The present volume is one of the two tracts which are based on my dissertation foundations and applications of Montague grammar. The two volumes present an interdisciplinary study between mathematics, philosophy, computer science, logic and linguistics. No knowledge of specific results in these fields is presupposed, although occasionally terminology or results from them are mentioned. Throughout the text it is assumed that the reader is acquainted with fundamental principles of logic, in particular of model theory, and that he is used to a mathematical kind of argumentation.
The volumes deal with many facets of syntax and semantics, discussing rather different kinds of subjects from this interdisciplinary field. They range from abstract universal algebra to linguistic observations, from the history of philosophy to formal language theory, and from idealized computers to human psychology.
Author(s): T.M.V.Janssen
Series: CWI Tracts
Publisher: Centrum voor Wiskunde en Informatics
Year: 1986
Language: English
Pages: 459
City: Amsterdam
CWI Tracts ......Page 1
Part 1: Philosophy, framework, computer science ......Page 2
Preface to Part 1 ......Page 4
Table of contents of Part 1 ......Page 6
Chapter 01. The principle of compositionality of meaning ......Page 8
1. An attractive principle ......Page 9
2.1. Introduction ......Page 12
2.2. Grundlagen ......Page 13
2.3. Sinn und Bedeutung ......Page 15
2.4. The principle ......Page 16
3. Towards a formalization ......Page 18
4. An algebraic framework ......Page 24
5.1. Introduction ......Page 35
5.3. Programming Language ......Page 36
5.4. Predicate Logic ......Page 37
5.6. Substitutional Interpretation ......Page 41
6. Motivation ......Page 42
Chapter 02. The algebraic framework ......Page 48
1. Introduction ......Page 49
2. Algebras and subalgebras ......Page 50
3. Algebras for syntax ......Page 57
4. Polynomials ......Page 63
5. Term algebras ......Page 68
6. Homomorphisms ......Page 74
7. A safe deriver ......Page 82
8. Montague grammar ......Page 88
9. Discussion ......Page 97
Chapter 03. Intensional logic ......Page 102
1.2. Model-part I ......Page 103
1.4. Laws ......Page 105
1.5. Method ......Page 106
2. Two-sorted type theory ......Page 107
3. The interpretation of Ty2 ......Page 110
4. Properties of Ty2 ......Page 113
5. Intensional Logic ......Page 120
6. Properties of IL ......Page 124
7. Extension and intension ......Page 130
Chapter 04. Montague grammar and programming languages ......Page 134
1.1. Introduction ......Page 135
1.2. Simple assignments ......Page 136
1.3. Other assignments ......Page 138
2.1. Why? ......Page 140
2.2. How? ......Page 142
3.1. Floyd's forward predicate transformer ......Page 144
3.3. Problems with Floyd's rule ......Page 146
3.4. Predicate transformers as meanings ......Page 148
4.1. The model ......Page 151
4.2. The logic ......Page 155
4.3. Theorems ......Page 157
5.1. The rules ......Page 159
5.2. Examples ......Page 161
6.1. Pointers ......Page 163
6.2. Arrays ......Page 165
7.1. The rules ......Page 168
7.2. The postulates ......Page 171
7.3. A model ......Page 173
8.1. State transition semantics ......Page 175
8.2. Strongest postconditions ......Page 176
8.3. Completeness ......Page 179
9.1. Problems with Hoare's rule ......Page 183
9.2. Backward predicate transformers ......Page 184
9.3. Weakest preconditions ......Page 185
9.4. Strongest and weakest ......Page 186
9.5. Correctness proof ......Page 189
10. Mutual relevance ......Page 192
Appendix. Safe and polynomial ......Page 196
Index of names ......Page 200
References ......Page 204
Part 2: Applications to natural languages ......Page 213
Preface to Part 2 ......Page 215
