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9780521149341

Independence-Friendly Logic: A Game-Theoretic Approach

by
  • ISBN13:

    9780521149341

  • ISBN10:

    0521149347

  • Format: Paperback
  • Copyright: 2011-06-06
  • Publisher: Cambridge University Press

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Summary

Bringing together over twenty years of research, this book gives a complete overview of independence-friendly logic. It emphasizes the game-theoretical approach to logic, according to which logical concepts such as truth and falsity are best understood via the notion of semantic games. The book pushes the paradigm of game-theoretical semantics further than the current literature by showing how mixed strategies and equilibria can be used to analyze independence-friendly formulas on finite models. The book is suitable for graduate students and advanced undergraduates who have taken a course on first-order logic. It contains a primer of the necessary background in game theory, numerous examples and full proofs.

Table of Contents

Introductionp. 1
tGame theoryp. 9
Extensive gamesp. 9
Strategic gamesp. 17
First-order logicp. 28
Syntaxp. 28
Modelsp. 30
Game-theoretic semanticsp. 32
Logical equivalencep. 39
Compositional semanticsp. 48
Satisfiabilityp. 55
Independence-friendly logicp. 59
Syntaxp. 59
Game-theoretic semanticsp. 62
Skolem semanticsp. 67
Compositional semanticsp. 76
Game-theoretic semantics reduxp. 83
Properties of IF logicp. 87
Basic propertiesp. 87
Extensions of IF logicp. 95
Logical equivalencep. 99
Model theoryp. 127
Expressive power of IF logicp. 134
Definabilityp. 134
Second-order logicp. 136
Existential second-order logicp. 139
Perfect recallp. 145
Probabilistic IF logicp. 150
Equilibrium semanticsp. 150
Monotonicity rulesp. 156
Behavioral strategies and compositional semanticsp. 170
Elimination of strategiesp. 171
Expressing the rationalsp. 183
Further topicsp. 185
Compositionalityp. 185
IF modal logicp. 197
Referencesp. 198
Indexp. 203
Table of Contents provided by Ingram. All Rights Reserved.

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The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

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