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Sergio A. Celani [15]Sergio Arturo Celani [2]
  1.  36
    Intuitionistic Modal Algebras.Sergio A. Celani & Umberto Rivieccio - forthcoming - Studia Logica:1-50.
    Recent research on algebraic models of _quasi-Nelson logic_ has brought new attention to a number of classes of algebras which result from enriching (subreducts of) Heyting algebras with a special modal operator, known in the literature as a _nucleus_. Among these various algebraic structures, for which we employ the umbrella term _intuitionistic modal algebras_, some have been studied since at least the 1970s, usually within the framework of topology and sheaf theory. Others may seem more exotic, for their primitive operations (...)
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  2.  18
    Complete and atomic Tarski algebras.Sergio Arturo Celani - 2019 - Archive for Mathematical Logic 58 (7-8):899-914.
    Tarski algebras, also known as implication algebras or semi-boolean algebras, are the \-subreducts of Boolean algebras. In this paper we shall introduce and study the complete and atomic Tarski algebras. We shall prove a duality between the complete and atomic Tarski algebras and the class of covering Tarski sets, i.e., structures \, where X is a non-empty set and \ is non-empty family of subsets of X such that \. This duality is a generalization of the known duality between sets (...)
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  3.  57
    Classical Modal De Morgan Algebras.Sergio A. Celani - 2011 - Studia Logica 98 (1-2):251-266.
    In this note we introduce the variety $${{\mathcal C}{\mathcal D}{\mathcal M}_\square}$$ of classical modal De Morgan algebras as a generalization of the variety $${{{\mathcal T}{\mathcal M}{\mathcal A}}}$$ of Tetravalent Modal algebras studied in [ 11 ]. We show that the variety $${{\mathcal V}_0}$$ defined by H. P. Sankappanavar in [ 13 ], and the variety S of Involutive Stone algebras introduced by R. Cignoli and M. S de Gallego in [ 5 ], are examples of classical modal De Morgan algebras. (...)
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  4.  31
    Distributive Lattices with a Negation Operator.Sergio Arturo Celani - 1999 - Mathematical Logic Quarterly 45 (2):207-218.
    In this note we introduce and study algebras of type such that is a bounded distributive lattice and ⌝ is an operator that satisfies the condition ⌝ = a ⌝ b and ⌝ 0 = 1. We develop the topological duality between these algebras and Priestley spaces with a relation. In addition, we characterize the congruences and the subalgebras of such an algebra. As an application, we will determine the Priestley spaces of quasi-Stone algebras.
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  5. Bounded distributive lattices with strict implication.Sergio A. Celani & Ramón Jansana Ferrer - 2005 - Mathematical Logic Quarterly 51 (3):219.
     
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  6.  26
    Hilbert Algebras with a Modal Operator $${\Diamond}$$ ◊.Sergio A. Celani & Daniela Montangie - 2015 - Studia Logica 103 (3):639-662.
    A Hilbert algebra with supremum is a Hilbert algebra where the associated order is a join-semilattice. This class of algebras is a variety and was studied in Celani and Montangie . In this paper we shall introduce and study the variety of $${H_{\Diamond}^{\vee}}$$ H ◊ ∨ -algebras, which are Hilbert algebras with supremum endowed with a modal operator $${\Diamond}$$ ◊ . We give a topological representation for these algebras using the topological spectral-like representation for Hilbert algebras with supremum given in (...)
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  7.  10
    Subordination Tarski algebras.Sergio A. Celani - 2019 - Journal of Applied Non-Classical Logics 29 (3):288-306.
    In this work we will study Tarski algebras endowed with a subordination, called subordination Tarski algebras. We will define the notion of round filters, and we will study the class of irreducible round filters and the maximal round filters, called ends. We will prove that the poset of all round filters is a lattice isomorphic to the lattice of the congruences that are compatible with the subordination. We will prove that every end is an irreducible round filter, and that in (...)
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  8.  27
    n‐linear weakly Heyting algebras.Sergio A. Celani - 2006 - Mathematical Logic Quarterly 52 (4):404-416.
    The present paper introduces and studies the variety [MATHEMATICAL SCRIPT CAPITAL W]ℋn of n-linear weakly Heyting algebras. It corresponds to the algebraic semantic of the strict implication fragment of the normal modal logic K with a generalization of the axiom that defines the linear intuitionistic logic or Dummett logic. Special attention is given to the variety [MATHEMATICAL SCRIPT CAPITAL W]ℋ2 that generalizes the linear Heyting algebras studied in [10] and [12], and the linear Basic algebras introduced in [2].
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  9.  29
    On the free implicative semilattice extension of a Hilbert algebra.Sergio A. Celani & Ramon Jansana - 2012 - Mathematical Logic Quarterly 58 (3):188-207.
