Abstract
In this paper we introduce a logic that we name semi Heyting–Brouwer logic, \({\mathcal{SHB}}\), 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 \({\mathcal{HB}}\) is an axiomatic extension of \({\mathcal{SHB}}\) and that the propositional calculi of intuitionistic logic \({\mathcal{I}}\) and semi-intuitionistic logic \({\mathcal{SI}}\) turn out to be fragments of \({\mathcal{SHB}}\).
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Cornejo, J.M. The Semi Heyting–Brouwer Logic. Stud Logica 103, 853–875 (2015). https://doi.org/10.1007/s11225-014-9596-6
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DOI: https://doi.org/10.1007/s11225-014-9596-6