This volume contains a collection of articles applying methods of logic or, more generally, of mathematics to solve problems, some of which come from logic itself, others from other sciences. Its range of subjects is far from complete, but broadly representative. The first group of papers in this volume consists of contributions to pure and applied modal logic. The problems discussed here range from the structure of lattices of normal and other modal propositional logics to modal proof theory and to the semantics of quantified modal logic. The second group of papers deals with Many-valued logics - an extensive domain of strictly logical investigations rooting in philosophical questions concerning the nature of logical values. Logical investigations in cognitive science have successfully utilized methods and systems of belief revision, non-monotonic logic and dynamic epistemic logic. Towards Mathematical Philosophy deals with focal issues of belief revision. The volume concludes with contributions which may be seen to belong to the field of formal epistemology, the area applying logical, probabilistic, game-theoretic and other formal methods to problems and issues in epistemology and philosophy of science, such as those concerning anti-realism, skepticism, theory comparison and theory choice, justification, sources of knowledge and learning theories.
Author(s): David Makinson, Jacek Malinowski, Heinrich Wansing (eds.)
Series: Trends in Logic 28
Publisher: Springer
Year: 2008
Language: English
Pages: 351
Contents......Page 6
Introduction......Page 14
Modal Logic......Page 16
Non-Classical and Many-Valued Logics......Page 17
Belief Management......Page 19
Introduction and Overview......Page 21
1. Model Structures......Page 24
2. Premodels and Models......Page 26
3. Soundness and M-Equivalence......Page 29
4. Validating CQ......Page 32
5. A Countermodel to CQ......Page 35
6. Completeness and the Barcan Formulas......Page 40
References......Page 42
1. Introduction......Page 43
2. The Calculi CSK[sup(*)]......Page 46
3. Admissibility of the Structural Rules......Page 49
4. The Adequateness of the Calculi......Page 55
5. Cut-Elimination Theorem for CSK[sup(*)]......Page 57
6. Conclusions and Further Work......Page 61
References......Page 62
1. Introduction......Page 64
2. Preliminaries......Page 65
3. Splitting......Page 67
4. Connected KTB-Frames......Page 70
5. Few Splittings Theorem......Page 72
6. Some Questions and Conjectures......Page 76
References......Page 77
1. Introduction......Page 79
2. Normative Temporal Logic......Page 80
3. Symbolic Representations......Page 90
4. Model Checking......Page 96
5. Case Study: Traffic Control......Page 103
6. Discussion......Page 110
References......Page 114
2. Hintikka's Logics of Knowledge......Page 117
4. Explicit Justifications......Page 120
5. Internalization......Page 123
6. Information Hiding and Recovery......Page 124
7. Original Intent......Page 125
8. Realizations As First-Class Objects......Page 126
9. Generalizations......Page 130
10. The Goal......Page 131
References......Page 132
7. Monotone Relations, Fixed Points and Recursive Definitions......Page 134
1. Partially Ordered Sets......Page 136
2. Monotone Relations......Page 143
3. Arithmetic Recursion and Fixed-Points......Page 155
4. The Downward Löwenheim-Skolem-Tarski Theorem......Page 170
References......Page 172
1. Introduction......Page 174
2. The Framework......Page 175
3. Existential Strategy for Standard Structures......Page 182
5. Proof Systems for the Existential Strategy......Page 188
6. Future Research......Page 193
References......Page 194
1. Introduction......Page 196
2. Classical Model Existence Theorem in Propositional Logics......Page 198
3. A Herbrand-Henkin Style Proof of the Classical Model Existence Theorem for Prenex Normal Form Sentences......Page 200
4. Prenex Normal Form Theorem Holds in Logics Weaker than First Order Logic......Page 204
5. Concluding Remarks......Page 206
References......Page 207
1. Introduction......Page 209
2. Preliminaries......Page 211
3. The Associative Case......Page 213
4. The Non-Associative Case......Page 215
5. Hilbert-Style Formalism......Page 217
References......Page 219
Introduction: Conditionals and de Finetti Coherence Criterion......Page 221
1. The i-Dimensional Volume of a Formula......Page 223
2. Conditionals in Lukasiewicz Propositional Logic L[sub(∞)]......Page 228
3. A Faithful Invariant Conditional for L[sub(∞)]......Page 230
4. Proof: Construction of a Faithful Conditional P......Page 232
5. Conclusion of the Proof: P is Invariant......Page 235
References......Page 239
1. Introduction......Page 241
2. Lakoff's Proposal......Page 242
3. Some New Machinery......Page 245
4. The Generic Fuzzy Logic for Non-Scalar Hedges FL[sub(h)]......Page 248
References......Page 255
13. The Procedures for Belief Revision......Page 257
1. Introduction......Page 258
2. Nonmonotonicity on Classical Base......Page 264
3. Nonmonotonicity on Intuitionistic Base......Page 271
4. Generalization......Page 274
References......Page 275
1. Introduction......Page 277
2. Representing Doxastic States: Prioritized Belief Bases, Entrenchment, Systems of Spheres......Page 278
3. Variants of Expansion......Page 283
4. Radical revision......Page 284
5. Conservative Revision......Page 285
6. Moderate Revision......Page 286
7. Restrained Revision......Page 287
8. Variants of Contraction......Page 288
9. Refinement: Neither Revision nor Contraction......Page 289
10. Two-Dimensional Operators: Revision by Comparison......Page 290
11. Two-Dimensional Operators: Cantwell's Lowering......Page 291
13. Two-Dimensional Operators: Raising and Lowering by Strict Comparisons......Page 293
14. Two-Dimensional Operators: Bounded Revision......Page 294
15. Conclusion......Page 296
References......Page 298
1. Introduction......Page 305
2. Internalist Coherence......Page 307
3. Application to Game Theory......Page 319
References......Page 325
Introduction......Page 327
1. Ideas......Page 328
2. Main Assumptions of the Theory of Syntax and Semantics......Page 330
3. Three Notions of Truthfulness......Page 342
4. Final Remarks......Page 347
References......Page 348
