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Modal logic:

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 di...

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Bibliographic Details
Main Authors:	Blackburn, Patrick 1959- (Author), Rijke, Maarten de 1961- (Author), Venema, Yde 1963- (Author)
Format:	Electronic eBook
Language:	English
Published:	Cambridge Cambridge University Press 2001
Series:	Cambridge tracts in theoretical computer science 53
Subjects:	Modality (Logic) Modallogik
Online Access:	DE-12 DE-92 DE-19 DE-703 DE-29 DE-739 Volltext
Summary:	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
Item Description:	Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Physical Description:	1 Online-Ressource (xxii, 554 Seiten)
ISBN:	9781107050884
DOI:	10.1017/CBO9781107050884

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505	8		\|a 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 --
505	8		\|a 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 --
505	8		\|a 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
520			\|a 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
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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
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series2	Cambridge tracts in theoretical computer science
spelling	Blackburn, Patrick 1959- Verfasser (DE-588)174091478 aut Modal logic Patrick Blackburn, Maarten de Rijke, Yde Venema Cambridge Cambridge University Press 2001 1 Online-Ressource (xxii, 554 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in theoretical computer science 53 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 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 Modality (Logic) Modallogik (DE-588)4074914-9 gnd rswk-swf Modallogik (DE-588)4074914-9 s 1\p DE-604 Rijke, Maarten de 1961- Verfasser (DE-588)1157364152 aut Venema, Yde 1963- Verfasser (DE-588)1145737048 aut Erscheint auch als Druck-Ausgabe, Hardcover 978-0-521-80200-0 Erscheint auch als Druck-Ausgabe, Paperback 978-0-521-52714-9 https://doi.org/10.1017/CBO9781107050884 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Blackburn, Patrick 1959- Rijke, Maarten de 1961- Venema, Yde 1963- Modal logic 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 Modality (Logic) Modallogik (DE-588)4074914-9 gnd
subject_GND	(DE-588)4074914-9
title	Modal logic
title_auth	Modal logic
title_exact_search	Modal logic
title_full	Modal logic Patrick Blackburn, Maarten de Rijke, Yde Venema
title_fullStr	Modal logic Patrick Blackburn, Maarten de Rijke, Yde Venema
title_full_unstemmed	Modal logic Patrick Blackburn, Maarten de Rijke, Yde Venema
title_short	Modal logic
title_sort	modal logic
topic	Modality (Logic) Modallogik (DE-588)4074914-9 gnd
topic_facet	Modality (Logic) Modallogik
url	https://doi.org/10.1017/CBO9781107050884
work_keys_str_mv	AT blackburnpatrick modallogic AT rijkemaartende modallogic AT venemayde modallogic

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