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Independence-friendly logic : a game-theoretic approach / Allen L. Mann, Gabriel Sandu, Merlijn Sevenster.

By: Contributor(s): Material type: TextTextSeries: London Mathematical Society lecture note series ; 386.Publisher: Cambridge : Cambridge University Press, 2011Description: 1 online resource (vi, 208 pages) : digital, PDF file(s)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9780511981418 (ebook)
Subject(s): Additional physical formats: Print version: : No titleDDC classification:
  • 511.3 22
LOC classification:
  • BC128 .M36 2011
Online resources:
Contents:
1. Introduction -- 2. Game theory -- 2.1. Extensive games -- 2.2. Strategic games -- 3. First-order logic -- 3.1. Syntax -- 3.2. Models -- 3.3. Game-theoretic semantics -- 3.4. Logical equivalence -- 3.5. Compositional semantics -- 3.6. Satisfiability -- 4. Independence-friendly logic -- 4.1. Syntax -- 4.2. Game-theoretic semantics -- 4.3. Skolem semantics -- 4.4. Compositional semantics -- 4.5. Game-theoretic semantics redux -- 5. Properties of IF logic -- 5.1. Basic properties -- 5.2. Extensions of IF logic -- 5.3. Logical equivalence -- 5.4. Model theory -- 6. Expressive power of IF logic -- 6.1. Definability -- 6.2. Second-order logic -- 6.3. Existential second-order logic -- 6.4. Perfect recall -- 7. Probabilistic IF logic -- 7.1. Equilibrium semantics -- 7.2. Monotonicity rules -- 7.3. Behavioral strategies and compositional semantics -- 7.4. Elimination of strategies -- 7.5. Expressing the rationals -- 8. Further topics -- 8.1. Compositionality -- 8.2. IF modal logic.
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.
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Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Machine generated contents note: 1. Introduction -- 2. Game theory -- 2.1. Extensive games -- 2.2. Strategic games -- 3. First-order logic -- 3.1. Syntax -- 3.2. Models -- 3.3. Game-theoretic semantics -- 3.4. Logical equivalence -- 3.5. Compositional semantics -- 3.6. Satisfiability -- 4. Independence-friendly logic -- 4.1. Syntax -- 4.2. Game-theoretic semantics -- 4.3. Skolem semantics -- 4.4. Compositional semantics -- 4.5. Game-theoretic semantics redux -- 5. Properties of IF logic -- 5.1. Basic properties -- 5.2. Extensions of IF logic -- 5.3. Logical equivalence -- 5.4. Model theory -- 6. Expressive power of IF logic -- 6.1. Definability -- 6.2. Second-order logic -- 6.3. Existential second-order logic -- 6.4. Perfect recall -- 7. Probabilistic IF logic -- 7.1. Equilibrium semantics -- 7.2. Monotonicity rules -- 7.3. Behavioral strategies and compositional semantics -- 7.4. Elimination of strategies -- 7.5. Expressing the rationals -- 8. Further topics -- 8.1. Compositionality -- 8.2. IF modal logic.

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.

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