Journal of Philosophical Logic

, Volume 27, Issue 4, pp 353–387

On Logics with Coimplication

  • Frank Wolter

DOI: 10.1023/A:1004218110879

Cite this article as:
Wolter, F. Journal of Philosophical Logic (1998) 27: 353. doi:10.1023/A:1004218110879


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.

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Frank Wolter
    • 1
  1. 1.School of Information ScienceJAISTTatsunokuchiJapan (e-mail