Independence-Friendly Logic

A Game-theoretic Approach

By: Allen Mann, Gabriel Sandu, Merlijn Sevenster

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Paperback | 5 May 2011

At a Glance

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216 Pages

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22.86 x 15.24 x 1.25

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Bringing together over twenty years of research, this book gives a complete overview of independence-friendly logic. It emphasises 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 analyse 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.

Industry Reviews

"This book satisfies admirably its placement in a Lecture Notes Series. It provides a concise but full, self-contained introduction to the main work on IFL... it is very well written, with excellent intuitive exposition combined with detailed proofs." Julian Bradfield, Bulletin of Symbolic Logic "The book will definitely be interesting to a wide spectrum of logicians, philosophers, computer scientists and even linguists... the advances in the area of game-theoretical semantics and its connections to logic that are presented in this book make it very valuable and recommendable." Walter Carnielli, Mathematical Reviews

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You Can Find This Book In

Non-Fiction Mathematics Mathematical Foundation Mathematical Logic Optimisation Game Theory Philosophy Philosophy & Logic

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.

Independence-Friendly Logic

A Game-theoretic Approach

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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