Dependence Logic: A New Approach to Independence Friendly LogicCambridge University Press, 10.05.2007 Dependence is a common phenomenon, wherever one looks: ecological systems, astronomy, human history, stock markets - but what is the logic of dependence? This book is the first to carry out a systematic logical study of this important concept, giving on the way a precise mathematical treatment of Hintikka's independence friendly logic. Dependence logic adds the concept of dependence to first order logic. Here the syntax and semantics of dependence logic are studied, dependence logic is given an alternative game theoretic semantics, and results about its complexity are proven. This is a graduate textbook suitable for a special course in logic in mathematics, philosophy and computer science departments, and contains over 200 exercises, many of which have a full solution at the end of the book. It is also accessible to readers, with a basic knowledge of logic, interested in new phenomena in logic. |
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Dependence Logic: A New Approach to Independence Friendly Logic Jouko Väänänen Keine Leseprobe verfügbar - 2007 |
Dependence Logic: A New Approach to Independence Friendly Logic Jouko Väänänen Keine Leseprobe verfügbar - 2007 |
Häufige Begriffe und Wortgruppen
arbitrary Assume Axiom of Extensionality bijection binary relation claim holds completes the proof consistency property continues from position contradiction D-formula D-sentence define Denote determine x1 dom(X dom(Z equivalent Exercise 7.4 existential quantification f M(s(x finite formula x0 function f G(so game continues Gödel numbers induction hypothesis isomorphic L₁ Lemma limit ordinal Limit(x Löwenheim-Skolem Theorem mapping minimal determining set natural number Niel Ti satisfies non-empty team Note one-to-one order formula order logic player Proposition 3.8 proves condition Px₁ quantification relation symbol rk(x s(x₁ s(xo sentence Skolem Normal Form subformula subset successor ordinal t₁ Table Team(M teams X TL-formula totally dependent truth definition type x0 V₁ variable whence x₁ Xin+1 Y U Z Y₁ Y₂ Χρ МЕх ф