Makinson / Malinowski / Wansing Towards Mathematical Philosophy

Papers from the Studia Logica conference Trends in Logic IV
1. Auflage 2008
ISBN: 978-1-4020-9084-4
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 344 Seiten

area and in applications to linguistics, formal epistemology, and the study of norms. The second contains papers on non-classical and many-valued logics, with an eye on applications in computer science and through it to engineering. The third concerns the logic of belief management,whichis likewise closely connected with recent work in computer science but also links directly with epistemology, the philosophy of science, the study of legal and other normative systems, and cognitive science. The grouping is of course rough, for there are contributions to the volume that lie astride a boundary; at least one of them is relevant, from a very abstract perspective, to all three areas. We say a few words about each of the individual chapters, to relate them to each other and the general outlook of the volume. Modal Logics The ?rst bundle of papers in this volume contains contribution to modal logic. Three of them examine general problems that arise for all kinds of modal logics. The ?rst paper is essentially semantical in its approach, the second proof-theoretic, the third semantical again: • Commutativity of quanti?ers in varying-domain Kripke models,by R. Goldblatt and I. Hodkinson, investigates the possibility of com- tation (i.e. reversing the order) for quanti?ers in ?rst-order modal logics interpreted over relational models with varying domains. The authors study a possible-worlds style structural model theory that does not v- idate commutation, but satis?es all the axioms originally presented by Kripke for his familiar semantics for ?rst-order modal logic.

Autoren/Hrsg.

Makinson, David

Malinowski, Jacek

Wansing, Heinrich

Inhaltsverzeichnis

1;Contents;6
2;List of Contributors;11
3;From Logic to Mathematical Philosophy;14
4;Commutativity of Quantifiers in Varying-Domain Kripke Models;21
4.1;Introduction and Overview;21
4.2;1. Model Structures;24
4.3;2. Premodels and Models;26
4.4;3. Soundness and M-Equivalence;29
4.5;4. Validating CQ;32
4.6;5. A Countermodel to CQ;35
4.7;6. Completeness and the Barcan Formulas;40
5;The Method of Tree-hypersequents for Modal Propositional Logic;43
5.1;1. Introduction;43
5.2;2. The Calculi CSK*;46
5.3;3. Admissibility of the Structural Rules;49
5.4;4. The adequateness of the calculi;55
5.5;5. Cut-elimination Theorem for CSK*;57
5.6;6. Conclusions and Further Work;61
6;All Splitting Logics in the Lattice NExt(KTB);64
6.1;1. Introduction;64
6.2;2. Preliminaries;65
6.3;3. Splitting;67
6.4;4. Connected KTB-frames;70
6.5;5. Few splittings theorem;72
6.6;6. Some questions and conjectures;76
7;A Temporal Logic of Normative Systems;79
7.1;1. Introduction;79
7.2;2. Normative Temporal Logic;80
7.3;3. Symbolic Representations;90
7.4;4. Model Checking;96
7.5;5. Case Study: Traffic Control;103
7.6;6. Discussion;110
8;Reasoning with Justifications;117
8.1;1. Introduction;117
8.2;2. Hintikka’s Logics of Knowledge;117
8.3;3. Awareness Logic;120
8.4;4. Explicit Justifications;120
8.5;5. Internalization;123
8.6;6. Information Hiding and Recovery;124
8.7;7. Original Intent;125
8.8;8. Realizations As First-Class Objects;126
8.9;9. Generalizations;130
8.10;10. The Goal;131
9;Monotone Relations, Fixed Points and Recursive Definitions;134
9.1;1. Partially Ordered Sets;136
9.2;2. Monotone relations;143
9.3;3. Arithmetic Recursion and Fixed-Points;155
9.4;4. The downward Loewenheim-Skolem-Tarski Theorem;170
10;Processing Information from a Set of Sources;174
10.1;1. Introduction;174
10.2;2. The framework;175
10.3;3. Existential strategy for standard structures;182
10.4;4. The universal strategy;188
10.5;5. Proof systems for the existential strategy;188
10.6;6. Future research;193
11;The Classical Model Existence Theorem in Subclassical Predicate Logics I;196
11.1;1. Introduction;196
11.2;2. Classical model existence theorem in propositional logics;198
11.3;3. A Herbrand-Henkin style proof of the classical model existence theorem for prenex normal form sentences;200
11.4;4. Prenex normal form theorem holds in logics weaker than first order logic;204
11.5;5. Concluding remarks;206
12;Weak Implicational Logics Related to the Lambek Calculus — Gentzen versus Hilbert Formalisms;209
12.1;1. Introduction;209
12.2;2. Preliminaries;211
12.3;3. The associative case;213
12.4;4. The non-associative case;215
12.5;5. Hilbert-style formalism;217
13;Faithful and Invariant Conditional Probability in Lukasiewicz Logic;221
13.1;Introduction: Conditionals and de Finetti coherence criterion;221
13.2;1. The i-dimensional volume of a formula;223
13.3;2. Conditionals in Lukasiewicz propositional logic L8;228
13.4;3. A faithful invariant conditional for L8;230
13.5;4. Proof: construction of a faithful conditional P;232
13.6;5. Conclusion of the proof: P is invariant;235
14;A Fuzzy Logic Approach to Non-scalar Hedges;241
14.1;1. Introduction;241
14.2;2. Lakoff’s proposal;242
14.3;3. Some new machinery;245
14.4;4. The generic fuzzy logic for non-scalar hedges FLh;248
14.5;5. Conclusion;255
15;The Procedures for Belief Revision;257
15.1;1. Introduction;258
15.2;2. Nonmonotonicity on classical base;264
15.3;3. Nonmonotonicity on intuitionistic base;271
15.4;4. Generalization;274
16;Shifting Priorities: Simple Representations for Twenty-seven Iterated Theory Change Operators;277
16.1;1. Introduction;277
16.2;2. Representing doxastic states: Prioritized belief bases, entrench-ment, systems of spheres;278
16.3;3. Variants of expansion;283
16.4;4. Radical revision;284
16.5;5. Conservative revision;285
16.6;6. Moderate revision;286
16.7;7. Restrained revision;287
16.8;8. Variants of contraction;288
16.9;9. Refinement: Neither revision nor contraction;289
16.10;10. Two-dimensional operators: Revision by comparison;290
16.11;11. Two-dimensional operators: Cantwell’s lowering;291
16.12;12. Gentle raising and lowering;293
16.13;13. Two-dimensional operators: Raising and lowering by strict comparisons;293
16.14;14. Two-dimensional operators: Bounded revision;294
16.15;15. Conclusion;296
17;The Coherence of Theories — Dependencies and Weights;305
17.1;1. Introduction;305
17.2;2. Internalist Coherence;307
17.3;3. Application to Game Theory;319
17.4;4. Summary and Discussion;325
18;On Meta-knowledge and Truth;327
18.1;Introduction;327
18.2;1. Ideas;328
18.3;2. Main Assumptions of the Theory of Syntax and Semantics;330
18.4;3. Three notions of truthfulness;342
18.5;4. Final remarks;347