Handbook of Logic and Language

Cover......Page 1
Date-line......Page 2
Preface......Page 3
Contents......Page 9
List of Contributors......Page 11
Abbreviations of Journal Titles......Page 19
Part 1. Frameworks......Page 23
Introduction......Page 25
1. B.H. Partee with H.L.W. Hendriks (Commentator: T. Janssen), Montague Grammar......Page 27
1. Introduction......Page 29
2.1. Earlier traditions in semantics......Page 30
2.2. Developments that made Montague grammar possible......Page 32
2.3. Montague and the idea of "English as a Formal Language"......Page 34
2.4. Semantics in linguistics before Montague and the introduction of Montague's work into linguistics......Page 36
3. The theory and the substance......Page 39
3.1. Universal Grammar: Syntax as algebra, semantics as algebra, compositionality as homomorphism......Page 40
3.2. Model theory; direct and indirect interpretation......Page 45
3.3. Type theory and intensionality......Page 46
3.4. The method of fragments......Page 50
3.5. The other two fragments: Brief notes......Page 71
4. The Montagovian revolution: Impact on linguistics and philosophy, further developments. Montague's legacy......Page 75
4.1. The Montagovian revolution. Initial impact......Page 76
4.2. Quantification......Page 77
4.3. Anaphora......Page 84
4.4. Type theory, ontology, theoretical foundations......Page 92
4.6. Typology and natural language metaphysics......Page 100
4.7. The naturalization of formal semantics and Montague's legacy......Page 102
Acknowledgements......Page 103
References......Page 104
2. M. Moortgat {Commentator: G. Morrill), Categorial type logics......Page 115
1. Introduction: Grammatical reasoning......Page 118
2. Linguistic inference: The Lambek systems......Page 122
2.1. Modeling grammatical composition......Page 123
2.2. Gentzen calculus, cut elimination and decidability......Page 127
2.3. Discussion: Options for resource management......Page 133
3. The syntax-semantics interface: Proofs and readings......Page 137
3.1. Term assignment for categorial deductions......Page 138
3.2. Natural language interpretation: The deductive view......Page 143
4. Grammatical composition: Multimodal systems......Page 149
4.1. Mixed inference: The modes of composition......Page 150
4.2. Grammatical composition: Unary operations......Page 155
5. Reasoning about multiple type assignments......Page 168
5.1. Additive and Boolean operations......Page 169
5.2. Dependent types, type schemata......Page 175
6.1. Combining type logic and feature logic......Page 179
6.2. Labeled Deductive Systems......Page 183
7.1. Proof normalization in Gentzen calculus......Page 185
7.2. Proof nets and labeled deduction......Page 188
8. Conclusions, directions for further research......Page 193
References......Page 194
3. J. van Eijck and H. Kamp (Commentator: C.F.M. Vermeulen), Representing discourse in context......Page 201
1. Introduction......Page 203
2. The problem of anaphoric linking in context......Page 204
3. Basic ideas of discourse representation......Page 205
4. Discourse representation structures......Page 213
5. The static and dynamic meaning of representation structures......Page 217
6. Sequential composition of representation structures......Page 220
7. Strategies for merging representation structures......Page 226
8. Disjoint merge and memory management......Page 233
9. Constructing DRSs for natural language fragments......Page 237
10. The proper treatment of quantification in DRT......Page 244
11. Representing tense and aspect in texts......Page 247
12. Extensions and variations......Page 255
13. Further reading......Page 257
References......Page 258
4. J. Seligman and L.S. Moss, Situation theory......Page 261
1. Introduction......Page 263
2. The structure of information......Page 264
2.1. Relational structures......Page 265
2.2. Simple information structures......Page 266
2.3. Roles......Page 269
2.4. Identity......Page 270
2.5. Arguments......Page 272
2.6. Circularity......Page 273
2.7. Appropriateness......Page 275
2.8. Partiality......Page 276
2.9. Representation theorems......Page 278
3. A theory of structural relations......Page 280
3.1. Extensional structures......Page 281
3.2. Structural descriptions and anti-foundedness......Page 283
3.3. Partiality and order......Page 287
3.4. Complex infons......Page 289
3.5. Substitution......Page 291
3.6. Infon structures......Page 293
