2005). As for algebraic structures, I followed Krifka (1998), Beavers
(2012).
Section 4.1 presented the semantic construction algorithm. At LF, each terminal node
of a syntactic structure receives a context-dependent interpretation. Compositionally, the
interpretations of the terminal nodes are combined bottom-up along the syntactic structure
by means of unification-based composition rules. As for the representation of LF, Discourse
Representation Theory (DRT) (Kamp and Reyle 1993, 2011, Kamp et al. 2011) was chosen; cf.
Section 4.1.2. One of the features of DRT is that interpretation involves a two-stage process:
(i) the construction of semantic representations referred to as Discourse Representation
Structures (DRSs), i.e. the LF-representation proper; and (ii) a model-theoretic interpretation
of those DRSs. Section 4.1.3 illustrated the semantic construction algorithm by reproducing a
textbook example, involving aspectual information.
Section 4.2 briefly discussed the general conceptualization of ‘Figure’ and ‘Ground’ in
language, as introduced by Talmy (1975, 2000).
Section 4.3 focused on the model-theoretic aspects relevant for the semantic modeling
of spatial prepositions. I presented two models of three-dimensional space: (i) the vector
space model of space, as advocated by Zwarts (1997, 2003b, 2005b), Zwarts and Winter (2000);
and (ii) the perception-driven model of space, as advocated by Kamp and Roßdeutscher
(2005), who base their approach on principles formulated by Lang (1990). In this thesis, I
adopted Kamp and Roßdeutscher’s (2005) parsimonious, perception-driven model of space.
Section 4.3.1 discussed material objects, which can be conceptualized as being one-, two- or
three-dimensional. Section 4.3.2 focused on the spatial ontology. In particular, the notions
‘region’, ‘point’, ‘line’, ‘line segment’, ‘direction’, ‘directed line segment’, and ‘plane’ were
introduced. Then, Section 4.3.3 introduced the Primary Perceptual Space (PPS), which
345
spans a three-dimensional space on the basis of our perceptual input (Lang 1990, Kamp
and Roßdeutscher 2005). The PPS consists of three axes that are orthogonal to one another:
(i) the vertical axis determined by gravity, (ii) the observer axis determined by vision, and
(iii) the transversal axis derived from the other two axes as being orthogonal to both. Six
orientations are identified on the three axes: up and down are orientations of the vertical axis;
fore and back are orientations of the observer axis; and left and right are orientations of the
transversal axis. Section 4.3.4 addressed boundaries of material objects and regions and how
they can be used to determine the inside and the outside of a material object. Section 4.3.5
briefly discussed how ‘spatial contact’ of two regions can be modeled. Then, Section 4.3.6
discussed conditions on line segments that figure in the modeling of spatial paths denoted by
route prepositions. Two types of conditions are proposed: (i) boundary conditions and (ii)
configurational conditions. Boundary conditions manifest themselves to the effect that a line
segment is either completely inside or completely outside the material object, i.e. an internal
or external line segment of a material object. A crucial property of both boundary conditions
is that one must be able to drop a perpendicular from the boundary of the material object
onto every point of the line segment. Configurational conditions describe the configuration
of line segments as related to material objects or the shape of line segments; three such
configurational conditions of line segments are proposed: (i) an L-shaped line segment is
a line segment that involves an orthogonal change of direction; (ii) a plumb-square line
segment of a material object is a line segment that is horizontally aligned and above the
material object (NB: the term is borrowed from a carpentry tool); and (iii) a spear-like line
segment of a material object is a line segment that is orthogonal to a cross section of the
material object.
Section 4.4 discussed the algebraic foundations. Section 4.4.1 presented the mereological
structures that figure for the modeling of spatial paths. In particular, plain/undirected
path structures H (Krifka 1998: 203) and directed path structures D (Krifka 1998: 203) were
presented. Spatial paths can serve as incremental themes measuring out events (Dowty 1979,
1991, Tenny 1992, Jackendoff 1996, Krifka 1998, Beavers 2012); thus, Section 4.4.2 presented
incremental relations between spatial paths and motion events. I briefly presented Beavers’
(2012) Figure/Path Relations (FPRs) that account for double incremental themes.
Section 4.5 focused on spatial paths. I briefly presented two approaches to spatial paths:
(i) an axiomatic approach, where spatial paths are taken as primitives in the universe of
discourse (Piñón 1993, Krifka 1998, Beavers 2012); and (ii) a constructive approach, where
spatial paths are defined as continuous functions from the real unit interval [0, 1] to positions
in some model of space (Zwarts 2005b: 748). The two approaches have different implications
on the notions ‘goal’ and ‘source’. In axiomatic approaches, ‘goal’ and ‘source’ are thematic
notions that typically derive when motion events and their spatial projections map onto one
another. In constructive approaches, ‘goal’ and ‘source’ are inherent extremities of spatial
paths (Zwarts 2005b: 758). In this thesis, I opted for an axiomatic approach to spatial paths.
346 7. Conclusions and prospect for future work
Section 4.6 explored the notion of ‘prepositional aspect’. Zwarts (2005b: 742) relates
prepositional aspect to the distinction between bounded and unbounded reference, which
is familiar from the verbal domain, e.g., and which shows itself also in the domain of PPs
denoting spatial paths (Jackendoff 1991, Verkuyl and Zwarts 1992, Piñón 1993). Following
Zwarts (2005b: 753), I assume that cumulativity is the algebraic property characterizing
prepositional aspect: unbounded PPs have cumulative reference, while bounded PPs nodes
not have cumulative reference.
Section 4.7 discussed the force-dynamic effect of the German topological preposition
auf (‘upon’), which can be characterized as ‘support form below’. In contrast to (Zwarts
2010a), who takes the view that prepositions can be forceful, I argued that prepositions
are not forceful but can show force-dynamic effects. Using Talmy’s (2000: 413, 415) terms
‘Agonist’ and ‘Antagonist’ for the force entities at issue, the force-dynamic effect of auf can be
characterized to the effect that the complement of the preposition serves as an Antagonist
providing a counterforce of an Agonist’s tendency to fall down. The equilibrium of forces
takes place along the vertical axis and leads to a resultant toward rest.
Section 4.8 summarized Chapter 4.
Chapter 5 spelled out the syntax, semantic, morphology of spatial prepositions in Ger-
man. This chapter is the core of this thesis because it illustrates how spatial prepositions
can be implemented in the Y-model of grammar.
Section 5.1 classified spatial prepositions according to several criteria. Section 5.1.1
presented a widely accepted typology of spatial prepositions (e.g. Jackendoff 1983, Piñón
1993, Zwarts 2006, Gehrke 2008, Kracht 2008, Svenonius 2010, Pantcheva 2011). On the one
hand, place prepositions denote static locations (regions), while path prepositions, on the
other hand, denote dynamic locations (spatial paths). Path prepositions can be directed or
undirected. Directed path prepositions are either goal prepositions or source prepositions.
Undirected path prepositions are route prepositions. In Section 5.1.2, I introduced a geometry-
based classification of spatial prepositions, which is orthogonal to the place/path typology.
I propose that spatial prepositions can be (i) geometric prepositions, (ii) pseudo-geometric
prepositions, or (iii) non-geometric prepositions. Geometric prepositions refer to geometric
relations that can be spelled out, for instance, in a parsimonious, perception-driven model
of space (Kamp and Roßdeutscher 2005). Examples are in (‘in, into’), aus (‘out of’), durch
(‘through’). Pseudo-geometric prepositions look like geometric prepositions, but do not refer
to geometric relations. Instead, they express functional locative relations. The peculiar goal
preposition nach (‘to’), which is obligatorily used, e.g., with determinerless toponyms, turns
out to be a special instance of a pseudo-geometric preposition. Pseudo-geometric prepositions
behave differently from geometric prepositions in several ways. For example, they do not
license a postpositional recurrence of the preposition and the choice of a pseudo-geometric
preposition is heavily influenced by denotational properties of the noun it co-occurs with.
The non-geometric prepositions bei (‘at’), zu (‘to’), and von (‘from’) form a third class of
347
spatial prepositions. They do not only impose semantic selection restrictions distinct from
geometric and pseudo-geometric prepositions, but also behave differently with regard to
lexical aspect. Section 5.1.3 classified path prepositions into bounded and unbounded path
prepositions. This was done according to Kracht’s (2002, 2008) classification: bounded
source prepositions denote coinitial paths, bounded goal prepositions denote cofinal paths,
bounded route prepositions denote transitory paths, unbounded source prepositions denote
recessive paths, unbounded goal prepositions denote approximative paths, and unbounded
route prepositions denote static paths. Section 5.1.4 mapped these classifications to syntactic
structure. The lexical category P is characteristic of prepositions in general. It can host one
of the following synsem features: (i) [LOC], which is characteristic of (pseudo)-geometric
prepositions (except for route prepositions), (ii) [AT], which is characteristic of non-geometric
prepositions; or (iii) [±NINF], which is characteristic of route prepositions. The lexical category
P can be dominated by the light preposition Q, which derives goal and source prepositions
from place prepositions. Q can host the synsem features [+TO] for goal prepositions or [−TO]
for source prepositions. Following (Den Dikken 2010), I adopt the Parallelism Hypothesis,
which states that the (functional) categories are structured in parallel across lexical domains,
and assume functional structure above the categories P and Q. The functional category
Asp dominates P or Q and can host the synsem features [+UNBD] for unbounded aspect or[−UNBD] for bounded aspect. The functional category Dx dominates Asp and can host the
synsem features [+PROX] for proximal deixis or [−PROX] for non-proximal (distal) deixis.
The functional category C dominates Dx and can host the synsem features [+MOTION] for
path prepositions or [−MOTION] for place prepositions.
Section 5.2 touched upon the cartographic decomposition of spatial prepositions. I briefly
presented Svenonius’ (2006, 2010) cartographic decomposition of place prepositions and
Pantcheva’s (2011) cartographic decomposition of path prepositions.
Section 5.3 introduced three abstract Content features that relate to geometric concepts and
that figure in the derivation of the geometric prepositions: (i) the place and goal preposition
in (‘in, into’), the source preposition aus (‘out of’), and the route preposition durch (‘through’)
share the abstract Content feature [ℵ] relating to interiority; (ii) the place and goal preposition
an (‘on, onto’) and the route preposition um (‘around’) share the abstract Content feature[ℶ] relating to contiguity; and (iii) the place and goal preposition auf (‘upon, up onto’)
and the route preposition über (‘over, across’) share the abstract Content feature [ℷ] relating
to verticality. Sections 5.3.1 to 5.3.3 discussed how the abstract Content features manifest
themselves semantically. Focusing on [ℵ] (interiority), Section 5.3.1 model-theoretically
defined in-regions and durch-bar-paths. Focusing on [ℶ] (contiguity), Section 5.3.2 model-
theoretically defined an-regions and um-bar-paths. Focusing on [ℷ] (verticality), Section 5.3.3
model-theoretically defined auf-regions and ueber-bar-paths.
Section 5.4 derived the lexical structure of spatial prepositions and spelled out PF-
instructions for their morphophonological realization and LF-instructions for their semantic
interpretation. Section 5.4.1 addressed place prepositions: geometric place prepositions
348 7. Conclusions and prospect for future work
were the subject of Section 5.4.1.1, pseudo-geometric place prepositions were the subject
of Section 5.4.1.2, and non-geometric place prepositions were the subject of Section 5.4.1.3.
Section 5.4.2 addressed goal and source prepositions: geometric goal and source prepositions
were the subject of Section 5.4.2.1, pseudo-geometric goal and source prepositions were the
subject of Section 5.4.2.2, and non-geometric goal and source prepositions were the subject of
Section 5.4.2.3. Section 5.4.3 addressed route prepositions.
Section 5.5 derived the functional structure of spatial prepositions and spelled out PF-
instructions for their morphophonological realization and LF-instructions for their semantic
interpretation. Section 5.5.1 addressed C-features, Section 5.5.2 addressed deictic features,
and Section 5.5.3 addressed aspectual features.
Section 5.6 illustrated how a fully-fledged PP, i.e. a prepositional CP, headed by a spatial
preposition can be integrated in various verbal contexts.
Section 5.7 summarized Chapter 5.
Chapter 6 discussed prepositional case in German. I presented (i) the case assignment
properties of (spatial) prepositions in German (Zwarts 2006); (ii) several previous approaches
to prepositional case (Bierwisch 1988, Arsenijevic´ and Gehrke 2009, Caha 2010, Den Dikken
2010); and (iii) a morphological case theory proposed for the verbal domain Marantz (1991),
McFadden (2004). This paved the way for a proposal of a morphological case approach to
spatial prepositions in German that is based on the syntacticosemantic analyses of spatial
prepositions presented in Chapter 5.
Section 6.1 presented the case assignment properties of spatial prepositions in German.
It picked up the classification of spatial prepositions into (i) place prepositions and (ii)
path prepositions; the latter subdivide into (ii.a) directed prepositions (goal and source
prepositions) and (ii.b) undirected prepositions (route prepositions). This classification was
combined with the one proposed in Section 5.1.2, namely that spatial prepositions can be
(pseudo)-geometric prepositions or non-geometric prepositions. It turned out that (pseudo)-
geometric goal prepositions and route prepositions co-occur with accusative case, while
(pseudo)-geometric place and source prepositions and non-geometric prepositions co-occur
with dative case. In addition, Section 6.1 briefly presented the German spatial prepositions
that assign genitive case.
Section 6.2 presented four previous approaches to prepositional case: Section 6.2.1 pre-
sented Den Dikken’s (2010) structural approach where prepositional case assignment is linked
to functional heads in the extended projection of prepositions; Section 6.2.2 presented Caha’s
(2010) peeling approach where DPs are assumed to peel off their hierarchically structured case
layers under movement; Section 6.2.3 presented Arsenijevic´ and Gehrke’s (2009) approach
where it is argued that accusative case in spatial PPs stems from PP-external structure; and
Section 6.2.4 presented Bierwisch’s (1988) lexicalist approach where the case assignment
properties of spatial prepositions are assigned to their lexical entries. Some drawbacks of the
approaches were discussed, too.
349
Section 6.3 motivated and outlined the hypothesis that case is not a phenomenon of the
syntax proper, but of the morphological component of the grammar. Section 6.3.1 discussed
the notions of abstract Case and morphological case (Pesetsky and Torrego 2011). Abstract
Case is linked to nominal licensing, while morphological case is linked to the morphophono-
logical realization of case. Section 6.3.2 presented the feature decomposition of case. In
particular, this section laid out the idea that the case categories nominative, accusative, dative,
and genitive are not grammatical primes, but the result of composite case features: nomi-
native case corresponds to the absence of case features, accusative case corresponds to the
feature [+INF] (for inferior), dative case corresponds to the feature bundle [+INF,+OBL] (obl
for oblique), and genitive case corresponds to the feature bundle [+INF,+OBL,+GEN] (gen for
genitive); cf. Bierwisch (1967), McFadden (2004), a.o. Section 6.3.3 presented a commonly
assumed classification of morphological case into (i) structural case and (ii) non-structural
case; the former further subdivides into (i.a) unmarked case and (i.b) marked case, while the
latter subdivides into (ii.a) inherent case and (ii.b) idiosyncratic case. This section also spelled
out the principles of structural and non-structural morphological case assignment proposed
for the verbal domain (Marantz 1991, McFadden 2004, 2007).
Section 6.4 laid out a morphological case theory for simplex spatial prepositions in German.
Using corpus data, a.o., I argued in Section 6.4.1 that the lexical category P triggers the
inherent assignment of the dative case features [+INF,+OBL] to a DP in its complement
position; see the morphological rule for Prepositional Case Assignment (PCA) in (585) on
page 332. In Section 6.4.2, I argued that the prepositions that assign accusative case are those
that contain the synsem feature bundle [LOC,+TO], characteristic of (pseudo)-geometric goal
prepositions, or the synsem feature [±NINF], characteristic of route prepositions. I proposed
that exactly those synsem features trigger the deletion of the oblique case feature [+OBL],
resulting in accusative case assignment; see the rule of Prepositional Case Impoverishment
(PCI) in (587) on page 334. In Section 6.4.3, I briefly looked at German prepositions that assign
genitive, and at how this approach might be extended to other languages.
Section 6.5 summarized Chapter 6.
Prospects for future work
This thesis has spelled out the syntax, semantics, and morphology of spatial prepositions
in German. In addition, it presented a morphological case approach to German spatial
prepositions. However, several topics and questions did not get the attention they deserve.
And, of course, some new questions arose. In the following, I briefly discuss some of them.
Section 5.6.4 sketched a potential derivation and LF-interpretation of the clause Paul
pinkelte in einen Pool (‘Paul peed into a pool’). It contains the unergative verb pinkeln (‘pee’),
which belongs to the class of verbs of bodily emission of fluids (Harley 2005). Unergative
verbs can be analyzed as involving a morphophonologically null verb taking a nominal
complement (here: pinkel, ‘pee’) (Hale and Keyser 1993, 2002, Harley 2005, a.o.). Mor-
350 7. Conclusions and prospect for future work
phophonologically, the nominal complement is assumed to conflate with the verb (Hale and
Keyser 2002). Semantically, I proposed that the discourse referent provided by the nominal
complement serves as a Figure. In particular, I proposed that this discourse referent saturates
the Figure-argument-slot of an abstract Figure/Path Relation dubbed send; cf. Beavers (2012).
In this regard, the clause could be paraphrased as Hans sent pee into the pool, where ‘send’ is
supposed to be a light verb with highly abstract meaning. If this analysis is on the right track,
the question would be whether it could be extended to other instances of unergative verbs,
examples of which are given in (599).
(599) Hans
Hans
blickte/lachte/...
looked/laughed/...
in
in
den
the.ACC
Sitzungsraum.
meeting room
‘Hans looked/laughed/... into the meeting room.’
As for unergative verbs, the following contrast should be mentioned. In German, the
verb tanzen (‘dance’) has at least two usages that can be told apart by the perfect auxiliary
they co-occur with. When taking a direct object as in (600a), the verb tanzen behaves like
an unergative verb; cf. Haugen (2009) for a Distributed Morphology-type of approach to
objects that are semantically, but not morphologically cognate. However, when co-occurring
with a goal PP as in (600b), the verb tanzen behaves similarly to an unaccusative manner of
motion verb like rennen (‘run’); cf. Section 5.6.2 for a sketch of a potential derivation and
LF-interpretation of the unaccusative manner of motion verb rennen in combination with a
path PP. The question would be what an appropriate syntacticosemantic analysis of verbs
showing the kind of ‘unergative/unaccusative alternation’ exemplified by tanzen in (600)
should look like.
(600) a. Hans
Hans
hat
has
den
the.ACC
Hochzeitswalzer
wedding waltz
getanzt.
danced
‘Hans danced the wedding waltz.’
b. Hans
Hans
ist
is
in
in
den
the.ACC
Ballsaal
ball room
getanzt.
danced
‘Hans danced into the ball room.’
The projective prepositions hinter (‘behind’), vor (‘in front of’), über (‘above’), unter (‘un-
der’), and neben (‘beside’) have not received much attention in this thesis. One could assume
a synsem feature that relates to projection on axes of the Primary Perceptual Space (PPS),
say [±PROJ]. Recall from Section 4.3.3 that the axes of the PPS are (i) the vertical axis, (ii)
the observer axis, and (iii) the transversal axis. Assuming that projective prepositions can
be characterized by P[LOC,±PROJ], one could relate them to the axes of the PPS as given in
Table 23.
