The Semi Heyting–Brouwer Logic

Studia Logica 103 (4):853-875 (2015)
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Abstract

In this paper we introduce a logic that we name semi Heyting–Brouwer logic, \, in such a way that the variety of double semi-Heyting algebras is its algebraic counterpart. We prove that, up to equivalences by translations, the Heyting–Brouwer logic \ is an axiomatic extension of \ and that the propositional calculi of intuitionistic logic \ and semi-intuitionistic logic \ turn out to be fragments of \

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References found in this work

A survey of abstract algebraic logic.J. M. Font, R. Jansana & D. Pigozzi - 2003 - Studia Logica 74 (1-2):13 - 97.
Synonymous logics.Francis Jeffry Pelletier & Alasdair Urquhart - 2003 - Journal of Philosophical Logic 32 (3):259-285.
On logics with coimplication.Frank Wolter - 1998 - Journal of Philosophical Logic 27 (4):353-387.
A remark on Gentzen's calculus of sequents.Johannes Czermak - 1977 - Notre Dame Journal of Formal Logic 18 (3):471-474.

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