Table of contents of Part 2 ......Page 217
Chapter 05. The PTQ-fragment ......Page 220
1. Introduction ......Page 221
2. John runs ......Page 223
3. The woman walks ......Page 235
4. Mary walks and she talks ......Page 239
5. John finds a unicorn ......Page 244
6. Every man loves a woman ......Page 251
7. Bill walks in the garden ......Page 257
8. John tries to find a unicorn ......Page 261
9. John believes that Mary will run ......Page 266
Chapter 06. Variants and deviations ......Page 272
1. Introduction ......Page 273
2.2. Easy to please ......Page 275
2.3. The horse Cannonero ......Page 276
3.1. Introduction ......Page 277
3.2. John who runs ......Page 278
3.3. Das Madchen gibt den Apfel dem Vater ......Page 280
3.4. Woman such that she loves him ......Page 281
4. Operators defined on representants ......Page 283
5.1. Introduction ......Page 287
5.2. Shake John awake ......Page 288
5.3. I and You ......Page 289
6.2. Keenan & Faltz count ......Page 290
6.3. Partee counts ......Page 292
7.1. Introduction ......Page 293
7.2. Hausser translates ......Page 294
7.4. Groenendijk & Stokhof translate ......Page 295
7.5. Keenan & Faltz on translations ......Page 296
Chapter 07. Partial rules ......Page 298
1. Restrictions of the framework ......Page 299
2.1. Partial grammars ......Page 302
2.2. Partial models ......Page 303
2.3. Discussion ......Page 306
3. Incorporating transformations ......Page 309
4.1. Introduction ......Page 312
4.3. Give John a book ......Page 313
4.4. Mary shakes John awake again ......Page 314
4.5. See himself ......Page 315
4.6. Easy to see ......Page 317
5.1. Hyperrules ......Page 318
5.2. Metarules ......Page 321
5.3. Variables ......Page 322
6. The well-formedness constraint ......Page 327
Chapter 08. Constituent structures ......Page 334
1. Structure - why? ......Page 335
2.1. Trees in Montague grammar ......Page 337
2.2. Algebraic considerations ......Page 340
2.3. Practical differences ......Page 341
3.1. Introduction ......Page 344
3.2. Operations on trees ......Page 345
3.3. Features and lexicon ......Page 346
3.4. Queries for information ......Page 350
4. PTQ syntax ......Page 352
Chapter 09. Relative clause formation ......Page 356
2.1. The discussion by Partee ......Page 357
2.2. The PTQ-rules ......Page 359
2.3. Fundamental problems ......Page 361
3.1. Cooper on Hittite ......Page 363
3.2. Bach & Cooper on English ......Page 364
3.3. Fundamental problems ......Page 366
4.1. Not-there ......Page 367
4.2. Left-over, proposal 1 ......Page 368
4.3. Left-over, proposal 2 ......Page 369
5. The variable principle ......Page 373
6.1. The CN-S analysis for English ......Page 377
6.2. The S-S analysis for Hittite ......Page 378
6.3. The T-S analysis for English ......Page 380
6.4. The Det-S analysis for English ......Page 382
6.5. Conclusion ......Page 383
7.1. Syntax: gender agreement ......Page 384
7.2. Semantics: scope ......Page 385
7.3. Conclusion ......Page 387
8. The general question ......Page 388
Chapter 10. Scope ambiguities of tense, aspect and negation ......Page 392
2.1. Introduction ......Page 393
2.3. Ambiguities ......Page 394
3. Basic verb modifiers ......Page 396
4. Compound verb modifiers ......Page 403
5.2. Conjoined verb phrases with positive verbs ......Page 406
5.3. Conjoined verb phrases with negated verbs ......Page 408
5.4. Terms ......Page 410
5.5. Embeddings ......Page 411
6. One of the rules ......Page 413
7.1. Introduction ......Page 418
7.2. Rules ......Page 419
7.4. Fins and Verb Phrase ......Page 424
7.5. Final remarks ......Page 425
Appendix 1. Individual concepts in PTQ ......Page 428
Appendix 2. Set manipulation in syntax ......Page 442
Index of names ......Page 446
References ......Page 448
