9 found
Order:
  1.  22
    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.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  2.  31
    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 $${\mathcal {SI}}$$.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  3.  28
    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.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  4.  18
    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.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  5.  12
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  6.  13
    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 \.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  7. 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.
     
    Export citation  
     
    Bookmark   1 citation  
  8.  3
    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.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  9.  6
    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.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark