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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...
| Clasificación: | Libro Electrónico |
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| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Basel : London :
Birkhäuser ; Springer [distributor],
2011.
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| Colección: | Studies in universal logic.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.
- 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.
- 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.
- 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.
- 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.