Maximal Kripke-type semantics for modal and superintuitionistic predicate logics

Annals of Pure and Applied Logic 63 (1):69-101 (1993)
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Abstract

Recent studies in semantics of modal and superintuitionistic predicate logics provided many examples of incompleteness, especially for Kripke semantics. So there is a problem: to find an appropriate possible- world semantics which is equivalent to Kripke semantics at the propositional level and which is strong enough to prove general completeness results. The present paper introduces a new semantics of Kripke metaframes' generalizing some earlier notions. The main innovation is in considering "n"-tuples of individuals as abstract "n"-dimensional vectors', together with some transformations of these vectors. Soundness of the semantics is proved to be equivalent to some non- logical properties of metaframes; and thus we describe the maximal semantics of Kripke- type

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Valentin Shehtman
Moscow State University

References found in this work

Semantical Investigations in Heyting's Intuitionistic Logic.Dov M. Gabbay - 1986 - Journal of Symbolic Logic 51 (3):824-824.
Logics containing k4. part I.Kit Fine - 1974 - Journal of Symbolic Logic 39 (1):31-42.
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Topology and duality in modal logic.Giovanni Sambin & Virginia Vaccaro - 1988 - Annals of Pure and Applied Logic 37 (3):249-296.
Incompleteness results in Kripke semantics.Silvio Ghilardi - 1991 - Journal of Symbolic Logic 56 (2):517-538.

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