Independence-friendly logic :
Mann, Allen L.
Independence-friendly logic : a game-theoretic approach / Allen L. Mann, Gabriel Sandu, Merlijn Sevenster. - Cambridge : Cambridge University Press, 2011. - 1 online resource (vi, 208 pages) : digital, PDF file(s). - London Mathematical Society lecture note series ; 386 . - London Mathematical Society lecture note series ; 386. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Machine generated contents note: Introduction -- Game theory -- Extensive games -- Strategic games -- First-order logic -- Syntax -- Models -- Game-theoretic semantics -- Logical equivalence -- Compositional semantics -- Satisfiability -- Independence-friendly logic -- Syntax -- Game-theoretic semantics -- Skolem semantics -- Compositional semantics -- Game-theoretic semantics redux -- Properties of IF logic -- Basic properties -- Extensions of IF logic -- Logical equivalence -- Model theory -- Expressive power of IF logic -- Definability -- Second-order logic -- Existential second-order logic -- Perfect recall -- Probabilistic IF logic -- Equilibrium semantics -- Monotonicity rules -- Behavioral strategies and compositional semantics -- Elimination of strategies -- Expressing the rationals -- Further topics -- Compositionality -- IF modal logic. 1. 2. 2.1. 2.2. 3. 3.1. 3.2. 3.3. 3.4. 3.5. 3.6. 4. 4.1. 4.2. 4.3. 4.4. 4.5. 5. 5.1. 5.2. 5.3. 5.4. 6. 6.1. 6.2. 6.3. 6.4. 7. 7.1. 7.2. 7.3. 7.4. 7.5. 8. 8.1. 8.2.
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.
9780511981418 (ebook)
First-order logic.
Game theory.
BC128 / .M36 2011
511.3
Independence-friendly logic : a game-theoretic approach / Allen L. Mann, Gabriel Sandu, Merlijn Sevenster. - Cambridge : Cambridge University Press, 2011. - 1 online resource (vi, 208 pages) : digital, PDF file(s). - London Mathematical Society lecture note series ; 386 . - London Mathematical Society lecture note series ; 386. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Machine generated contents note: Introduction -- Game theory -- Extensive games -- Strategic games -- First-order logic -- Syntax -- Models -- Game-theoretic semantics -- Logical equivalence -- Compositional semantics -- Satisfiability -- Independence-friendly logic -- Syntax -- Game-theoretic semantics -- Skolem semantics -- Compositional semantics -- Game-theoretic semantics redux -- Properties of IF logic -- Basic properties -- Extensions of IF logic -- Logical equivalence -- Model theory -- Expressive power of IF logic -- Definability -- Second-order logic -- Existential second-order logic -- Perfect recall -- Probabilistic IF logic -- Equilibrium semantics -- Monotonicity rules -- Behavioral strategies and compositional semantics -- Elimination of strategies -- Expressing the rationals -- Further topics -- Compositionality -- IF modal logic. 1. 2. 2.1. 2.2. 3. 3.1. 3.2. 3.3. 3.4. 3.5. 3.6. 4. 4.1. 4.2. 4.3. 4.4. 4.5. 5. 5.1. 5.2. 5.3. 5.4. 6. 6.1. 6.2. 6.3. 6.4. 7. 7.1. 7.2. 7.3. 7.4. 7.5. 8. 8.1. 8.2.
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.
9780511981418 (ebook)
First-order logic.
Game theory.
BC128 / .M36 2011
511.3