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Kripke bundles for intermediate predicate logics and Kripke frames for intuitionistic modal logics

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Abstract

Shehtman and Skvortsov introduced Kripke bundles as semantics of non-classical first-order predicate logics. We show the structural equivalence between Kripke bundles for intermediate predicate logics and Kripke-type frames for intuitionistic modal prepositional logics. This equivalence enables us to develop the semantical study of relations between intermediate predicate logics and intuitionistic modal propositional logics. New examples of modal counterparts of intermediate predicate logics are given.

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Authors and Affiliations

  1. Department of Mathematics, Joetsu University of Education, 943, Joetsu, Japan

    Nobu -Yuki Suzuki

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  1. Nobu -Yuki Suzuki
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The author would like to express his gratitude to Professor Hiroakira Ono for his comments, and to Professor Tadashi Kuroda for his encouragement.

The author wishes to express his gratitude to Professors V. B. Shehtman, D. P. Skvortsov and M. Takano for their comments.

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Suzuki, N.Y. Kripke bundles for intermediate predicate logics and Kripke frames for intuitionistic modal logics. Stud Logica 49, 289–306 (1990). https://doi.org/10.1007/BF00370365

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