Handbook of Logic and Language (eBook)

Front Cover 1
Handbook of Logic and Language 4
Copyright 5
Table of Contents 6
Preface 12
List of Contributors 16
Part 1: Frameworks 24
Chapter 1. Montague Grammar 26
1.1. Introduction 26
1.2. Montague Grammar in Historical Context 27
1.3. The Theory and the Substance 37
1.4. The Montagovian Revolution: Impact on Linguistics and Philosophy, Further Developments. Montague's Legacy 75
Acknowledgments 104
References 106
Chapter 2. Categorial Type Logics 118
Part I. Excerpts from the 1997 Chapter 118
2.1. Introduction: Grammatical Reasoning 118
2.2. Linguistic Inference: the Lambek Systems 123
2.3. The Syntax-Semantics Interface: Proofs and Readings 138
2.4. Grammatical Composition: Multimodal Systems 149
Part II. Update 2009 169
2.5. 1997–2009: A Road Map 169
2.6. Four Views on Compositionality 171
2.7. Proof Nets and Processing 185
2.8. Recognizing Capacity, Complexity 189
2.9. Related Approaches 192
2.10. Concluding Remarks 194
References 194
Chapter 3. Discourse Representation in Context 204
3.1. Overview 204
3.2. Interpretation of Text in Context 205
3.3. The Problem of Anaphoric Linking in Context 206
3.4. Basic Ideas of Discourse Representation 208
3.5. Discourse Representation Structures 215
3.6. The Static and Dynamic Meaning of Representation Structures 219
3.7. Sequential Composition of Representation Structures 223
3.8. Strategies for Merging Representation Structures 229
3.9. Disjoint Merge and Memory Management 236
3.10. Constructing DRSs for Natural Language Fragments 240
3.11. The Proper Treatment of Quantification in DRT 247
3.12. Representing Tense and Aspect in Texts 251
3.13. Extensions and Variations 259
3.14. Addendum to the Second Edition 261
A. Simplified Representation of Contexts 261
B. Pronouns and Anaphoric Reference 266
C. Once More: DRSs for Natural Language Fragments 267
D. Salience Updating as Context Manipulation 268
E. Further Reading 270
Acknowledgments 272
References 272
Chapter 4. Situation Theory 276
4.1. Introduction 276
4.2. The Structure of Information 277
4.3. A Theory of Structural Relations 294
4.4. Truth and Circumstance 316
4.5. Guide to the Literature 344
References 345
Further Reading 348
Chapter 5. Situations, Constraints and Channels (Update of Chapter 4) 352
5.1. From Situation Semantics to Situation Theory 352
5.2. Early Channel Theory 353
5.3. Situated Inference 356
5.4. Modern Channel Theory 358
References 366
Chapter 6. GB Theory: An Introduction 368
6.1. Phrase Structure 369
6.2. Limitations of Phrase-Structure Description 374
6.3. D-Structure and S-Structure 380
6.4. Logical Form 388
6.5. Formal Development and Applications 391
6.6. Beyond GB: Checking and Copying 405
6.7. Minimalism and Derivational and Non-Derivational Syntax 411
References 416
Chapter 7. After Government and Binding Theory (Update of Chapter 6) 418
7.1. Theoretical Developments 418
7.2. Algebraic Analyses 423
7.3. Logical and Categorial Analyses 429
7.4. The Future 432
References 432
Chapter 8. Game-Theoretical Semantics 438
8.1. Formal Languages 438
8.2. Natural Languages 456
8.3. A Survey of Games in Logic and in Language Theory 476
Note on Recent Developments 484
References 484
Chapter 9. Game-Theoretical Pragmatics (Update of Chapter 8) 490
9.1. Introduction 490
9.2. Signaling Games 491
9.3. Rational Communication 494
9.4. Information States and Message Costs 502
9.5. Connection to Optimality Theory 508
9.6. Conclusion 511
Acknowledgments 512
References 512
Part 2: General Topics 516
Chapter 10. Compositionality 518
10.1. The Principle of Compositionality of Meaning 518
10.2. Illustrations of Compositionality 520
10.3. Towards Formalization 525
10.4. Examples of Non-Compositional Semantics 529
10.5. Logic as Auxiliary Language 533
10.6. Alledged Counterexamples to Compositionality 536
10.7. Fundamental Arguments Against Compositionality 540
10.8. A Mathematical Model of Compositionality 546
10.9. The Formal Power of Compositionality 552
10.10. Other Applications of Compositionality 558
10.11. Conclusion and Further References 560
Acknowledgments 561
A. Appendix: Related Principles 561
B. Appendix: Genitives – A Case Study (by B. Partee) 564
References 571
Chapter 11. Types 578
