Kripke's worlds /

Possible worlds models were introduced by Saul Kripke in the early 1960s. Basically, a possible world's model is nothing but a graph with labelled nodes and labelled edges. Such graphs provide semantics for various modal logics (alethic, temporal, epistemic and doxastic, dynamic, deontic, descr...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Otros Autores: Gasquet, Olivier
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Basel : London : Birkhäuser ; Springer [distributor], 2011.
Colección:Studies in universal logic.
Temas:
Nonclassical mathematical logic.
Logique mathématique non classique.
Nonclassical mathematical logic
Acceso en línea:Texto completo

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245 0 0 |a Kripke's worlds /  |c by Olivier Gasquet [and others]. 
260 |a Basel :  |b Birkhäuser ;  |a London :  |b Springer [distributor],  |c 2011. 
300 |a 1 online resource (1 volume). 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
490 1 |a Studies in Universal Logic 
588 0 |a Print version record. 
505 0 |a Kripke's Worlds; Preface; Why Did We Write This Book?; LoTREC: An Ubiquitous Tool in This Book; Overview of the Chapters; Audience and Prerequisites; Acknowledgments; Contents; Chapter 1: Modelling with Graphs; 1.1 Actions, Events, Programs; 1.2 Time; 1.3 Knowledge and Belief; 1.4 Obligations and Permissions; 1.5 Relations Between Objects; 1.6 Kripke Models: The Formal Definition; 1.7 Kripke Models: Building Them with LoTREC; 1.8 The Typewriter Font Convention; 1.9 Modelling Theories by Classes of Kripke Models; 1.10 Summary; Chapter 2: Talking About Graphs; 2.1 The Formal Language. 
505 8 |a 2.1.1 Atomic Formulas2.1.2 Boolean Connectives; 2.1.3 Modal Connectives; 2.1.4 Duality of Modal Connectives; 2.1.5 The Definition of Formulas; 2.1.6 Analysing a Formula: Subformulas, Formula Length, Arity; 2.1.7 Parenthesis Conventions; 2.2 Syntax Declaration in LoTREC; 2.2.1 Prefix Notation; 2.2.2 Defining Atomic Labels; 2.2.3 Defining Connectives; 2.2.4 Complex Labels in LoTREC; 2.2.5 Displaying Formulas; 2.3 Truth Conditions; 2.4 How to Do Model Checking in LoTREC; 2.5 Modal Logics and Reasoning Problems; 2.6 Modal Logics and Their Axiomatisations; 2.7 A Note on Computational Complexity. 
505 8 |a 2.8 SummaryChapter 3: The Basics of the Model Construction Method; 3.1 Definition of Labelled Graphs; 3.2 Building an Example Model by Hand; 3.2.1 The Idea: Apply the Truth Conditions; 3.2.2 Decomposing the Example Formula; 3.2.3 Extracting a Kripke Model from a Premodel; 3.3 How to Turn Truth Conditions into Tableau Rules; 3.4 Tableaux: Some Fundamental Notions; 3.5 The Language of Tableau Rules in LoTREC; 3.6 Strategies: How to Combine LoTREC Rules; 3.6.1 Rule Application in LoTREC: Everywhere and Simultaneously; 3.6.2 Stopping and Killing Strategies. 
505 8 |a 3.6.3 A Strategy for Any Formula: Saturation by Rule Iteration3.6.4 Nesting Strategies; 3.6.5 Prioritising Rule Application; 3.7 Exercises: Adding Connectives; 3.8 From Monomodal K to Multimodal Logic Kn; 3.9 Description Logic ALC; 3.10 Taming the Rule for Disjunction; 3.10.1 Redundant Disjunctions; 3.10.2 The Cut Rules; 3.11 Soundness, Termination, and ... Completeness; 3.12 Summary; Chapter 4: Logics with Simple Constraints on Models; 4.1 K2 Inclusion: Inclusion of Relations; 4.2 KT: Reflexivity; 4.3 KB: Symmetry; 4.4 K. Alt1: Partial Function; 4.5 KD: Seriality; 4.6 K.2: Confluence. 
505 8 |a 4.7 S5: A Single Equivalence Relation4.8 HL: Hybrid Logic Nominals; 4.9 A General Termination Theorem; 4.9.1 Execution Trace; 4.9.2 Monotonic Rules; 4.9.3 Size of Labels; 4.9.4 Sublabels Modulo Negation; 4.9.5 Strictly Analytic Rules, Connected Rules; 4.9.6 The Theorem; 4.9.7 Proof of the Termination Theorem; 4.10 Summary; Chapter 5: Logics with Transitive Accessibility Relations; 5.1 K4: Transitivity; 5.2 Marking Nodes and Expressions in LoTREC; 5.3 Intuitionistic Logic: Reflexivity, Transitivity and Persistence; 5.4 GL: Transitivity and Noetherianity; 5.5 Completeness vs. Termination. 
520 |a Possible worlds models were introduced by Saul Kripke in the early 1960s. Basically, a possible world's model is nothing but a graph with labelled nodes and labelled edges. Such graphs provide semantics for various modal logics (alethic, temporal, epistemic and doxastic, dynamic, deontic, description logics) and also turned out useful for other nonclassical logics (intuitionistic, conditional, several paraconsistent and relevant logics). All these logics have been studied intensively in philosophical and mathematical logic and in computer science, and have been applied increasingly in domains. 
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650 0 |a Nonclassical mathematical logic. 
650 6 |a Logique mathématique non classique. 
650 7 |a Nonclassical mathematical logic  |2 fast 
700 1 |a Gasquet, Olivier. 
758 |i has work:  |a Kripke's worlds (Text)  |1 https://id.oclc.org/worldcat/entity/E39PCGHmrcbWGqwkKmpc4kCYT3  |4 https://id.oclc.org/worldcat/ontology/hasWork 
776 0 8 |i Print version:  |t Kripke's worlds.  |d Basel : Birkhäuser ; London : Springer [distributor], 2011  |z 9783764385033  |z 3764385030 
830 0 |a Studies in universal logic. 
856 4 0 |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=1592054  |z Texto completo 
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938 |a ProQuest Ebook Central  |b EBLB  |n EBL1592054 
994 |a 92  |b IZTAP 

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