PP-2007-20: Equivalence and quantier rules for logic with imperfect information

PP-2007-20: Caicedo, Xavier and Dechesne, Francien and Janssen, Theo M.V. (2007) Equivalence and quantier rules for logic with imperfect information. [Report]

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In this paper, we present a normal 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 for signalling phenomena. In particular, nested quantfiication over the same variable is shown to cause problems. For instance, renaming of bound variables may change the interpretations of a formula, there is only a restricted quantier extraction theorem, and slashed connectives cannot be so easily removed. Thus we correct some claims from Hintikka (1996), Caicedo & Krynicki (1999) and Hodges (1997a). We refine definitions, in particular the notion of equivalence, and sharpen preconditions, allowing us to restore (restricted versions of) those claims, including the prenex normal form theorem of Caicedo & Krynicki (1999). Further important results are several quantifier rules for IF-logic and a surprising improved version of the Skolem form theorem for classical logic.

Item Type: Report
Report Nr: PP-2007-20
Series Name: Prepublication (PP) Series
Year: 2007
Uncontrolled Keywords: IF logic; games; imperfect information; Hintikka; prenex form; Skolem form; renaming variables.
Subjects: Logic
Depositing User: tjansse1
Date Deposited: 12 Oct 2016 14:36
Last Modified: 12 Oct 2016 14:36
URI: https://eprints.illc.uva.nl/id/eprint/254

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