On logics with coimplication

Journal of Philosophical Logic 27 (4):353-387 (1998)
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Abstract

This paper investigates (modal) extensions of Heyting-Brouwer logic, i.e., the logic which results when the dual of implication (alias coimplication) is added to the language of intuitionistic logic. We first develop matrix as well as Kripke style semantics for those logics. Then, by extending the Gö;del-embedding of intuitionistic logic into S4, it is shown that all (modal) extensions of Heyting-Brouwer logic can be embedded into tense logics (with additional modal operators). An extension of the Blok-Esakia-Theorem is proved for this embedding

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References found in this work

An essay in classical modal logic.Krister Segerberg - 1971 - Uppsala,: Filosofiska föreningen och Filosofiska institutionen vid Uppsala universitet.
Constructivism in mathematics: an introduction.A. S. Troelstra - 1988 - New York, N.Y.: Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.. Edited by D. van Dalen.
[Omnibus Review].Robert Goldblatt - 1986 - Journal of Symbolic Logic 51 (1):225-227.

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