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

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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 κ1 into κ2 then the logic characterized by κ1 is contained in the logic characterized by κ2. 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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Authors and Affiliations

  1. Department of Computer and Information Sciences Faculty of Engineering, Ibaraki University, 316, Hitachi, Japan

    Nobu-Yuki Suzuki

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  1. Nobu-Yuki Suzuki
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Dedicated to Professor Takeshi Kotake on his 60th birthday

This research was partially supported by Grant-in-Aid for Encouragement of Young Scientists No. 03740107, Ministry of Educatin, Science and Culture, Japan.

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Suzuki, NY. Some results on the Kripke sheaf semantics for super-intuitionistic predicate logics. Stud Logica 52, 73–94 (1993). https://doi.org/10.1007/BF01053065

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