Handbook of Philosophical Logic (eBook)

CONTENTS 6
PREFACE TO THE SECOND EDITION 7
ODINALDO RODRIGUES, DOV GABBAY ANDALESSANDRA RUSSO 14
1 INTRODUCTION AND HISTORICAL PERSPECTIVE 14
2 FORMALISATION OF THE PROBLEM OF BELIEF REVISION 18
2.1 AGM postulates for belief revision 21
2.2 Counterfactual statements and the Ramsey Test 25
2.3 Grove’s systems of spheres 29
2.4 AGM revision for finite belief bases 33
2.5 Epistemic entrenchment 36
2.6 Discussion 37
3 BELIEF REVISION OPERATORS 39
3.1 Measuring information change 39
3.2 Dalal’s revision operator 47
4 ITERATION OF THE REVISION PROCESS 50
4.1 The problem of iteration and the need for extralogical informationto guide the process 51
4.2 Darwiche and Pearl’s approach 53
4.3 Lehmann’s approach: belief revision, revised 58
4.4 Iterated revision according to Boutilier 59
4.5 Prioritised base revision 62
4.6 Prioritised databases 64
4.7 Ordered theory presentations 70
5 SPECIALISED BELIEF REVISION 73
5.1 Resource-bounded revision 74
5.2 Controlled revision 76
5.3 Multiple belief revision 80
5.4 Revision by translation 92
6 COMPLEXITY ISSUES 96
7 APPLICATIONS 98
7.1 Belief Revision in Requirements Engineering 98
8 CONCLUSIONS 110
BIBLIOGRAPHY 119
REFUTATION SYSTEMS IN PROPOSITIONALLOGIC 128
1 INTRODUCTION 128
1.1 Basic Concepts 128
1.2 A Problem 130
1.3 Proving Syntactic Completeness 133
1.4 Reduction Procedures 134
1.5 General Remarks 134
2 INTUITIONISTIC LOGIC 136
2.1 Preliminaries 136
2.2 Proof System 137
2.3 Normal Forms 142
2.4 Refutation System 145
2.5 Syntactic Completeness 146
2.6 Classical Logic 149
3 THE MODAL LOGIC S4 150
3.1 Preliminaries 150
3.2 Proof System 151
3.3 Normal Forms 152
3.4 Refutation System 153
3.5 Syntactic Completeness 154
4 REDUCTION PROCEDURES 155
4.1 Reduction Rules 155
4.2 Reduction Systems 157
4.3 Intuitionistic Logic 158
4.4 Classical Logic 161
4.5 The Modal Logic S4 162
5 SYMMETRIC INFERENCE SYSTEMS 165
5.1 Preliminaries 165
5.2 Syntactic Refutability 165
5.3 Syntactic Properties 166
BIBLIOGRAPHY 170
QUANTIFIER SCOPE IN FORMALLINGUISTICS 171
1 INTRODUCTION 171
2 CHARACTERIZING INVERSE SCOPE EFFECTS 172
2.1 A “direct scope” grammar for a fragment of English 172
2.2 Incompleteness of the grammar’s “direct scope” strategy 174
2.3 Methodological and empirical principles in the study of quantifierscope 176
2.3.1 Pragmatic effects 177
2.3.2 Logical dependence between readings 178
2.3.3 A note on cross-linguistic variation 180
3 SOME PROBLEMS OF QNP SCOPE 181
3.1 Overview of some scope phenomena 181
3.2 Restrictions on scope 184
3.3 Unexpected wide scope: simple indefinites 185
3.4 Absence of inverse scope 186
3.5 Mixed scope 189
3.6 Summary of QNP scope problems 190
4 LOGICAL AND LINGUISTIC THEORIES OF QUANTIFIERSCOPE 190
4.1 Preliminaries on quantifier scope 190
4.2 “Standard scope” mechanisms 192
4.2.1 Quantifier Raising 192
4.2.2 Quantifying-in 201
4.2.3 Cooper Storage 204
4.2.4 Type Flexibility 205
4.2.5 Categorial approaches 207
4.2.6 Discussion — different emphases by different approaches to QNPscope 211
4.3 Non-Standard Scope Mechanisms 212
4.3.1 Branching quantification 212
4.3.2 Cumulative quantification 216
4.3.3 Wide-scope indefinites and quantification over Skolem functions 218
5 TWO EMPIRICAL EXTENSIONS 222
5.1 Quantifier scope reconstruction — syntactic and semanticaccounts 223
5.2 Antecedent Contained Deletion (ACD) 226
6 CONCLUSIONS 229
BIBLIOGRAPHY 231
NON-DETERMINISTIC SEMANTICS FORLOGICAL SYSTEMS 238
1 INTRODUCTION 238
1.1 The Key Idea 238
1.2 Some Intuitive Motivations 239
1.3 Things To Come 244
PART I: THE PROPOSITIONAL CASE 245
2 PRELIMINARIES 245
2.1 Logics, Consequence Relations and Abstract Rules 245
3 INTRODUCING NMATRICES 250
4 CANONICAL DEDUCTION SYSTEMS AND NMATRICES 255
4.1 Canonical Calculi for Nmatrices 260
4.2 Nmatrices for Canonical Calculi 263
5 USING NMATRICES FOR NON-CANONICAL SYSTEMS 268
5.1 Extensions of Classical Logic 268
5.2 Extensions of Intuitionistic Logic 275
6 NMATRICES FOR LOGICS OF FORMAL INCONSISTENCY 282
6.1 LFIs with Finite Characteristic Nmatrices 283
6.2 LFIs with Infinite Characteristic Nmatrices 287
PART II: THE FIRST-ORDER CASE AND BEYOND 290
7 MANY-VALUED MATRICES WITH QUANTIFERS 291
8 NMATRICES WITH QUANTIFIERS 295
9 THE FIRST-ORDER CASE 299
10 AN APPLICATION: NMATRICES FOR FIRST-ORDER LOGICSOF FORMAL INCONSISTENCY 302
11 CANONICAL DEDUCTION SYSTEMS AND NMATRICES WITHMORE GENERAL QUANTIFIERS 306
BIBLIOGRAPHY 311
INDEX 316