Logic Journal of the IGPL 17 (1):91-129 (2008)

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Abstract
In this paper, we present a prenex form theorem for a version of Independence Friendly logic, a logic with imperfect information. Lifting classical results to such logics turns out not to be straightforward, because independence conditions make the formulas sensitive to signalling phenomena. In particular, nested quantification over the same variable is shown to cause problems. For instance, renaming of bound variables may change the interpretations of a formula, there are only restricted quantifier extraction theorems, and slashed connectives cannot be so easily removed. Thus we correct some claims from Hintikka [8], Caicedo & Krynicki [3] and Hodges [11]. We refine definitions, in particular the notion of equivalence, and sharpen preconditions, allowing us to restore those claims, including the prenex form theorem of Caicedo & Krynicki [3], and, as a side result, we obtain an application to Skolem forms of classical formulas. It is a known fact that a complete calculus for IF-logic is impossible, but with our results we establish several quantifier rules that form a partial calculus of equivalence for a general version of IF-logic reflecting general properties of information flow in games
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DOI 10.1093/jigpal/jzn030
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References found in this work BETA

The Principles of Mathematics Revisited.Jaakko Hintikka - 1996 - Cambridge University Press.
Compositional Semantics for a Language of Imperfect Information.W. Hodges - 1997 - Logic Journal of the IGPL 5 (4):539-563.
On the Semantics of Informational Independence.Jouko Väänänen - 2002 - Logic Journal of the IGPL 10 (3):339-352.
Logic Games Are Complete for Game Logics.Johan van Benthem - 2003 - Studia Logica 75 (2):183-203.

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Citations of this work BETA

How Indefinites Choose Their Scope.Adrian Brasoveanu & Donka F. Farkas - 2011 - Linguistics and Philosophy 34 (1):1-55.
On Existential Declarations of Independence in If Logic.Fausto Barbero - 2013 - Review of Symbolic Logic 6 (2):254-280.
Epistemic Operators in Dependence Logic.Pietro Galliani - 2013 - Studia Logica 101 (2):367-397.
Equilibrium Semantics of Languages of Imperfect Information.Merlijn Sevenster & Gabriel Sandu - 2010 - Annals of Pure and Applied Logic 161 (5):618-631.

View all 17 citations / Add more citations

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