11.1. Categories, Functions and Types 578
11.2. The Typed Lambda Calculus 580
11.3. Higher-Order Logic 598
11.4. Universal Types and Nominalization 607
11.5. Constructive Type Theories 617
11.6. Types in Semantics, Logic and Computation 625
References 627
Chapter 12. Dynamics 630
12.0. Introduction 630
12.1. Some Specific Dynamic Systems 633
12.2. Logical Observations 658
References 686
Chapter 13. Dynamic Epistemic Logic (Update of Chapter 12) 694
13.1. Introduction 694
13.2. An Example Scenario 695
13.3. A History of DEL 697
13.4. DEL and Language 704
Acknowledgments 710
References 711
Further Reading 713
Chapter 14. Partiality 714
14.0. Introduction 714
14.1. Sources of Partiality 714
14.2. Partiality and Models for Linguistic Structure 726
14.3. Partiality and the Structure of Knowledge 731
References 745
Chapter 15. Formal Learning Theory 748
15.1. Introduction 748
15.2. Identification 750
15.3. Remarks About the Identification Paradigm 752
15.4. More Refined Paradigms 755
15.5. The Need for Complementary Approaches 763
15.6. Ontology and Basic Concepts 765
15.7. First Paradigm: Absolute Solvability 768
15.8. Second Paradigm: Probabilistic Solvability 770
15.9. Third Paradigm: Solvability with Specified Probability 772
15.10. Empirical Evaluation 774
15.11. Concluding Remarks 775
15.12. Appendix: Proofs 775
References 782
Chapter 16. Computational Language Learning (Update of Chapter 15) 788
16.1. Introduction 788
16.2. Settings 789
16.3. Paradigms 798
16.4. Conclusion 800
References 800
Chapter 17. Non-monotonicity in Linguistics 804
17.1. Non-monotonicity and Linguistic Theory 804
17.2. Overview of Nonmonotonic Reasoning 807
17.3. Non-monotonicity and Feature Structures 827
17.4. Applications in Phonology 833
17.5. Applications in Morphology 836
17.6. Syntax 845
17.7. Applications in Semantics 845
17.8. Applications in Discourse 848
References 853
Chapter 18. Non-Monotonic Reasoning in Interpretation (Update of Chapter 17) 862
18.1. Introduction 862
18.2. Implicatures as Non-Monotonic Inferences 862
18.3. More on Non-Monotonic Reasoning and Linguistics 871
18.4. Conclusions 876
References 877
Part 3: Descriptive Topics 880
Chapter 19. Generalized Quantifiers in Linguistics and Logic 882
19.1. Introduction 882
19.2. Generalized Quantifiers in Natural Language: Interpretations of Noun Phrases and Determiners 884
19.3. Polyadic Quantification 910
References 929
Chapter 20. On the Learnability of Quantifiers (Update of Chapter 19) 934
20.1. Some Computational Properties of Determiners 935
20.2. The Learnability of First-Order Determiners 939
20.3. Higher-Order Determiners 943
References 945
Chapter 21. Temporality 948
21.1. A Case-study in Knowledge Representation 948
21.2. Temporal Ontology 950
21.3. Temporal Relations 956
21.4. Temporal Reference 980
21.5. Conclusion 985
21.6. Further Reading 985
Acknowledgments 986
References 986
Further Reading 992
Chapter 22. Tense, Aspect, and Temporal Representation (Update of Chapter 21 
994 
22.1. Introduction 994
22.2. Issues of Aspectuality 
994 
22.3. Tense 1002
22.4. Preparing for Discourse 1007
22.5. Conclusion 1008
References 1009
Chapter 23. Plurals and Collectives 1012
23.1. Introduction 1012
23.2. Setting the Stage 1013
23.3. Higher-Order Approaches 1019
23.4. First-Order Approaches 1030
23.5. Reading Plural NPs 1043
23.6. Non-Denotational Approaches 1049
23.7. Further Directions 1052
Acknowledgment 1053
References 1053
Chapter 24. Plural Discourse Reference (Update of Chapter 23) 1058
24.1. Plural Reference and Plural Discourse Reference 1058
24.2. Multiple Interdependent Anaphora 1059
24.3. Ontology and Logic 1066
24.4. Compositionality 1072
24.5. Conclusion 1078
References 1078
Chapter 25. Questions 1082
25.1. Preliminary 1082
25.2. Setting the Stage 1083
25.3. The Pragmatic Approach 1086
25.4. The Semantic Approach 1102
25.5. Logical and Computational Theories 1125
25.6. Linguistic Theories 1131
Acknowledgments 1152
References 1152
Chapter 26. Questions: Logic and Interactions (Update of Chapter 25) 1156
26.1. Overview 1156
26.2. The Ontology and Logic of Questions 1156
26.3. Questions in Interaction 1161
26.4. Other Question-Related Work 1166
26.5. Conclusions 1166
References 1166