    Hilbert algebras provide the equivalent algebraic semantics in the sense of Blok and Pigozzi to the implication fragment of intuitionistic logic. They are closely related to implicative semilattices. Porta proved that every Hilbert algebra has a free implicative semilattice extension. In this paper we introduce the notion of an optimal deductive filter of a Hilbert algebra and use it to provide a different proof of the existence of the free implicative semilattice extension of a Hilbert algebra as well as a (...)
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  10.  7
    Relational representation for subordination Tarski algebras.Sergio A. Celani - forthcoming - Journal of Applied Non-Classical Logics:1-22.
    1. A quasi-modal operator in a Boolean algebra A is a map Δ of A into the lattice Id(A) of ideals of A satisfying conditions similar to the modal operators in Boolean algebras. Every quasi-modal op...
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  11.  22
    Properties of Saturation in Monotonic Neighbourhood Models and Some Applications.Sergio A. Celani - 2015 - Studia Logica 103 (4):733-755.
    In this paper we shall discuss properties of saturation in monotonic neighbourhood models and study some applications, like a characterization of compact and modally saturated monotonic models and a characterization of the maximal Hennessy-Milner classes. We shall also show that our notion of modal saturation for monotonic models naturally extends the notion of modal saturation for Kripke models.
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  12.  50
    Frontal Operators in Weak Heyting Algebras.Sergio A. Celani & Hernán J. San Martín - 2012 - Studia Logica 100 (1-2):91-114.
    In this paper we shall introduce the variety FWHA of frontal weak Heyting algebras as a generalization of the frontal Heyting algebras introduced by Leo Esakia in [ 10 ]. A frontal operator in a weak Heyting algebra A is an expansive operator τ preserving finite meets which also satisfies the equation $${\tau(a) \leq b \vee (b \rightarrow a)}$$, for all $${a, b \in A}$$. These operators were studied from an algebraic, logical and topological point of view by Leo Esakia (...)
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  13.  15
    Frontal Operators in Weak Heyting Algebras.Sergio A. Celani & Hern?N. J. San Mart?N. - 2012 - Studia Logica 100 (1-2):91-114.
    In this paper we shall introduce the variety FWHA of frontal weak Heyting algebras as a generalization of the frontal Heyting algebras introduced by Leo Esakia in [10]. A frontal operator in a weak Heyting algebra A is an expansive operator r preserving finite meets which also satisfies the equation?? b V, for all a,b? A. These operators were studied from an algebraic, logical and topological point of view by Leo Esakia in [10]. We will study frontal operators in weak (...)
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  14.  7
    Hilbert Algebras with Hilbert–Galois Connections.Sergio A. Celani & Daniela Montangie - 2023 - Studia Logica 111 (1):113-138.
    In this paper we introduce Hilbert algebras with Hilbert–Galois connections (HilGC-algebras) and we study the Hilbert–Galois connections defined in Heyting algebras, called HGC-algebras. We assign a categorical duality between the category HilGC-algebras with Hilbert homomorphisms that commutes with Hilbert–Galois connections and Hilbert spaces with certain binary relations and whose morphisms are special functional relations. We also prove a categorical duality between the category of Heyting Galois algebras with Heyting homomorphisms that commutes with Hilbert–Galois connections and the category of spectral Heyting (...)
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  15. On the free implicative semilattice extension of a Hilbert algebra.Sergio A. Celani & Ramón Jansana Ferrer - 2012 - Mathematical Logic Quarterly 58 (3):188-207.
     
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  16.  18
    Weak‐quasi‐Stone algebras.Sergio A. Celani & Leonardo M. Cabrer - 2009 - Mathematical Logic Quarterly 55 (3):288-298.
    In this paper we shall introduce the variety WQS of weak-quasi-Stone algebras as a generalization of the variety QS of quasi-Stone algebras introduced in [9]. We shall apply the Priestley duality developed in [4] for the variety N of ¬-lattices to give a duality for WQS. We prove that a weak-quasi-Stone algebra is characterized by a property of the set of its regular elements, as well by mean of some principal lattice congruences. We will also determine the simple and subdirectly (...)
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  17.  25
    Weak-quasi-Stone algebras.Sergio A. Celani & Leonardo M. Cabrer - 2009 - Mathematical Logic Quarterly 55 (3):288-298.
    In this paper we shall introduce the variety WQS of weak-quasi-Stone algebras as a generalization of the variety QS of quasi-Stone algebras introduced in [9]. We shall apply the Priestley duality developed in [4] for the variety N of ¬-lattices to give a duality for WQS. We prove that a weak-quasi-Stone algebra is characterized by a property of the set of its regular elements, as well by mean of some principal lattice congruences. We will also determine the simple and subdirectly (...)
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