3.7. Abstraction......Page 297
3.8. Application......Page 299
4. Truth and circumstance......Page 300
4.1. Fact structures......Page 302
4.2. Logic in fact structures......Page 304
4.3. Restriction......Page 306
4.4. Internal definability......Page 308
4.5. Situation structures......Page 310
4.6. Parts of the world......Page 312
4.7. Logic in situation structures......Page 315
4.8. Propositions......Page 316
4.9. Constraints and the flow of information......Page 320
5. Guide to the literature......Page 326
References......Page 328
5. J. Higginbotham (Commentators: E. Stabler and M. Kracht), GB theory: An introduction......Page 333
1. Phrase structure......Page 336
2. Limitations of phrase-structure description......Page 340
2.1. easy and eager......Page 341
2.2. Long-distance dependencies......Page 342
3.1. Heads, projections, and movement......Page 346
3.2. Types of transformations......Page 348
3.3. Empty categories......Page 349
3.4. Analysis of easy versus eager......Page 352
3.5. Long-distance dependencies in LGB......Page 353
4. Logical form......Page 354
4.1. Negative polarity......Page 355
4.2. Antecedent-contained deletion......Page 356
5. Formal development and applications......Page 357
5.1. Trees, ordering, and labels......Page 358
5.2. Definable binary relations......Page 359
5.3. Introduced binary relations......Page 365
6.1. Morphosyntax and feature checking......Page 371
6.2. Movement and copying......Page 374
7. Minimalism and derivational and non-derivational syntax......Page 376
7.1. Generation of S-Structures......Page 377
7.3. Modes of formalization......Page 379
References......Page 381
6. J. Hintikka and G. Sandu (Commentator: W. Hodges), Game-theoretical semantics......Page 383
1.1. Background......Page 385
1.2. The strategic viewpoint......Page 387
1.4. Extensions: Informational independence......Page 388
1.5. IF first-order logic and partiality......Page 391
1.6. IF first-order logic and the failure of compositionality......Page 392
1.7. IF first-order logic and the failure of the substitutional account of quantification......Page 393
1.8. The nature of negation......Page 395
1.9. Constructivism and game strategies......Page 397
1.10. Epistemic logic......Page 398
1.11. The definability of truth and its significance......Page 401
2.1. Game rules for quantifier phrases......Page 402
2.2. The scope of scope......Page 404
2.3. Ordering principles......Page 405
2.4. The treatment of pronouns in GTS......Page 407
2.5. Comparisons with other approaches......Page 411
2.6. Conditionals......Page 413
2.7. Game rules for other expressions in English......Page 415
2.8. Is and Aristotelian categories......Page 418
2.9. Abstract vs. strategic meaning......Page 419
2.10. De dicto vs. de re distinction......Page 420
3.1. Games in logic......Page 422
3.2. Games in philosophical language theory......Page 424
3.3. Differences between different games......Page 425
3.4. Interrelations between different kinds of games......Page 426
3.5. What is essential about games?......Page 427
References......Page 429
Part 2. General Topics......Page 433
Introduction......Page 435
7. T.M.V. Janssen (Commentators: T. Zimmermann and E. Goguen), Compositionality (with an appendix by Barbara H. Partee)......Page 439
1.2. Occurrences of the principle......Page 441
1.3. On the history of the principle......Page 442
2.3. Identifiers in programming languages......Page 443
2.4. Tarski's interpretation of predicate logic......Page 444
2.5. Situation semantics......Page 446
2.6. Conclusion......Page 447
3.2. Assumptions......Page 448
3.3. Options in syntax......Page 449
3.4. Conclusion......Page 450
4.2. Arrays in programming languages......Page 451
4.3. Syntactic rules as conditions......Page 452
4.4. Discourse representation theory......Page 453
4.5. Substitutional interpretation of quantifiers......Page 454
4.6. Conclusion......Page 455
5.2. Restriction on the use of logic......Page 456
5.3. A new operator: CAUSE......Page 457
5.5. Conclusion......Page 458
6.2. Counterexamples......Page 459
6.3. Compositional solutions......Page 461
6.4. General methods for compositionality......Page 462
7.2. Ambiguity......Page 463
7.3. Ontology......Page 465
7.4. Synonymy......Page 466
7.5. Psychology......Page 467
7.6. Flexibility......Page 468
8.1. Introduction......Page 469
8.3. Generators......Page 470
8.4. Terms......Page 471
8.5. Homomorphisms......Page 472
8.6. Polynomials......Page 473
8.7. Past and future of the model......Page 474
9.2. Not every grammar can be used......Page 475
9.3. Power from syntax......Page 476
9.4. Power from semantics......Page 478
9.5. Restriction to recursiveness......Page 479
10.1. Semantics of programming languages......Page 480
10.2. Other translations......Page 482
Acknowledgements......Page 483
Appendix A. Related principles......Page 484
Appendix B. Genitives - A case study (by B. Partee)......Page 486
References......Page 492
8. W.C. Rounds (Commentator: P. Blackburn), Feature logics......Page 497
1.2. Some background......Page 499
2. Formalizing feature systems......Page 501
3. Feature logics......Page 504
3.1. Kasper-Rounds logic......Page 505
3.2. Modal feature logics......Page 506
3.3. Heterogeneous modalities......Page 508
3.4. Reape's polyadic modal logic......Page 509
3.5. Negation and implication......Page 511
3.6. Intuitionistic logic......Page 513
3.7. Fixed-point extensions......Page 514
3.8. The logic of typed feature structures......Page 518
3.9. Attribute-value logics......Page 520
3.10. Feature logics as constraint systems......Page 523
4.1. Axiomatizations for Kasper-Rounds-style logics......Page 525
4.2. Axiomatizing intuitionistic feature logic......Page 528
4.3. Axiomatizing other forms of feature logic......Page 532
5. Complexity and decidability issues......Page 534
6. Order-theoretic aspects of feature structures......Page 539
7. An application......Page 546
References......Page 552
9. R. Turner (Commentator: S. Feferman), Types......Page 557
1.2. Categories and types......Page 559
2. The typed lambda calculus......Page 560
2.1. The Church calculus (CT)......Page 561
2.2. The loosely typed calculus (C)......Page 563
2.3. The untyped lambda calculus......Page 568
2.4. The Curry calculus (CU)......Page 572
2.5. Categorial grammar and the typed lambda calculus......Page 575
3.1. Church higher order logic......Page 578
3.2. HOLC......Page 581
3.3. Higher-order logic and the untyped calculus......Page 584
3.4. The Curry theory......Page 585
4.1. Nominalization......Page 587
4.2. Universal types......Page 589
4.3. Nominalized HOL (NHOL)......Page 593
5.1. Prepositional theories......Page 596
5.2. Dependent types......Page 599
5.3. Second-order theories and beyond......Page 602
6.1. More flexible typing......Page 604
6.4. Universal types......Page 605
References......Page 606
10. R. Muskens, J. van Benthem and A. Visser (Commentator: D. McCarty), Dynamics......Page 609
0. Introduction......Page 611
1.1. The kinematics of context change: Stalnaker, Karttunen, Heim and Veltman......Page 613
1.2 Change of assignments: Heim, Kamp, Groenendijk and Stokhof......Page 619
1.3. Change of attentional state: Grosz and Sidner......Page 628
1.4. Change of assumptions: Intuitionistic prepositional logic in Zeinstra's style......Page 631
1.5. Change of beliefs: Gardenfors' theory of belief revision......Page 634
2.1. General dynamic logic......Page 637
2.2. Categories for dynamic semantics......Page 648
2.3. Dynamics related to statics......Page 651
2.4. General perspectives......Page 657
References......Page 665
11. J.E. Fenstad (Commentator: L. Humberstone), Partiality......Page 671
1.1. Grammatical form......Page 673
1.2. The structure of knowledge......Page 675
1.3. Rules......Page 677
1.4. Self-reference......Page 680
2.1. Representional form......Page 684
2.2. A relational theory of meaning......Page 686
3.1. Partiality and prepositional logic......Page 689
3.2. Partial predicates......Page 696
References......Page 702
12. W. Buszkowski, Mathematical linguistics and proof theory......Page 705
1. Introduction......Page 707
2.1. Prepositional deductive systems......Page 710
2.2. Beyond prepositional logic......Page 717
3. Proofs and syntactic structures......Page 718
3.1. String languages and tree languages......Page 719
3.2. Proof theory and generative capacity......Page 724
3.3. Other topics......Page 733
4.1. Type-theoretic semantics......Page 734
4.2. Proofs versus lambda terms......Page 736
4.3. Fine aspects of semantics......Page 740
5.1. Residuated algebras and Kripke frames......Page 744
5.2. Powerset frames......Page 747
5.3. Gentzen-style Labeled Deductive Systems......Page 751
5.4. L-frames and grammars......Page 754
References......Page 755
