UID:
almahu_9948233530002882
Umfang:
1 online resource (xxii, 554 pages) :
,
digital, PDF file(s).
ISBN:
9781107050884 (ebook)
Serie:
Cambridge tracts in theoretical computer science ; 53
Inhalt:
This is an advanced 2001 textbook on modal logic, a field which caught the attention of computer scientists in the late 1970s. Researchers in areas ranging from economics to computational linguistics have since realised its worth. The book is for novices and for more experienced readers, with two distinct tracks clearly signposted at the start of each chapter. The development is mathematical; prior acquaintance with first-order logic and its semantics is assumed, and familiarity with the basic mathematical notions of set theory is required. The authors focus on the use of modal languages as tools to analyze the properties of relational structures, including their algorithmic and algebraic aspects, and applications to issues in logic and computer science such as completeness, computability and complexity are considered. Three appendices supply basic background information and numerous exercises are provided. Ideal for anyone wanting to learn modern modal logic.
Anmerkung:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
,
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.
Weitere Ausg.:
Print version: ISBN 9780521802000
Sprache:
Englisch
URL:
https://doi.org/10.1017/CBO9781107050884
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