Some results on the Kripke sheaf semantics for super-intuitionistic predicate logics

Studia Logica 52 (1):73 - 94 (1993)

Abstract

Some properties of Kripke-sheaf semantics for super-intuitionistic predicate logics are shown. The concept ofp-morphisms between Kripke sheaves is introduced. It is shown that if there exists ap-morphism from a Kripke sheaf 1 into 2 then the logic characterized by 1 is contained in the logic characterized by 2. Examples of Kripke-sheaf complete and finitely axiomatizable super-intuitionistic (and intermediate) predicate logics each of which is Kripke-frame incomplete are given. A correction to the author's previous paper Kripke bundles for intermediate predicate logics and Kripke frames for intuitionistic modal logics (Studia Logica, 49(1990), pp. 289–306 ) is stated.

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References found in this work

Semantical Investigations in Heyting's Intuitionistic Logic.Dov M. Gabbay - 1986 - Journal of Symbolic Logic 51 (3):824-824.
Mathematical Intuitionism. Introduction to Proof Theory.A. G. Dragalin & E. Mendelson - 1990 - Journal of Symbolic Logic 55 (3):1308-1309.
Applications of Trees to Intermediate Logics.Dov M. Gabbay - 1972 - Journal of Symbolic Logic 37 (1):135-138.
Directed Frames.Giovanna Corsi & Silvio Ghilardi - 1989 - Archive for Mathematical Logic 29 (1):53-67.

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