Modal logic [E-Book] / Patrick Blackburn, Maarten de Rijke, Yde Venema.
Blackburn, Patrick, (author)
Rijke, Maarten de, (author) / Venema, Yde, (author)
Cambridge : Cambridge University Press, 2001
1 online resource (xxii, 554 pages)
englisch
9780521802000
9781107050884
9780521527149
Cambridge tracts in theoretical computer science ; 53
Full Text
Table of Contents:
  • Machine generated contents note: 1 Basic Concepts
  • 1.1 Relational Structures
  • 1.2 Modal Languages
  • 1.3 Models and Frames
  • 1.4 General Frames
  • 1.5 Modal Consequence Relations
  • 1.6 Normal Modal Logics
  • 1.7 Historical Overview
  • 1.8 Summary of Chapter 1
  • 2 Models
  • 2.1 Invariance Results
  • 2.2 Bisimulations
  • 2.3 Finite Models
  • 2.4 The Standard Translation
  • 2.5 Modal Saturation via Ultrafilter Extensions
  • 2.6 Characterization and Definability
  • 2.7 Simulation and Safety
  • 2.8 Summary of Chapter 2
  • Notes
  • 3 Frames
  • 3.1 Frame Definability
  • 3.2 Frame Definability and Second-Order Logic
  • 3.3 Definable and Undefinable Properties
  • 3.4 Finite Frames
  • 3.5 Automatic First-Order Correspondence
  • 6 Sahlqvist Formulas
  • .7 More about Sahlqvist Formulas
  • 2: r ii
  • 3.8 Advanced Frame Theory
  • 3.9 Summary of Chapter 3
  • Notes
  • 4 Completeness
  • 4.1 Preliminaries
  • 4.2 Canonical Models
  • 4.3 Applications
  • 4.4 Limitative Results
  • 4.5 Transforming the Canonical Model
  • 4.6 Step by Step
  • 4.7 Rules for the Undefinable
  • 4.8 Finitary Methods I
  • 4.9 Finitary Methods II
  • 4.10 Summary of Chapter 4
  • Notes
  • 5 Algebras and General Frames
  • 5.1 Logic as Algebra
  • 5.2 Algebraizing Modal Logic
  • 5.3 The J6nsson-Tarski Theorem
  • 5.4 Duality Theory
  • 5.5 General Frames
  • 5.6 Persistence
  • 5.7 Summary of Chapter 5
  • Notes
  • 6 Computability and Complexity
  • 6.1 Computing Satisfiability
  • 6.2 Decidability via Finite Models
  • 6.3 Decidability via Interpretations
  • 6.4 Decidability via Quasi-models and Mosaics
  • 6.5 Undecidability via Tiling
  • 6.6 NP
  • 6.7 PSPACE
  • 6.8 EXPTIME
  • 6.9 Summary of Chapter 6
  • Notes
  • 7 Extended Modal Logic
  • 7.1 Logical Modalities
  • 7.2 Since and Until
  • 7.3 Hybrid Logic
  • 7.4 The Guarded Fragment
  • - - : * : ii: : ~~~~Ii::-:1
  • 7.5 Multi-Dimensional Modal Logic
  • 7.6 A Lindstr6m Theorem for Modal Logic
  • 7.7 Summary of Chapter 7
  • Notes
  • Appendix A A Logical Toolkit
  • Appendix B An Algebraic Toolkit
  • Appendix C A Computational Toolkit
  • Appendix D A Guide to the Literature
  • Bibliography
  • List of Notation
  • Index.