One question would be whether one could also exploit the abstract Content features[ℵ] (for interiority), [ℶ] (for contiguity), and [ℷ] (for verticality) to derive the projective
prepositions. As for the vertical axis, which relates to über and unter, the matter is obvious.
351
P[LOC,+PROJ] P[LOC,−PROJ]
vertical axis über (‘above’) unter (‘under’)
observer axis vor (‘in front of’) hinter (‘behind’)
transversal axis neben (‘beside’)
Table 23: Projective prepositions and the axes of the PPS
Arguably, über and unter involve the abstract Content feature [ℷ]. But what about the observer
and the transversal axes? Is it reasonable to relate the abstract Content features [ℵ] and [ℶ] to
the other two axes of the PPS? If yes, which feature should relate to which axis?
Projective prepositions raise a further question. In certain respects, they behave like
the topological prepositions. For instance, they participate in the place/goal (i.e. da-
tive/accusative) alternation. In other respects, however, topological and projective preposi-
tions behave differently. For instance, measure phrases can attach to PPs headed by projective
prepositions (602), but not to PPs headed by topological prepositions (601).
(601) a. Das
the
Buch
book
lag
lay
(*10
(*10
cm)
cm)
auf
upon
dem
the.DAT
Tisch.
table
b. Der
the
Statue
statue
stand
stood
(??2
(??2
Meter)
meter)
in
in
der
the.DAT
Aula.
assembly hall
(602) a. Die
the
Lampe
lamp
hing
hang
(50
(50
cm)
cm)
über
above
dem
the.DAT
Tisch.
table
‘The lamp hang (50 cm) above the table.’
b. Die
the
Statue
statue
stand
stood
(2
(2
Meter)
meter)
vor
in front of
der
the.DAT
Vitrine.
glass cabinet
‘The statue stood (2 meter) in front of the glass cabinet.’
Considering these data, one should raise the question of what sort of discourse referent is
needed at LF in order to properly account for the measurability of the projective PPs such as
those in (602). Clearly, regions, as used for the topological prepositions, are not enough.
Many prepositional elements, and in particular those related to the topological preposition
an (‘on’), auf (‘upon’), and in (‘in’), lead a double life, as prepositions and verbal particles.
This obviously raises the question: Can we exploit abstract Content features in order to
account for verbal particles? Concerning verbal particles, I refer the reader to Roßdeutscher
(2011, 2012, 2013, 2014).
Ora Matushansky (pc) has made me aware of an interesting question concerning pseudo-
geometric prepositions. It seems that pseudo-geometric prepositions are common in the
context of weak definites (e.g. Aguilar Guevara 2014). If this turns out to be on the right
track, then the following question arises: What is the syntacticosemantic relation between
pseudo-geometric prepositions and weak definites?
In Section 4.7, I argued that forces do not primarily figure in the semantics of spatial
prepositions; pace Zwarts (2010a). I argued that the topological preposition auf (‘upon’)
352 7. Conclusions and prospect for future work
shows a force-dynamic effect that can be characterized as ‘support from below.’ However,
some non-spatial prepositions such as gegen (‘against’) obviously relate to forces in some way.
This becomes clear when one considers the fact that they readily co-occur with force-dynamic
verbs such as drücken (‘push’) or schlagen (‘hit’). One could now generally raise the question
of whether forces figure in the semantics of prepositions like gegen. If it turns out that forces
do figure in the semantics of certain prepositions and if one assumes a DRT-based syntax-
semantics interface – as I did in this thesis – where one can separate semantic representations
from their model-theoretic interpretations, then the question would be if forces figure at the
level of semantic representation, i.e. at LF, or ‘only’ in the model-theory.
As for morphological case, Section 6.4.3 already sketched some prospects for future work.
Here, a central question is: How can one extend the account proposed in this thesis to other
languages, in particular to the Slavic languages?
Appendix A
Synopses
A.1 Synopsis of spatial prepositions at the interfaces
Structures
The lexical category P is characteristic of prepositions. The light preposition Q can optionally
dominate P; it derives goal and source prepositions. P can undergo Primary Merge and
thereby form a Root position (De Belder and Van Craenenbroeck 2015). At Root positions,
(abstract) Content features can enter a derivation; by doing so, they become Roots. PP
and QP can be dominated by functional structure involving the functional categories C (for
complementizer) > Dx (for deixis) > Asp (for aspect) (Van Riemsdijk 1990, Koopman 2000,
Den Dikken 2010). The general structure of spatial prepositions is given in (603).
(603) CP
DxP
AspP
(QP)
PP
DPP○
P○∅
(Q○)
Asp○
Dx○
C○
353
354 Synopses
Several syntacticosemantic (synsem) features can reside in the lexical category P < light
category Q: P can host [LOC] for (pseudo)-geometric prepositions, [AT] for non-geometric
prepositions, [−NINF] for bounded route prepositions, and [+NINF] for unbounded route
prepositions. Q derives goal and source prepositions; it can host [+TO] for goal prepositions
and [−TO] for source prepositions.
(Pseudo)-geometric prepositions host the synsem feature [LOC], i.e. locative. Route
prepositions host the synsem feature [±NINF], i.e. non-initial, non-final. The abstract Content
feature that determines the (pseudo)-geometric prepositions in (‘in, into’), aus (‘out of’), and
durch (‘through’) is [ℵ] relating to interiority; the abstract Content feature that determines the
(pseudo)-geometric prepositions an (‘on, onto’) and um (‘around’) is [ℶ] relating to contiguity;
and the abstract Content feature that determines the (pseudo)-geometric prepositions auf
(‘upon, up onto’) and über (‘over, across’) is [ℷ] relating to verticality. Geometric prepositions
contain abstract Content features in their Root position, while pseudo-geometric prepositions
have an empty Root position. The latter receive an abstract Content feature at PF; an abstract
Content feature is copied from within the DP-complement to P.
place goal path source path route path
prepositions prepositions prepositions prepositions
PP
DPP○
P○[LOC]∅
QP
PP
DPP○
P○[LOC]∅
Q○[+TO]
QP
PP
DPP○
P○[LOC]∅
Q○[−TO]
PP
DPP○
P○[±NINF]∅
[ℵ] in (‘in’) in (‘into’) aus (‘out of’),
(von in ‘from in’)
durch (‘through’)
[ℶ] an (‘on’) an (‘onto’) (von an ‘from on’) um (‘around’)[ℷ] auf (‘upon’) auf (‘up onto’) (von auf ‘from upon’) über (‘over, across’)
A.1. Synopsis of spatial prepositions at the interfaces 355
Non-geometric prepositions host the synsem feature [AT]; they have an empty Root
position.
place goal path source path
preposition preposition preposition
PP
DPP○
P○[AT]∅
QP
PP
DPP○
P○[AT]∅
Q○[+TO]
QP
PP
DPP○
P○[AT]∅
Q○[−TO]
bei (‘at’) zu (‘to’) von (‘from’)
Several syntacticosemantic (synsem) features can reside in the functional categories: Asp
can host [+UNBD] for unbounded aspect (or [−UNBD] for bounded aspect); Dx can host[+PROX] for proximal deixis or [−PROX] for distal deixis; and C can host [+MOTION] for path
prepositions or [−MOTION] for place prepositions.
