11 found
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  1.  5
    A Logic for Dually Hemimorphic Semi-Heyting Algebras and its Axiomatic Extensions.Juan Manuel Cornejo & Hanamantagouda P. Sankappanavar - 2022 - Bulletin of the Section of Logic 51 (4):555-645.
    The variety \(\mathbb{DHMSH}\) of dually hemimorphic semi-Heyting algebras was introduced in 2011 by the second author as an expansion of semi-Heyting algebras by a dual hemimorphism. In this paper, we focus on the variety \(\mathbb{DHMSH}\) from a logical point of view. The paper presents an extensive investigation of the logic corresponding to the variety of dually hemimorphic semi-Heyting algebras and of its axiomatic extensions, along with an equally extensive universal algebraic study of their corresponding algebraic semantics. Firstly, we present a (...)
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  2.  35
    Semi-intuitionistic Logic.Juan Manuel Cornejo - 2011 - 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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  3.  27
    Semi-intuitionistic Logic with Strong Negation.Juan Manuel Cornejo & Ignacio Viglizzo - 2018 - Studia Logica 106 (2):281-293.
    Motivated by the definition of semi-Nelson algebras, a propositional calculus called semi-intuitionistic logic with strong negation is introduced and proved to be complete with respect to that class of algebras. An axiomatic extension is proved to have as algebraic semantics the class of Nelson algebras.
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  4.  14
    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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  5.  32
    Free‐decomposability in varieties of semi‐Heyting algebras.Manuel Abad, Juan Manuel Cornejo & Patricio Díaz Varela - 2012 - 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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  6.  6
    A note on chain‐based semi‐Heyting algebras.Juan Manuel Cornejo, Luiz F. Monteiro, Hanamantagouda P. Sankappanavar & Ignacio D. Viglizzo - 2020 - Mathematical Logic Quarterly 66 (4):409-417.
    We determine the number of non‐isomorphic semi‐Heyting algebras on an n‐element chain, where n is a positive integer, using a recursive method. We then prove that the numbers obtained agree with those determined in [1]. We apply the formula to calculate the number of non‐isomorphic semi‐Heyting chains of a given size in some important subvarieties of the variety of semi‐Heyting algebras that were introduced in [5]. We further exploit this recursive method to calculate the numbers of non‐isomorphic semi‐Heyting chains with (...)
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  7.  20
    The Semi Heyting–Brouwer Logic.Juan Manuel Cornejo - 2015 - 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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  8.  23
    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.
  9. Free-decomposability in varieties of semi-Heyting algebras.Manuel Abad, Juan Manuel Cornejo & José Patricio Díaz Varela - 2012 - Mathematical Logic Quarterly 58 (3):168-176.
     
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  10.  10
    Dually hemimorphic semi-Nelson algebras.Juan Manuel Cornejo & HernÁn Javier San MartÍn - 2020 - Logic Journal of the IGPL 28 (3):316-340.
    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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  11. On a Class of Subreducts of the Variety of Integral srl-Monoids and Related Logics.Juan Manuel Cornejo, Hernn Javier San Martín & Valeria Sígal - forthcoming - Studia Logica:1-31.
    An integral subresiduated lattice ordered commutative monoid (or integral srl-monoid for short) is a pair \(({\textbf {A}},Q)\) where \({\textbf {A}}=(A,\wedge,\vee,\cdot,1)\) is a lattice ordered commutative monoid, 1 is the greatest element of the lattice \((A,\wedge,\vee )\) and _Q_ is a subalgebra of _A_ such that for each \(a,b\in A\) the set \(\{q \in Q: a \cdot q \le b\}\) has maximum, which will be denoted by \(a\rightarrow b\). The integral srl-monoids can be regarded as algebras \((A,\wedge,\vee,\cdot,\rightarrow,1)\) of type (2, 2, (...)
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