13. D. Osherson, D. de Jongh, E. Martin and S. Weinstein, Formal learning theory......Page 759
1.1. Empirical inquiry......Page 761
1.2. Paradigms......Page 762
2. Identification......Page 763
3.2. Reliability......Page 765
3.3. Comparative grammar......Page 766
4.1. Memory limitation......Page 768
4.3. Computability......Page 769
4.4. Consistency, conservatism, prudence......Page 770
4.6. Exact identification......Page 772
4.7. Efficiency......Page 773
4.9. Identifying the child's program for language acquisition......Page 774
5. The need for complementary approaches......Page 775
6.1. Overview......Page 776
6.3. Environments......Page 777
6.5. Solvability for environments......Page 778
6.7. Relation to language acquisition......Page 779
7.1. Solving arbitrary collections of structures......Page 780
7.2. Solving elementary classes of structures......Page 781
8.1. Measures over environments......Page 782
8.3. Comparison with absolute solvability......Page 783
9.1. Definitions and principal theorem......Page 784
10. Empirical evaluation......Page 785
11. Concluding remarks......Page 786
12.3. Model-theoretic locking sequences......Page 787
12.5. Proof of Lemma 36......Page 788
12.7. Proof of Lemma 43......Page 790
12.8. Proof of Proposition 47......Page 791
References......Page 793
14. R.H. Thomason, Nonmonotonicity in linguistics......Page 799
1.1. Monotonicity and nonmonotonicity arc properties of logical consequence......Page 801
1.3. Nonmonotonicity and linguistics......Page 802
2.1. Default logic......Page 804
2.2. Autoepistemic logic......Page 810
2.3. Circumscription......Page 811
2.4. Model preference theories......Page 812
2.5. Conditional theories......Page 813
2.6. Inheritance......Page 815
3.1. Classical feature structures and unification......Page 822
3.2. Need for nonmonotonic unification......Page 824
3.3. Bouma's default unification......Page 825
3.4. Young and Rounds' nonmonotonic sorts......Page 826
4. Applications in phonology......Page 828
4.2. Making phonological theories declarative......Page 829
4.3. Underspecification theory......Page 830
5. Applications in morphology......Page 831
5.1. Implications for linguistic theory: A preliminary examination......Page 832
5.2. Taking procedures into account......Page 834
5.3. An example: The Dutch verb......Page 837
7. Applications in semantics......Page 840
7.1. Causality......Page 841
7.3. Resultatives......Page 842
8. Applications in discourse......Page 843
8.2. Recognizing intentions and discourse structure......Page 844
8.3. Discourse and commonsense entailment......Page 846
8.5. Mutual defaults......Page 847
References......Page 848
Part 3. Descriptive Topics......Page 855
Introduction......Page 857
15. E.L. Keenan and D. Westerstahl (Commentator: J. van der Does), Generalized quantifiers in linguistics and logic......Page 859
0. Introduction......Page 861
1.1. Type (1) quantification......Page 862
1.2. Type (1,1) quantification......Page 869
1.3. Type ((1,1),1) quantification......Page 888
2. Polyadic quantification......Page 889
2.1. Iteration......Page 891
2.2. Other polyadic quantifiers......Page 898
2.3. Polyadic lifts......Page 906
References......Page 912
16. M. Steedman (Commentator: A. ter Meulen), Temporality......Page 917
1. A case-study in knowledge representation......Page 919
2.1. Basic phenomena and descriptive frameworks......Page 920
2.2. Logical and computational approaches......Page 926
3.1. Basic phenomena and descriptive frameworks......Page 927
3.2. Logical and computational approaches......Page 938
4.1. Basic phenomena and descriptive frameworks......Page 949
4.2. Logical and computational approaches......Page 951
5. Conclusion......Page 954
Acknowledgements......Page 955
References......Page 956
17. D.I. Beaver, Presupposition......Page 961
1. Introduction......Page 963
1.1. The presupposition triggers......Page 965
1.2. Projection/Heritability......Page 966
1.3. From projection data to theories of projection......Page 968
2. Static accounts: Multivalence and partiality......Page 969
2.1. Trivalent accounts......Page 970
2.2. Supervaluations......Page 975
2.3. Two dimensions......Page 978
2.4. Pragmatic extensions......Page 980
3. Context dependence and part-time presupposition......Page 981
3.1. Plugs, holes and filters......Page 982
3.2. Global cancellation......Page 983
3.3. The pre- in presupposition......Page 987
4.1. From projection to satisfaction......Page 989