Rules at Logical Form (LF)
(604) LF-instructions for P:
a. P ↔ v′
durch-bar(v′, x)
ninf±(v′, w, x)
/ _ [±NINF,ℵ]
b. ↔ v′
um-bar(v′, x)
ninf±(v′, w, x)
/ _ [±NINF,ℶ]
c. ↔ v′
ueber-bar(v′, x)
ninf±(v′, w, x)
/ _ [±NINF, ℷ]
d. ↔ r′
in(r′, x) / _ [LOC,ℵ]
e. ↔ r′
an(r′, x) / _ [LOC,ℶ]
f. ↔ r′
auf(r′, x) / _ [LOC, ℷ]
g. ↔ r′
func(r′, x) / _ [LOC]
h. ↔ r′
at(r′, x) / _ [AT]
356 Synopses
(605) LF-instructions for Q:
a. Q ↔
enter(w, r, e) / [ _ [+TO] ... P[LOC]]
b. ↔
leave(w, r, e) / [ _ [−TO] ... P[LOC]]
c. ↔
to(w, r, e) / _ [+TO]
d. ↔
from(w, r, e) / _ [−TO]
(606) Reinterpretation of Q[±TO] under Asp[+UNBD]:
a.
to(w, r, e) → towards(w, r, e) / Q[+TO] ∧ Asp[+UNBD]
b.
from(w, r, e) → away-from(w, r, e) / Q[−TO] ∧ Asp[+UNBD]
(607) LF-intructions for Dx:
a. Dx ↔ ⟨{ ri } , rd ⊆ ri ⟩ / _ [+PROX]
b. ↔ ⟨{ ri } , ¬ rd ⊗ ri ⟩ / _ [−PROX]
(608) Dx-Adjustment at LF:
a. ⟨{ ri } , rd ⊆ ri ⟩ → ⟨{ ri , e0 } ,
r′
r′ ⊆ ri
to(v, r′, e0) ⟩ / P[−NINF]
b. ⟨{ ri } , ¬ rd ⊗ ri ⟩ → ⟨{ ri , e0 } ,
r′¬ r′ ⊗ ri
to(v, r′, e0) ⟩ / P[−NINF]
(609) LF-instructions for C:
a. C ↔ w′
RFPR(y, w′, e) / _ [+MOTION]
b. ↔ r′
s ∶ ROCC(y, r′) / _ [−MOTION]
A.1. Synopsis of spatial prepositions at the interfaces 357
Rules at Phonological Form (PF)
(610) PF-instructions for P:
a. P ↔ /na:x/ / [ _ [LOC,+TO] ... D[¬∃φ]]
b. ↔ /au<s/ / _ [LOC,ℵ,−TO]
c. ↔ /fOn/ / _ [−TO]
d. ↔ /dUrç/ / _ [±NINF,ℵ]
e. ↔ /Um/ / _ [±NINF,ℶ]
f. ↔ /y:b5/ / _ [±NINF, ℷ]
g. ↔ /In/ / _ [LOC,ℵ]
h. ↔ /an/ / _ [LOC,ℶ]
i. ↔ /au<f/ / _ [LOC, ℷ]
j. ↔ /ts<u:/ / _ [+TO]
k. ↔ /bai</ / _ [AT]
(611) PF-instructions for Q:
a. Q ↔ /fOn/ / _ [−TO] ∧ ¬∃P○/Q○
b. ↔ ∅ elsewhere
(612) Q-to-P-Lowering and subsequent P/Q-Fusion:
Q○ lowers to and fuses with P○.
(613) PF-instructions for Asp:
a. Asp ↔ /ts<u:/ / _ [+UNBD] ∧ Q[+TO]
b. ↔ /vEk/ / _ [+UNBD] ∧ Q[−TO]
c. ↔ ∅ elsewhere
(614) Readjustment of P under Q[+TO] and Asp[+UNBD]:
/ts<u:/ → /au<f/ / Q[+TO] ∧ Asp[+UNBD]
(615) PF-instrunctions for Dx:
a. Dx ↔ /hEr/ / ℘(C) /= ∅ ∧ _ [+PROX]
b. ↔ /hIn/ / ℘(C) /= ∅ ∧ _ [−PROX]
c. ↔ /dr/ / ℘(C) /= ∅
d. ↔ ∅ elsewhere
(616) Proximity Impoverishment:
a. Delete [±PROX] hosted by Dx in the context of C[−MOTION].
b. Optionally delete [±PROX] hosted by Dx in the context of C[+MOTION],
however do not delete [±PROX] if, in addition, P hosts [ℵ].
(617) PF-instructions for prepositional C:
a. C ↔ ℘(P) / ℘(Dx) /= ∅ ∧ [ P[ℵ] ∨ P[ℶ] ∨ P[ℷ] ]
b. ↔ ∅ elsewhere
(618) /In/ → /ai<n/ / ℘(C) = /In/ ∧ C[+MOTION]
358 Synopses
A.2 Synopsis of morphological case assignment
Reconsider the case generalizations in (499), which I repeat here as (619).
(619) Case generalizations concerning simplex spatial prepositions in German:
a. When functioning as goal prepositions,
(pseudo)-geometric prepositions take an accusative complement.
(an ‘onto’, auf ‘up onto’, in ‘into’, nach ‘to’)
b. Route prepositions take an accusative complement.
(durch ‘through’, über ‘across, over’, um ‘around’)
c. All other prepositions take a dative complement.
(an ‘on’, auf ‘upon’, aus ‘out of’, bei ‘at’, in ‘in’, von ‘from’, zu ‘to’)
Section 6.4 has proposed the underlined parts of the morphological case-assignment rules in
(620), in order to account for these generalizations.
(620) a. Non-structural case assignment:
(i) Idiosyncratic case assignment:
Assign [+INF,+OBL,+GEN] to a DP in the complement position of V○ that
contains one of the following Roots:
√
harr,
√
zeih, ..., and to a DP in
the complement position of P○ that contains one of the following Roots:√
wegen,
√
trotz, ...
