Handbook of Philosophical Logic (eBook)

CONTENTS 6
PREFACE TO THE SECOND EDITION 7
LAMBDA CALCULI: A GUIDE 14
1 INTRODUCTION 14
2 SYNTAX 15
3 THE BASIC THEORY 19
3.1 The theory . 19
3.2 Substitution 22
3.3 Extensionality 27
4 REDUCTION 30
4.1 Notions of Reduction 30
4.2 The Church–Rosser Theorem 35
4.3 Delta Rules 39
4.4 Residuals 41
4.5 Head Normal Forms 43
4.6 The Standardisation Theorem 45
5 MODELS 46
5.1 .-algebras 47
5.2 .-models 50
5.3 Term models 51
6 COMPUTABILITY 52
6.1 Fixed Points 52
6.2 Numeral Systems 54
6.3 .-definability 58
6.4 Decidability 61
7 TYPED CALCULI 63
7.1 Typed .-calculus 63
7.2 The Polymorphic .-calculus 67
7.3 Polymorphic Type Inference 69
7.4 Intersection Types 75
8 CONCLUSIONS 77
BIBLIOGRAPHY 78
INTERPOLATION AND DEFINABILITY 80
1 INTRODUCTION AND DISCUSSION 80
1.1 General discussion 80
1.2 Interpolation in general logics 94
2 INTERPOLATION AND DEFINABILITY IN MODAL ANDINTUITIONISTIC LOGICS 104
2.1 Interrelations between interpolation, definabillity and jointconsistency 105
2.2 Lyndon’s interpolation in some modal systems 109
2.3 Overview of interpolation and definability in modal and intuitionisticlogics 116
3 FURTHER RESULTS AND DISCUSSION 121
3.1 Further results 122
3.2 Further discussion 129
BIBLIOGRAPHY 133
DISCOURSE REPRESENTATION THEORY 137
1 INTRODUCTION 137
2 A DYNAMIC AND REPRESENTATIONAL ACCOUNT OFMEANING 139
2.1 Truth Conditions, Discourse and Interpretation in Context 140
2.2 Donkey Sentences 141
2.3 DRT — the Basic Ingredients 142
3 BASIC DRS LANGUAGES AND THEIR INTERPRETATIONS 156
3.1 A First-Order, Extensional DRS Language 157
3.2 Intensional Semantics, Propositions, Information States andContext Change Potential 165
3.3 Generalised Quantifiers 175
3.4 Plural 193
3.5 Tense and Aspect 208
3.6 A First-Order DRT Calculus 261
4 PRESUPPOSITION 271
4.1 Introduction 271
4.2 Examples 274
4.3 Syntax and Semantics of Preliminary Representations 302
4.4 Accommodation and Inference. 318
4.5 Construction of Preliminary Representations 327
4.6 Conclusion 336
5 PROPOSITIONAL ATTITUDES 338
5.1 Introduction 338
5.2 Extending DRT to a Formalism Capable of Describing AttitudinalStates and Attitude Attributions. Some ExamplesSemi-Formally Treated 340
5.3 Syntax and Semantics of the Extended Formalism 354
5.4 Construction of Representations of Attitude Attributing Sentencesand Texts 371
BIBLIOGRAPHY 399
INDEX 407