4.2. Context change potential......Page 991
4.3. Quantifying-in to presuppositions......Page 994
4.4. Accommodation......Page 998
4.5. Accommodation as a transformation on DRSs......Page 999
4.6. Accommodation as context selection......Page 1005
5. Syntheses......Page 1007
5.1. Cancellation and filtering......Page 1008
5.2. Trivalent and dynamic semantics......Page 1009
5.3. From cancellation to accommodation......Page 1010
5.4 The transformation from Russell to Van der Sandt......Page 1011
5.5. Accommodation as a journey through mental space......Page 1012
6.1. Anaphoricity......Page 1013
6.2. Accommodation and the taxonomy of triggers......Page 1017
6.3. Projection from binary connectives......Page 1018
References......Page 1023
18. J.J. Lonning (Commentator: G. Link), Plurals and collectivity......Page 1031
1. Introduction......Page 1033
2.1. The rules of the game......Page 1034
2.2. Plurals, but not collective......Page 1036
2.3. Collectively read NPs......Page 1037
3.1. Ontology......Page 1039
3.2. Compositionality......Page 1040
3.3. Logic......Page 1042
4.1. Background......Page 1050
4.2. Basics......Page 1051
4.3. Ontology......Page 1054
4.4. Compositionality......Page 1056
4.5. Logic......Page 1058
4.6. Mass terms......Page 1060
4.7. Alternatives......Page 1062
5.1. Collective and distributive readings......Page 1064
5.2. Neutral readings......Page 1066
5.3. Cumulative readings......Page 1068
6.1. Reducing the collective readings?......Page 1069
6.2. Branching generalized quantifiers......Page 1070
6.3. Rejecting collections......Page 1071
7. Further directions......Page 1072
References......Page 1073
19. J. Groenendijk and M. Stokhof (Commentator: J. Ginzburg), Questions......Page 1077
1. Preliminary......Page 1079
2. Setting the stage......Page 1080
3. The pragmatic approach......Page 1083
3.1. Starting points......Page 1086
3.2. General framework......Page 1087
3.3. Criticisms of the semantic approach......Page 1088
3.4. Questions as requests......Page 1092
3.5. Asking a question as a basic speech act......Page 1094
3.6. Summing up sofar......Page 1095
4. The semantic approach......Page 1097
4.1. 'Hamblin's picture'......Page 1098
4.2. Criteria of adequacy......Page 1100
4.3. Adequacy of the Hamblin-picture......Page 1102
4.4. Questions in prepositional logic......Page 1104
4.5. The predicate logical case......Page 1111
5.1. Logical theories......Page 1119
5.2. Computational theories......Page 1122
6.1. Overview......Page 1124
6.2. Key data......Page 1130
6.3. A flexible approach?......Page 1137
6.4. Other empirical issues......Page 1138
6.5. Extending the scope......Page 1142
References......Page 1144
20. F.J. Pelletier and N. Asher, Generics and defaults......Page 1147
1.1. Generic reference vs. generic predication......Page 1149
1.2. Why are there any generic sentences at all?......Page 1150
1.3. Generics and exceptions, two bad attitudes......Page 1151
1.4. Exceptions and generics, some other attitudes......Page 1153
1.5. Generics and intensionality......Page 1155
1.7. A little notation......Page 1157
1.8. Generics vs. explicit statements of regularities......Page 1159
2.1. Relevant quantification......Page 1160
2.2. Abstract objects......Page 1161
2.3. Prototypes......Page 1162
2.4. Stereotypes......Page 1164
2.5. Modal conditional approaches......Page 1165
2.7. Default reasoning approaches......Page 1167
3. Default approaches and generics......Page 1168
3.1. A general characterization of nonmonotonicity and patterns of nonmonotonic reasoning......Page 1169
3.2. Evaluation of default approaches I: Default logic and update semantics......Page 1173
3.3. Evaluation of default approaches II: Autoepistemic logic......Page 1176
3.4. Evaluation of default theories III: Circumscription......Page 1177
3.5. Evaluation of default approaches IV: Probabilistic analyses......Page 1178
3.6. A general evaluation of default reasoning approaches......Page 1179
4.1. Requirements for the monotonic semantics for generics......Page 1181
4.2. Interim evaluation......Page 1186
4.3. Nonmonotonic reasoning and epistemic semantics for generics......Page 1189
4.4. Patterns of reasonable and defeasible inference with generics......Page 1190
5. Summary and conclusions......Page 1192
Appendix......Page 1194
References......Page 1196
Glossary......Page 1201
Author Index......Page 1237
Subject Index......Page 1249