(ii) Inherent case assignment (incl. prepositional case assignment):
Assign [+INF,+OBL] to a DP in the specifier position of Appl○,
and to a DP in the complement position of P○.
b. Structural case assignment:
Assign [+INF] to a DPi if and only if
(i) there is a DPj within the same phase, and
(ii) DPj c-commands DPi, and
(iii) DPj does not bear a non-structural case.
c. Prepositional case impoverishment:
Delete [+OBL] in the local context of
(i) P/Q[LOC,+TO], (ii) P[±NINF], or (iii) P/Q[AT,+TO] plus Asp[+UNBD], ...
Appendix B
Proofs
B.1 Negative NINF-paths give rise to bounded route PPs
This section proves that a PP such as durch den Park (‘through the park’) with a negative
NINF-path is bounded. The DRS in (B.1) is the LF-representation of the bounded PP durch den
Park.
w′ v′ x′
ninf −(v′, w′, x′) durch-bar(v′, x′)
the-park(x′)
RFPR(y, w′, e)
(B.1)
Ignoring the anticipated Figure/Path Relation, we can translate this to the intermediate
model-theoretic representation:
λw∃v′[ninf −(v′, w, THE-PARK)∧ durch-bar(v′, THE-PARK)] (B.2)
A PP is bounded iff it does not have cumulative reference. Thus, the hypothesis is that (B.2) is
not cumulative. Assume the concatenation w1?w2 exists.168 (B.2) is not cumulative iff not all
concatenations of paths w1, w2 that individually qualify for (B.2) also qualify for (B.2). That is:
¬∀w1, w2[∃v′[ninf −(v′, w1, THE-PARK)∧ durch-bar(v′, THE-PARK)] (B.3a)∧∃v′′[ninf −(v′′, w2, THE-PARK)∧ durch-bar(v′′, THE-PARK)] (B.3b)
168Assuming that the concatenation w1?w2 exists is not trivial. In the case of durch den Park (‘through the
park’) you could imagine a scenario where you enter and leave the park (= w1) and then turn around and enter
and leave the park (= w2) again. As the tail paths of a route path are always qualitatively indistinguishable,
such an assumption is reasonable. However, I leave the formal proof that the concatenation w1?w2 exists for
future work.
359
360 Proofs
→ ∃v′′′[ninf −(v′′′, w1?w2, THE-PARK)∧ durch-bar(v′′′, THE-PARK)]] (B.3c)
This is equivalent to:
∃w1, w2[∃v′[ninf −(v′, w1, THE-PARK)∧ durch-bar(v′, THE-PARK)] (B.4a)∧∃v′′[ninf −(v′′, w2, THE-PARK)∧ durch-bar(v′′, THE-PARK)] (B.4b)∧¬∃v′′′[ninf −(v′′′, w1?w2, THE-PARK)∧ durch-bar(v′′′, THE-PARK)]] (B.4c)
That is, there is no negative NINF-path v′′′ of w1?w2 such that v′′′ is a durch-bar-path of ‘the
park’. We can prove this by contradiction. Assume there is a negative NINF-path v′′′ of
w1?w2 such that v′′′ is a durch-bar-path of ‘the park’.
∃w1, w2[∃v′[ninf −(v′, w1, THE-PARK)∧ durch-bar(v′, THE-PARK)] (B.5a)∧∃v′′[ninf −(v′′, w2, THE-PARK)∧ durch-bar(v′′, THE-PARK)] (B.5b)∧∃v′′′[ninf −(v′′′, w1?w2, THE-PARK)∧ durch-bar(v′′′, THE-PARK)]] (B.5c)
We can substitute the durch-bar-conditions:
∃w1, w2[∃v′[ninf −(v′, w1, THE-PARK)∧ intlis(v′, THE-PARK)∧ spear-like(v′, THE-PARK)]
(B.6a)∧∃v′′[ninf −(v′′, w2, THE-PARK)∧ intlis(v′′, THE-PARK)∧ spear-like(v′′, THE-PARK)]
(B.6b)∧∃v′′′[ninf −(v′′′, w1?w2, THE-PARK)∧ intlis(v′′′, THE-PARK)∧ spear-like(v′′′, THE-PARK)]]
(B.6c)
Identifying the predicate B in the definition of ninf (cf. (430) on page 252) with the boundary
condition intlis, we can substitute the ninf-conditions:
∃w1, w2[∃v′[v′ < w1 ∧ intlis(v′, THE-PARK) (B.7a)∧ ∃x′, y′[x′, y′ < w1 (B.7b)∧ w1 = x′ ⊕ v′ ⊕ y′ ∧ x′∞ v′∞ y′ (B.7c)∧ ¬ intlis(x′, THE-PARK)∧¬ intlis(y′, THE-PARK)] (B.7d)∧ intlis(v′, THE-PARK)∧ spear-like(v′, THE-PARK)] (B.7e)∧ ∃v′′[v′′ < w2 ∧ intlis(v′′, THE-PARK) (B.7f)∧ ∃x′′, y′′[x′′, y′′ < w2 (B.7g)
B.1. Negative NINF-paths give rise to bounded route PPs 361
∧ w2 = x′′ ⊕ v′′ ⊕ y′′ ∧ x′′∞ v′′∞ y′′ (B.7h)∧ ¬ intlis(x′′, THE-PARK)∧¬ intlis(y′′, THE-PARK)] (B.7i)∧ intlis(v′′, THE-PARK)∧ spear-like(v′′, THE-PARK)] (B.7j)∧ ∃v′′′[v′′′ < w1?w2 ∧ intlis(v′′′, THE-PARK) (B.7k)∧ ∃x′′′, y′′′[x′′′, y′′′ < w1?w2 (B.7l)∧ w1?w2 = x′′′ ⊕ v′′′ ⊕ y′′′ ∧ x′′′∞ v′′′∞ y′′′ (B.7m)∧¬ intlis(x′′′, THE-PARK)∧¬ intlis(y′′′, THE-PARK)] (B.7n)∧ intlis(v′′′, THE-PARK)∧ spear-like(v′′′, THE-PARK)]] (B.7o)
The concatenation operation is defined as the mereological sum – if it exists – for non-
overlapping elements. This means that the concatenation w1?w2 can be resolved as:
w1?w2 = x′ ⊕ v′ ⊕ y′ ⊕ x′′ ⊕ v′′ ⊕ y′′ (B.8)
Due to the adjacency conditions of v′, v′′ in (B.7c) and (B.7h), there are four disjunctive
configurations for w1?w2:
x′∞ v′∞ y′∞ x′′∞ v′′∞ y′′ (B.9)
x′∞ v′∞ y′∞ y′′∞ v′′∞ x′′ (B.10)
y′∞ v′∞ x′∞ x′′∞ v′′∞ y′′ (B.11)
y′∞ v′∞ x′∞ y′′∞ v′′∞ x′′ (B.12)
Consider (B.9). We can identify the tail paths x′′′, y′′′ of w1?w2:
x′′′ = x′ ∧ y′′′ = y′′ (B.13)
Further, we can identify the NINF-path v′′′ of w1?w2:
v′′′ = v′ ⊕ y′ ⊕ x′′ ⊕ v′′ (B.14)
It is stated in (B.7o) that v′′′ is an internal line segment of ‘the park’. Due to the universal
quantification in the definition of internal line segments in (245) on page 141 (boundary
condition), all subparts of v′′′ must be internal line segments of ‘the park’. That is:
362 Proofs
intlis(v′, THE-PARK)∧ intlis(y′, THE-PARK)∧ intlis(x′′, THE-PARK)∧ intlis(v′′, THE-PARK)
(B.15)
However, it is stated in (B.7d) and (B.7i) that y′, x′′ are not internal line segments of ‘the park’.
