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  1.  12
    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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  2.  4
    Diego Castaño & Juan Manuel Cornejo (forthcoming). Gentzen-Style Sequent Calculus for Semi-Intuitionistic Logic. Studia Logica:1-21.
    The variety \ of semi-Heyting algebras was introduced by H. P. Sankappanavar [13] as an abstraction of the variety of Heyting algebras. Semi-Heyting algebras are the algebraic models for a logic HsH, known as semi-intuitionistic logic, which is equivalent to the one defined by a Hilbert style calculus in Cornejo :9–25, 2011) [6]. In this article we introduce a Gentzen style sequent calculus GsH for the semi-intuitionistic logic whose associated logic GsH is the same as HsH. The advantage of this (...)
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  3.  5
    Juan Manuel Cornejo (2015). The Semi Heyting–Brouwer Logic. Studia Logica 103 (4):853-875.
    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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  4.  2
    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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  5. 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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