Independence-Friendly Logic: A Game-Theoretic

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.

Introduction	p. 1
tGame theory	p. 9
Extensive games	p. 9
Strategic games	p. 17
First-order logic	p. 28
Syntax	p. 28
Models	p. 30
Game-theoretic semantics	p. 32
Logical equivalence	p. 39
Compositional semantics	p. 48
Satisfiability	p. 55
Independence-friendly logic	p. 59
Syntax	p. 59
Game-theoretic semantics	p. 62
Skolem semantics	p. 67
Compositional semantics	p. 76
Game-theoretic semantics redux	p. 83
Properties of IF logic	p. 87
Basic properties	p. 87
Extensions of IF logic	p. 95
Logical equivalence	p. 99
Model theory	p. 127
Expressive power of IF logic	p. 134
Definability	p. 134
Second-order logic	p. 136
Existential second-order logic	p. 139
Perfect recall	p. 145
Probabilistic IF logic	p. 150
Equilibrium semantics	p. 150
Monotonicity rules	p. 156
Behavioral strategies and compositional semantics	p. 170
Elimination of strategies	p. 171
Expressing the rationals	p. 183
Further topics	p. 185
Compositionality	p. 185
IF modal logic	p. 197
References	p. 198
Index	p. 203
Table of Contents provided by Ingram. All Rights Reserved.

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Independence-Friendly Logic: A Game-Theoretic Approach

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