This leads to a contradiction:
intlis(y′, THE-PARK)∧ intlis(x′′, THE-PARK) (B.16a)∧ ¬ intlis(y′, THE-PARK)∧¬ intlis(x′′, THE-PARK) (B.16b)→ – (B.16c)
We can diagram this as below; the paths that are internal line segments of ‘the park’ are
shaded gray.
x′ v′ y′ x′′ v′′ y′′ (B.17)
Applying the same reasoning to the other three cases in (B.10)–(B.12), we arrive at parallel
contradictions. We can conclude that there is no path w1?w2 such that its NINF-path is an
internal line segment of ‘the park’.
Q.E.D.
B.2 Positive NINF-paths give rise to unbounded route PPs
This section proves that a PP such as durch den Park (‘through the park’) with a positive
NINF-path is unbounded. The DRS in (B.18) is the LF-representation of the unbounded PP
durch den Park.
w′ v′ x′
ninf +(v′, w′, x′) durch-bar(v′, x′)
the-park(x′)
RFPR(y, w′, e)
(B.18)
Ignoring the anticipated Figure/Path Relation, we can translate this to the intermediate
model-theoretic representation:
B.2. Positive NINF-paths give rise to unbounded route PPs 363
λw∃v′[ninf +(v′, w, THE-PARK)∧ durch-bar(v′, THE-PARK)] (B.19)
A PP is unbounded iff it has cumulative reference. Thus, the hypothesis is that (B.19) is cu-
mulative. Assume the concatenation w1?w2 exists. (B.19) is cumulative iff all concatenations
of paths w1, w2 that individually qualify for (B.19) also qualify for (B.19). That is:
∀w1, w2[∃v′[ninf +(v′, w1, THE-PARK)∧ durch-bar(v′, THE-PARK)] (B.20a)∧∃v′′[ninf +(v′′, w2, THE-PARK)∧ durch-bar(v′′, THE-PARK)] (B.20b)→ ∃v′′′[ninf +(v′′′, w1?w2, THE-PARK)∧ durch-bar(v′′′, THE-PARK)]] (B.20c)
That is, for any w1, w2 there is a positive NINF-path v′′′ of w1?w2 such that v′′′ is a durch-bar-
path of ‘the park’. We can show that this is a tautology.
We can substitute the durch-bar-conditions:
∀w1, w2[∃v′[ninf +(v′, w1, THE-PARK)∧ intlis(v′, THE-PARK)∧ spear-like(v′, THE-PARK)]
(B.21a)∧∃v′′[ninf +(v′′, w2, THE-PARK)∧ intlis(v′′, THE-PARK)∧ spear-like(v′′, THE-PARK)]
(B.21b)→ ∃v′′′[ninf +(v′′′, w1?w2, THE-PARK)∧ intlis(v′′′, THE-PARK)∧ spear-like(v′′′, THE-PARK)]]
(B.21c)
Identifying the predicate B in the definition of ninf (cf. (430) on page 252) with the boundary
condition intlis, we can substitute the ninf-conditions:
∀w1, w2[∃v′[v′ < w1 ∧ intlis(v′, THE-PARK) (B.22a)∧ ∃x′, y′[x′, y′ < w1 (B.22b)∧ w1 = x′ ⊕ v′ ⊕ y′ ∧ x′∞ v′∞ y′ (B.22c)∧ intlis(x′, THE-PARK)∧ intlis(y′, THE-PARK)] (B.22d)∧ intlis(v′, THE-PARK)∧ spear-like(v′, THE-PARK)] (B.22e)∧ ∃v′′[v′′ < w2 ∧ intlis(v′′, THE-PARK) (B.22f)∧ ∃x′′, y′′[x′′, y′′ < w2 (B.22g)∧ w2 = x′′ ⊕ v′′ ⊕ y′′ ∧ x′′∞ v′′∞ y′′ (B.22h)∧ intlis(x′′, THE-PARK)∧ intlis(y′′, THE-PARK)] (B.22i)∧ intlis(v′′, THE-PARK)∧ spear-like(v′′, THE-PARK)] (B.22j)
364 Proofs
→ ∃v′′′[v′′′ < w1?w2 ∧ intlis(v′′′, THE-PARK) (B.22k)∧ ∃x′′′, y′′′[x′′′, y′′′ < w1?w2 (B.22l)∧ w1?w2 = x′′′ ⊕ v′′′ ⊕ y′′′ ∧ x′′′∞ v′′′∞ y′′′ (B.22m)∧ intlis(x′′′, THE-PARK)∧ intlis(y′′′, THE-PARK)] (B.22n)∧ intlis(v′′′, THE-PARK)∧ spear-like(v′′′, THE-PARK)]] (B.22o)
The concatenation operation is defined as the mereological sum – if it exists – for non-
overlapping elements. This means that the concatenation w1?w2 can be resolved as:
w1?w2 = x′ ⊕ v′ ⊕ y′ ⊕ x′′ ⊕ v′′ ⊕ y′′ (B.23)
Due to the adjacency conditions of v′, v′′ in (B.22c) and (B.22h), there are four disjunctive
configurations for w1?w2:
x′∞ v′∞ y′∞ x′′∞ v′′∞ y′′ (B.24)
x′∞ v′∞ y′∞ y′′∞ v′′∞ x′′ (B.25)
y′∞ v′∞ x′∞ x′′∞ v′′∞ y′′ (B.26)
y′∞ v′∞ x′∞ y′′∞ v′′∞ x′′ (B.27)
Consider (B.24). We can identify the tail paths x′′′, y′′′ of w1?w2:
x′′′ = x′ ∧ y′′′ = y′′ (B.28)
It is stated in (B.22d) and (B.22i) that x′, y′′ are internal line segments of ‘the park’. It is further
stated in (B.22n) that x′′′, y′′′ are internal line segments of ‘the park’. This leads to a tautology:
intlis(x′′′, THE-PARK)∧ intlis(x′, THE-PARK) (B.29a)∧ intlis(y′′′, THE-PARK)∧ intlis(y′′, THE-PARK) (B.29b)→ ⊺ (B.29c)
Further, we can identify the NINF-path v′′′ of w1?w2:
v′′′ = v′ ⊕ y′ ⊕ x′′ ⊕ v′′ (B.30)
B.2. Positive NINF-paths give rise to unbounded route PPs 365
It is stated in (B.22o) that v′′′ is an internal line segment of ‘the park’. Due to the universal
quantification in the definition of internal line segments in (245) on page 141 (boundary
condition), all subparts of v′′′ must be internal line segments of ‘the park’. It is stated in
(B.22a) and (B.22f) that v′, v′′ are internal line segments of ‘the park’. Likewise, it is stated in
(B.22d) and (B.22i) that y′, x′′ are internal line segments of ‘the park’. This leads to a tautology:
intlis(v′′′, THE-PARK) (B.31a)∧ intlis(v′, THE-PARK)∧ intlis(y′, THE-PARK) (B.31b)∧ intlis(x′′, THE-PARK)∧ intlis(v′′, THE-PARK) (B.31c)→ ⊺ (B.31d)
We can diagram this as below; the paths that are internal line segments of ‘the park’ are
shaded gray.
