On logics with coimplication

Journal of Philosophical Logic 27 (4):353-387 (1998)
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
Keywords Philosophy
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DOI 10.1023/A:1004218110879
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References found in this work BETA
A. S. Troelstra (1988). Constructivism in Mathematics: An Introduction. Sole Distributors for the U.S.A. And Canada, Elsevier Science Pub. Co..
S. K. Thomason (1972). Semantic Analysis of Tense Logics. Journal of Symbolic Logic 37 (1):150-158.
Kit Fine (1985). Logics Containing K4. Part II. Journal of Symbolic Logic 50 (3):619-651.

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Citations of this work BETA
Heinrich Wansing (2008). Constructive Negation, Implication, and Co-Implication. Journal of Applied Non-Classical Logics 18 (2-3):341-364.

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