12 found
Order:
  1.  14
    Subdirectly Irreducible IKt-Algebras.Aldo V. Figallo, Inés Pascual & Gustavo Pelaitay - 2017 - Studia Logica 105 (4):673-701.
    The IKt-algebras that we investigate in this paper were introduced in the paper An algebraic axiomatization of the Ewald’s intuitionistic tense logic by the first and third author. Now we characterize by topological methods the subdirectly irreducible IKt-algebras and particularly the simple IKt-algebras. Finally, we consider the particular cases of finite IKt-algebras and complete IKt-algebras.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  2.  13
    A Categorical Equivalence for Tense Nelson Algebras.Aldo V. Figallo, Jonathan Sermento & Gustavo Pelaitay - 2021 - Studia Logica 110 (1):241-263.
    In this paper we present a category equivalent to that of tense Nelson algebras. The objects in this new category are pairs consisting of an IKt-algebra and a Boolean IKt-congruence and the morphisms are a special kind of IKt-homomorphisms. This categorical equivalence permits understanding tense Nelson algebras in terms of the better–known IKt-algebras.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  3.  17
    Principal and Boolean Congruences on $$\varvec{IKt}$$ IKt -Algebras.Aldo V. Figallo, Inés Inés Pascual & Gustavo Pelaitay - 2018 - Studia Logica 106 (4):857-882.
    The IKt-algebras were introduced in the paper An algebraic axiomatization of the Ewald’s intuitionistic tense logic by the first and third author. In this paper, our main interest is to investigate the principal and Boolean congruences on IKt-algebras. In order to do this we take into account a topological duality for these algebras obtained in Figallo et al. :673–701, 2017). Furthermore, we characterize Boolean and principal IKt-congruences and we show that Boolean IKt-congruence are principal IKt-congruences. Also, bearing in mind the (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  4.  7
    Cn algebras with Moisil possibility operators.Aldo V. Figallo, Gustavo Pelaitay & Jonathan Sarmiento - 2020 - Logic Journal of the IGPL 28 (6):1141-1154.
    In this paper, we continue the study of the Łukasiewicz residuation algebras of order $n$ with Moisil possibility operators initiated by Figallo. More precisely, among other things, a method to determine the number of elements of the $MC_n$-algebra with a finite set of free generators is described. Applying this method, we find again the results obtained by Iturrioz and Monteiro and by Figallo for the case of Tarski algebras and $I\varDelta _{3}$-algebras, respectively.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  5.  14
    A topological duality for tense $\boldsymbol{LM_n}$-algebras and applications1.Aldo V. Figallo, Inés Pascual & Gustavo Pelaitay - 2018 - Logic Journal of the IGPL 26 (4):339-380.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  6.  11
    Tense Operators on Distributive Lattices with Implication.Gustavo Pelaitay & William Zuluaga - 2023 - Studia Logica 111 (4):687-708.
    Inspired by the definition of tense operators on distributive lattices presented by Chajda and Paseka in 2015, in this paper, we introduce and study the variety of tense distributive lattices with implication and we prove that these are categorically equivalent to a full subcategory of the category of tense centered Kleene algebras with implication. Moreover, we apply such an equivalence to describe the congruences of the algebras of each variety by means of tense 1-filters and tense centered deductive systems, respectively.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  7.  18
    Discrete Duality for Nelson Algebras with Tense Operators.Aldo V. Figallo, Gustavo Pelaitay & Jonathan Sarmiento - 2023 - Studia Logica 111 (1):1-19.
    In this paper, we continue with the study of tense operators on Nelson algebras (Figallo et al. in Studia Logica 109(2):285–312, 2021, Studia Logica 110(1):241–263, 2022). We define the variety of algebras, which we call tense Nelson D-algebras, as a natural extension of tense De Morgan algebras (Figallo and Pelaitay in Logic J IGPL 22(2):255–267, 2014). In particular, we give a discrete duality for these algebras. To do this, we will extend the representation theorems for Nelson algebras given in Sendlewski (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  8.  7
    Monadic $$k\times j$$ k × j -rough Heyting algebras.Federico Almiñana & Gustavo Pelaitay - 2022 - Archive for Mathematical Logic 61 (5):611-625.
    In this paper, we introduce the variety of algebras, which we call monadic \-rough Heyting algebras. These algebras constitute an extension of monadic Heyting algebras and in \ case they coincide with monadic 3-valued Łukasiewicz–Moisil algebras. Our main interest is the characterization of simple and subdirectly irreducible monadic \-rough Heyting algebras. In order to this, an Esakia-style duality for these algebras is developed.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  9.  7
    On Heyting Algebras with Negative Tense Operators.Federico G. Almiñana, Gustavo Pelaitay & William Zuluaga - 2023 - Studia Logica 111 (6):1015-1036.
    In this paper, we will study Heyting algebras endowed with tense negative operators, which we call tense H-algebras and we proof that these algebras are the algebraic semantics of the Intuitionistic Propositional Logic with Galois Negations. Finally, we will develop a Priestley-style duality for tense H-algebras.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  10.  16
    A Topological Approach to Tense LMn×m-Algebras.Aldo V. Figallo, Inés Pascual & Gustavo Pelaitay - 2020 - Bulletin of the Section of Logic 49 (1).
    In 2015, tense n × m-valued Lukasiewicz–Moisil algebras were introduced by A. V. Figallo and G. Pelaitay as an generalization of tense n-valued Łukasiewicz–Moisil algebras. In this paper we continue the study of tense LMn×m-algebras. More precisely, we determine a Priestley-style duality for these algebras. This duality enables us not only to describe the tense LMn×m-congruences on a tense LMn×m-algebra, but also to characterize the simple and subdirectly irreducible tense LMn×m-algebras.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  11.  13
    Tense Polyadic N × M-Valued Łukasiewicz–Moisil Algebras.Aldo V. Figallo & Gustavo Pelaitay - 2015 - Bulletin of the Section of Logic 44 (3/4):155-181.
    In 2015, A.V. Figallo and G. Pelaitay introduced tense n×m-valued Łukasiewicz–Moisil algebras, as a common generalization of tense Boolean algebras and tense n-valued Łukasiewicz–Moisil algebras. Here we initiate an investigation into the class tpLMn×m of tense polyadic n × m-valued Łukasiewicz–Moisil algebras. These algebras constitute a generalization of tense polyadic Boolean algebras introduced by Georgescu in 1979, as well as the tense polyadic n-valued Łukasiewicz–Moisil algebras studied by Chiriţă in 2012. Our main result is a representation theorem for tense polyadic (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  12.  3
    Monadic k×j\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k\times j$$\end{document}-rough Heyting algebras. [REVIEW]Gustavo Pelaitay & Federico Almiñana - 2021 - Archive for Mathematical Logic 61 (5-6):611-625.
    In this paper, we introduce the variety of algebras, which we call monadic k×j\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k\times j$$\end{document}-rough Heyting algebras. These algebras constitute an extension of monadic Heyting algebras and in 3×2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3\times 2$$\end{document} case they coincide with monadic 3-valued Łukasiewicz–Moisil algebras. Our main interest is the characterization of simple and subdirectly irreducible monadic k×j\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k\times j$$\end{document}-rough Heyting algebras. (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark