On logics with coimplication

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

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
Keywords Philosophy
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Reprint years 2004
DOI 10.1023/A:1004218110879
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References found in this work BETA

Properties of Independently Axiomatizable Bimodal Logics.Marcus Kracht & Frank Wolter - 1991 - Journal of Symbolic Logic 56 (4):1469-1485.
Semantic Analysis of Tense Logics.S. K. Thomason - 1972 - Journal of Symbolic Logic 37 (1):150-158.
Logics Containing K4. Part II.Kit Fine - 1985 - Journal of Symbolic Logic 50 (3):619-651.

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Citations of this work BETA

Constructive Negation, Implication, and Co-Implication.Heinrich Wansing - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):341-364.
Bi-Simulating in Bi-Intuitionistic Logic.Guillermo Badia - 2016 - Studia Logica 104 (5):1037-1050.
A Modal Translation for Dual-Intuitionistic Logic.Yaroslav Shramko - 2016 - Review of Symbolic Logic 9 (2):251-265.

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