x′ v′ y′ x′′ v′′ y′′ (B.32)
It is further stated in (B.22o) that v′′′ is an spear-like line segment of ‘the park’. Due to the
existential quantification of spear-like line segments in (249) on page 145 (configurational
condition), at least one subpart of v′′′ must be a spear-like line segment of ‘the park’. It is
stated in (B.22e) and (B.22j) that v′, v′′ are spear-like line segments of ‘the park’. This leads to
a tautology:
spear-like(v′′′, THE-PARK) (B.33a)∧ [spear-like(v′, THE-PARK)∨ spear-like(v′′, THE-PARK)] (B.33b)→ ⊺ (B.33c)
We can diagram this as below; the paths that are spear-like line segments of ‘the park’ are
shaded gray.
366 Proofs
x′ v′ y′ x′′ v′′ y′′ (B.34)
Applying the same reasoning to the other three cases in (B.25)–(B.27), we arrive at parallel
tautologies. We can conclude that for all w1?w2 there is a NINF-path that is an internal line
segment of ‘the park’ and a spear-like line segment of ‘the park’.
Q.E.D.
Appendix C
Grapheme/phoneme mapping
Table 24 lists the phonemic IPA-representations169 (cf. Duden 6, Klosa et al. 2000).
graphemic representation phonemic representation
an /an/
auf /au<f/
aus /au<s/
bei /bai</
dr /dr/
durch /dUrç/
ein /ai<n/
Haiti /ha"i:ti/
her /hEr/
hin /hIn/
Hispaniola /hIsp"ani
“
o:la/
in /In/
Kuba /"ku:ba/
nach /na:x/
über /y:b5/
um /Um/
von /fOn/
weg /vEk/
zu /ts<u:/
Table 24: Grapheme/phoneme mapping
169URL: https://www.internationalphoneticassociation.org/ (27.06.2017)
367
368 Grapheme/phoneme mapping
Appendix D
Picture credits
Page 2, Figure 1: Cu-map.png. [Public Domain], via Wikimedia Commons. https://commons.wikimedia.
org/w/index.php?curid=137715. Guantanamo.jpg. [Public Domain], via Wikimedia Commons. https:
//commons.wikimedia.org/w/index.php?curid=990012. Further derivative work by Boris Haselbach.
Page 124, Figure 9: Part of “Profil Perdu 16 + 17”, one-continuous-line-drawing by Boris Schmitz, 2014. http:
//borisschmitz.tumblr.com/post/96490797197/profil-perdu-16-17. Further derivative work
by Boris Haselbach.
Page 137, Figure 10: Koordinatensysteme L+R.svg. By Qniemiec (LRHREGEL de.png) [CC0], via Wikimedia Com-
mons. https://commons.wikimedia.org/wiki/File%3AKoordinatensysteme_L%2BR.svg. Fur-
ther derivative work by Boris Haselbach.
Page 144, Figure 15: Cc&j-fig24–plumb square.png. By Paul N. Hasluck (Cassells’ Carpentry and Joinery)
[Public domain], via Wikimedia Commons. https://commons.wikimedia.org/wiki/File%3ACc%26j-
fig24--plumb_square.png.
Page 145, Figure 17: olive-155932_1280.png. [CC0], via Pixabay. https://pixabay.com/photo-155932/.
Further derivative work by Boris Haselbach.
Page 173, Figure 33.a: Explain on under between by in over thrue 20.svg. By Thirunavukkarasye-Raveendran (Own
work) [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Com-
mons. https://commons.wikimedia.org/wiki/File%3AExplain_on_under_between_by_in_over_
thrue_20.svg. Further derivative work by Boris Haselbach.
Page 173, Figure 33.b: Explain on under between by in over thrue 21.svg. By Thirunavukkarasye-Raveendran (Own
work) [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Com-
mons. https://commons.wikimedia.org/wiki/File%3AExplain_on_under_between_by_in_over_
thrue_21.svg. Further derivative work by Boris Haselbach.
Page 219, Figure 40: ‘Greater Antilles; Inset map of Jamaica’. In The Citizen’s Atlas of the World, by John
Bartholomew. Published by John Bartholomew & Son limited, Edinburgh; 10th Edition, 1952.
Page 223, Figure 41: Campaign poster by Green Party (Bündnis 90/Die Grünen), Baden-Württemberg state
election 1996. Permalink: http://www.landesarchiv-bw.de/plink/?f=1-830257
369
370 Picture credits
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Eigenständigkeitserklärung
Hiermit versichere ich, dass ich die vorliegende Arbeit selbstständig verfasst und keine
anderen Quellen und Hilfsmittel als die angegebenen benutzt habe. Passagen und Gedanken
aus fremden Quellen sind als solche kenntlich gemacht.
Declaration of Authorship
I hereby declare that I have created this work completely on my own and used no other
sources or tools than the ones listed. Passages and ideas from other sources have been clearly
indicated.
Stuttgart, 12.10.2017 Boris P. Haselbach