CONTENTS
Preface = xiii
Acknowledgements = xix
Chapter 1 : Introduction = 1
1.1 Truth and Reference = 1
1.2 Topics in Semantics = 10
1.3 Topics in Pragmatics = 22
1.4 Methodology = 30
Exercises = 35
Chapter 2 : Simply Typed λ-Calculus = 37
2.1 Simple Types = 39
2.2 λ-Terms = 41
2.3 Functional Models = 45
2.4 Proof Theory for Simply Typed λ-Calculus = 49
2.5 Combinators and Variable-Free Logic = 60
2.6 Products = 64
2.7 Sums = 69
Exercises = 72
Chapter 3 : Higher-Order Logic = 75
3.1 Higher-Order Syntax = 75
3.2 Higher-Order Models = 77
3.3 Quantifiers in Natural Language = 83
3.4 Negative Polarity Items = 94
3.5 Definite Descriptions = 96
3.6 Proof Theory for Higher-Order Logic = 101
Excrcise = 104
Chapter 4 : Applicative Categorial Grammar = 111
4.1 The Category System = 112
4.2 Semantic Domains = 114
4.3 Categorial Lexicons = 115
4.4 Phrase Structure = 116
4.5 A Categorial Lexicon = 119
4.6 Tree Admissibility = 121
4.7 Ambiguity, Vagueness, and Meaning Postulates = 126
Exercises = 135
Chapter 5 : The Lambek Calculus = 139
5.1 Lambek's Sequent Calculus = 140
5.2 The Natural-Deduction Lambek Calculus = 153
5.3 Products = 164
5.4 Categorial Grammar as Logic = 168
Exercises = 174
Chapter 6 : Coordination and Unbounded Dependencies = 177
6.1 Coordination = 177
6.2 Conjunctive and Disjunctive Categories = 187
6.3 Unbounded Dependency Constructions = 199
Exercises = 209
Chapter 7 : Quantifiers and Scope = 213
7.1 Quantifying In = 215
7.2 Cooper Storage = 216
7.3 Scoping Constructor = 220
7.4 Type Raising and Quantifier Coordination = 228
7.5 Embedded Quantifiers = 232
7.6 Quantifiers and Coordinate Structures = 241
7.7 Quantification and Negation = 244
7.8 Quantification and Definite Descriptions = 247
7.9 Possessives = 251
7.10 Indefinites = 254
7.11 Generics = 259
7.12 Comparatives = 263
7.13 Expletives and the Unit Type = 281
Exercises = 286
Chapter 8 : Plurals = 293
8.1 An Ontology of Groups = 293
8.2 A Plural Grammar = 297
8.3 Distributors and Collectors = 302
8.4 Coordination, Negation, and Argument Lowering = 307
8.5 Adverbial Distribution = 311
8.6 Plural Quantification = 314
8.7 Partitives and Pseudopartitives = 318
8.8 Nonboolean Coordination = 322
8.9 Comitative Complements = 326
8.10 Mass Terms = 328
Exercises = 333
Chapter 9 Pronouns and Dependency = 339
9.1 Pronouns and Reflexives = 339
9.2 Pronouns and Agreement = 342
9.3 Pronouns as Variables = 344
9.4 A Quantificational Approach to Reflexives = 347
9.5 Plural Pronouns = 352
9.6 Reciprocals and Generalized Quantification = 354
9.7 Pied Piping = 364
9.8 Ellipsis and Sloppy Anaphora = 367
9.9 interrogatives = 368
Exercises = 373
Chapter 10 Modal Logic = 379
10.1 modes of Truth = 379
10.2 S5 : A Modal Logic of Necessity = 382
10.3 Indexicality = 390
10.4 General Modal Logics = 390
10.5 Strict Implication and Counterfactuals = 395
10.6 First-Order Tense Logics = 399
10.7 Tense Logic and Natural Language = 408
10.8 Temporal-Period Structures = 411
10.9 Higher-Order Modal Logic = 418
Exercises = 420
Chapter 11 Intensionality = 425
11.1 An Intemional Grammar = 425
11.2 Individual Concepts and Quantificational Definites = 450
11.3 Alternatives to Possible Worlds = 457
11.4 Lexical Relations = 465
Exercises = 471
Chapter 12 Tense and Aspect = 479
12.1 Reichenbach's Approach to Simple and Perfect Tenses = 479
12.2 Tense and Discourse = 481
12.3 Vendler's Verb Classes = 482
12.4 A Semantic Approach to Aspect = 485
12.5 A Grammar of Tense and Aspect = 487
Exercises = 504
Appendix A
Mathematical Preliminaries = 509
A.1 Set Theory = 509
A.2 Functions and Relations = 511
A.3 Orderings, Well Orderings, and Lattices = 515
A.4 Proof by Induction = 517
A.5 Formal Languages = 519
A.6 Trees = 520
A.7 First-Order Logic = 523
A.8 Algebras and Equality = 529
References = 537
Index = 569
