Thompson Transformations for If-Logic

Synthese 149 (2):285-309 (2006)

Abstract
In this paper we study connections between game theoretical concepts and results, and features of IF-predicate logic, extending observations from J. van Benthem (2001) for IF-propositional logic. We highlight how both characteristics of perfect recall can fail in the semantic games for IF-formulas, and we discuss the four Thompson transformations in relation with IF-logic. Many (strong) equivalence schemes for IF-logic correspond to one or more of the transformations. However, we also find one equivalence that does not fit in this picture, by the type of imperfect recall involved. We point out that the connection between the transformations and logical equivalence schemes is less direct in IF-first order logic than in the propositional case. The transformations do not generate a reduced normal form for IF-logic, because the IF-language is not flexible enough.
Keywords Philosophy   Philosophy   Epistemology   Logic   Metaphysics   Philosophy of Language
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DOI 10.1007/s11229-005-3876-7
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References found in this work BETA

The Principles of Mathematics Revisited.Jaakko Hintikka - 1996 - Cambridge University Press.
Independent Choices and the Interpretation of IF Logic.Theo M. V. Janssen - 2002 - Journal of Logic, Language and Information 11 (3):367-387.
Partiality and Games: Propositional Logic.G. Sandu & A. Pietarinen - 2001 - Logic Journal of the IGPL 9 (1):101-121.
On the Semantics of Informational Independence.Jouko Väänänen - 2002 - Logic Journal of the IGPL 10 (3):339-352.

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Generalized Quantifiers.Dag Westerståhl - 2008 - Stanford Encyclopedia of Philosophy.

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