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On logics with coimplication. (English) Zbl 0976.03020
Summary: 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 Gödel-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.

MSC:
03B45 Modal logic (including the logic of norms)
03B20 Subsystems of classical logic (including intuitionistic logic)
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