A New Introduction to Modal LogicThis long-awaited book replaces Hughes and Cresswell's two classic studies of modal logic: An Introduction to Modal Logic and A Companion to Modal Logic. |
Contents
The language of PC 3 Interpretation 4 Further operators | 6 |
Some valid wff of PC 13 Basic modal notions 13 The language | 17 |
The Systems K T and D | 23 |
and M 33 Validity and soundness 36 The system T 41 A definition | 45 |
The Systems S4 S5 B Triv and Ver | 51 |
Iterated modalities 51 The system S4 53 Modalities in S4 54 Validity | 60 |
Collapsing into PC 64 Exercises 3 68 Notes 70 | 70 |
Semantic diagrams 73 Alternatives in a diagram 80 S4 diagrams 85 | 85 |
Strict Implication | 193 |
200 Validity in S2 and S3 201 Entailment 202 Exercises 11 205 | 205 |
Axiomatic PC 210 Natural deduction 211 Multiply modal logics 217 | 217 |
logics 224 Syntactical approaches to modality 225 Probabilistic | 230 |
Interpretation 237 The Principle of replacement 240 Axiomatization | 241 |
modal LPC 243 Systems of modal predicate logic 244 Theorems | 250 |
The Completeness of Modal LPC | 256 |
Canonical models for Modal LPC 256 Completeness in modal | 262 |
S5diagrams 91 Exercises 4 92 Notes 93 | 93 |
Conjunctive Normal Form | 94 |
Equivalence transformations 94 Conjunctive normal form 96 Modal | 108 |
Maximal consistent sets of wff 113 Maximal consistent extensions 114 | 114 |
Consistent sets of wff in modal systems 116 Canonical models 117 | 121 |
Canonical Models | 127 |
Convergence 134 The frames of canonical models 136 A noncanonical | 142 |
the finite model property 153 Exercises 8 156 Notes 156 | 156 |
Frames and models 159 An incomplete modal system 160 KH and | 164 |
Frames and Systems | 172 |
Frames for T S4 B and S5 172 Irreflexiveness 176 Compactness | 188 |
monadic modal LPC 271 Exercises 14 272 Notes 272 | 272 |
Canonical models without BF 280 Completeness 282 Incompleteness | 287 |
Modality and Existence | 289 |
Changing domains 289 The existence predicate 292 Axiomatization | 302 |
Identity in LPC 312 Soundness and completeness 314 Definite | 329 |
Contingent identity 330 Contingent identity systems 334 Quantifying | 342 |
Firstorder modal theories 349 Multiple indexing 350 Counterpart | 358 |
Bibliography | 384 |
398 | |