Article

Journal of Philosophical Logic

, Volume 27, Issue 4, pp 353-387

First online:

On Logics with Coimplication

  • Frank WolterAffiliated withSchool of Information Science, JAIST

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

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 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.