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  1. Juan Manuel Cornejo (forthcoming). The Semi Heyting–Brouwer Logic. Studia Logica:1-23.
    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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  2. Manuel Abad, Juan Manuel Cornejo & José Patricio Díaz Varela (2012). Free-Decomposability in Varieties of Semi-Heyting Algebras. Mathematical Logic Quarterly 58 (3):168-176.
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  3. Manuel Abad, Juan Manuel Cornejo & Patricio Díaz Varela (2012). Free‐Decomposability in Varieties of Semi‐Heyting Algebras. Mathematical Logic Quarterly 58 (3):168-176.
    In this paper we prove that the free algebras in a subvariety equation image of the variety equation image of semi-Heyting algebras are directly decomposable if and only if equation image satisfies the Stone identity.
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  4. Juan Manuel Cornejo (2011). Semi-Intuitionistic Logic. Studia Logica 98 (1-2):9-25.
    The purpose of this paper is to define a new logic $${\mathcal {SI}}$$ called semi-intuitionistic logic such that the semi-Heyting algebras introduced in [ 4 ] by Sankappanavar are the semantics for $${\mathcal {SI}}$$ . Besides, the intuitionistic logic will be an axiomatic extension of $${\mathcal {SI}}$$.
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