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  1. Dually Hemimorphic Semi-Nelson Algebras.Juan Manuel Cornejo & HernÁn Javier San MartÍn - forthcoming - Logic Journal of the IGPL.
    Extending the relation between semi-Heyting algebras and semi-Nelson algebras to dually hemimorphic semi-Heyting algebras, we introduce and study the variety of dually hemimorphic semi-Nelson algebras and some of its subvarieties. In particular, we prove that the category of dually hemimorphic semi-Heyting algebras is equivalent to the category of dually hemimorphic centered semi-Nelson algebras. We also study the lattice of congruences of a dually hemimorphic semi-Nelson algebra through some of its deductive systems.
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  • Semi-Heyting Algebras and Identities of Associative Type.Juan M. Cornejo & Hanamantagouda P. Sankappanavar - 2019 - Bulletin of the Section of Logic 48 (2).
    An algebra A = ⟨A, ∨, ∧, →, 0, 1⟩ is a semi-Heyting algebra if ⟨A, ∨, ∧, 0, 1⟩ is a bounded lattice, and it satisfies the identities: x ∧ ≈ x ∧ y, x ∧ ≈ x ∧ [ → ], and x → x ≈ 1.
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  • A Categorical Equivalence Between Semi-Heyting Algebras and Centered Semi-Nelson Algebras.Juan Manuel Cornejo & Hernán Javier San Martín - 2018 - Logic Journal of the IGPL 26 (4):408-428.
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  • Gentzen-Style Sequent Calculus for Semi-Intuitionistic Logic.Diego Castaño & Juan Manuel Cornejo - 2016 - Studia Logica 104 (6):1245-1265.
    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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