Handbook of modal logic

Medientyp: E-Book

Titel: Handbook of modal logic

Enthält: Front Cover; Handbook of Modal Logic; Copyright Page; Table of Contents; List of Contributors; Preface; Part 1. Basic Theory; Chapter 1 Modal Logic: A Semantic Perspective; 1 Introduction; 2 Basic modal logic; 2.1 First steps in relational semantics; 2.2 The standard translation; 3 Bisimulation and definability; 3.1 Drawing distinctions; 3.2 Bisimulation; 3.3 Invariance and definability in first-order logic; 3.4 Invariance and definability in modal logic; 3.5 Modal logic and first-order logic compared; 3.6 Bisimulation as a game; 4 Computation and complexity; 4.1 Model checking
4.2 Satisfiability and validity: decidability4.3 Satisfiability and validity: complexity; 4.4 Other reasoning tasks; 5 Richer logics; 5.1 Axioms and relational frame properties; 5.2 Frame definability and undefinability; 5.3 Frame correspondence and second-order logic; 5.4 First-order frame definability; 5.5 Correspondence in richer languages; 5.6 Remarks on computability; 6 Richer languages; 6.1 The universal modality; 6.2 Hybrid logic; 6.3 Temporal logic with Until and Since operators; 6.4 Conditional logic; 6.5 The guarded fragment; 6.6 Propositional Dynamic Logic; 6.7 The modal µ-calculus
6.8 Combined logics6.9 First-order modal logic; 6.10 General perspectives; 7 Alternative semantics; 7.1 Algebraic semantics; 7.2 Neighbourhood semantics; 7.3 Topological semantics; 8 Modal logic and its changing environment; Acknowledgements; Bibliography; Chapter 2 Modal Proof Theory; 1 Introduction; 2 Modal Axiomatics; 2.1 Normal Axiom Systems; 2.2 Soundness and Completeness; 2.3 Difficulties, and GL; 2.4 Sahlqvist Formulas; 3 Deduction, and the Deduction Theorem; 4 Natural Deduction; 4.1 Classical Natural Deduction; 4.2 Modal Natural Deduction; 5 Semantic Tableaus
5.1 A Classical Tableau System5.2 Destructive Modal Tableaus; 5.3 Soundness and Completeness; 5.4 The Logic GL; 5.5 Tableau Remarks; 6 Prefixed Tableaus; 6.1 A Prefixed System for K; 6.2 Soundness and Completeness; 6.3 Other Modal Logics; 7 Gentzen Systems; 7.1 Classical Propositional Sequents; 7.2 Modal Propositional Sequents; 8 Hypersequents; 8.1 Hypersequents for S5; 8.2 Examples; 8.3 Soundness and Completeness; 9 Logics of Knowledge; 9.1 A Basic Logic of Knowledge; 9.2 Common Knowledge; 10 Converse; 11 The Universal Modality and the Difference Modality; 12 What Are the Limitations
13 Quantified Modal Logic13.1 Syntax and Semantics; 13.2 Constant Domain Tableaus; 13.3 Soundness and Completeness; 13.4 Variations; 14 Conclusion; Bibliography; Chapter 3 Complexity of Modal Logic; 1 Introduction; 1.1 Examples of decision problems in modal logic; 1.2 A simple and a hard problem; 1.3 The model checking problem; 1.4 The consequence problem; 1.5 A tiling logic; 2 Decision algorithms; 2.1 Selection of points; 2.2 Filtration; 2.3 Hintikka set elimination; 2.4 Hintikka set elimination without constraints; 2.5 Forcing exponentially deep paths; 2.6 Tree automata; 2.7 Pseudo-models
3 Complexity

Beteiligte: Blackburn, Patrick [Sonstige Person, Familie und Körperschaft]; Benthem, Johan van [Sonstige Person, Familie und Körperschaft]; Wolter, Frank [Sonstige Person, Familie und Körperschaft]

Erschienen: Amsterdam [u.a.]: Elsevier, 2007

Ausgabe: 1. ed.

Umfang: Online Ressource (xxiii, 1231 p.)

Sprache: Englisch

ISBN: 0444516905; 9780080466668; 0080466664; 9780444516909

RVK-Notation: SK 130 : Logik und Grundlagen, Metamathematik,
ST 125 : Schaltungstheorie, Rechnerarithmetik, Logik
CC 2400 : Einführungen, Handbücher, Sammelbände und Bibliografien

Schlagwörter: Modallogik
Modallogik

Reproduktionsreihe: ScienceDirect

Entstehung:

Anmerkungen: Includes bibliographical references and index. - Description based on print version record

Beschreibung: List of Contributors -- -- Preface (P. Blackburn, J. van Benthem and F. Wolter) -- -- Part 1. Basic Theory -- Modal Logic: A Semantic Perspective (J. van Benthem and P. Blackburn) -- Modal Proof Theory (M. Fitting) -- Complexity of Modal Logic (M. Marx) -- Computational Modal Logic (I. Horrocks, U. Hustadt, U. Sattler, R. Schmidt) -- Part 2. Advanced Theory -- Model Theory of Modal Logic (V. Goranko and M. Otto) -- Algebras and Co-algebras (Y. Venema) -- Modal Decision Problems (F. Wolter and M. Zakharyaschev) -- Modal Consequence Relations (M. Kracht) -- Part 3. Variations and Extensions -- First-order Modal Logic (T. Br̃uner and S. Ghilardi) -- Higher Order Modal Logic (R. Muskens) -- Temporal Logic (I. Hodkinson and M. Reynolds) -- Modal Mu-Calculi (J. Bradfield and C. Stirling) -- Description Logic (F. Baader and C. Lutz) -- Hybrid Logics (C. Areces and B. ten Cate) -- Combining Modal Logics (A. Kurucz) -- Part 4. Variations and Extensions -- Modal Logic in Mathematics (S. Artemov) -- Automata-theoretic Techniques for Temporal Reasoning (M. Vardi) -- Intelligent Agents and Common-sense Reasoning (J.-J. Meyer and F. Veltman) -- Applications of Modal Logic in Lingistics (L. Moss and H.-J. Tiede) -- Modal Logic for Games and Information (W. van der Hoek and M. Pauly) -- Modal Logic and Philosophy (S. Lindstṟm and K. Segerberg) -- Index

The Handbook of Modal Logic contains 20 articles, which collectively introduce contemporary modal logic, survey current research, and indicate the way in which the field is developing. The articles survey the field from a wide variety of perspectives: the underling theory is explored in depth, modern computational approaches are treated, and six major applications areas of modal logic (in Mathematics, Computer Science, Artificial Intelligence, Linguistics, Game Theory, and Philosophy) are surveyed. The book contains both well-written expository articles, suitable for beginners approaching the subject for the first time, and advanced articles, which will help those already familiar with the field to deepen their expertise. Please visit: http://people.uleth.ca/~woods/RedSeriesPromo_WP/PubSLPR.html - Compact modal logic reference - Computational approaches fully discussed - Contemporary applications of modal logic covered in depth

Handbook of modal logic - [1. ed.]

Merkliste

Nur in Feld suchen:

Zuletzt gesuchte Begriffe: