15 found
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  1.  43
    On the Infinite-Valued Łukasiewicz Logic That Preserves Degrees of Truth.Josep Maria Font, Àngel J. Gil, Antoni Torrens & Ventura Verdú - 2006 - Archive for Mathematical Logic 45 (7):839-868.
    Łukasiewicz’s infinite-valued logic is commonly defined as the set of formulas that take the value 1 under all evaluations in the Łukasiewicz algebra on the unit real interval. In the literature a deductive system axiomatized in a Hilbert style was associated to it, and was later shown to be semantically defined from Łukasiewicz algebra by using a “truth-preserving” scheme. This deductive system is algebraizable, non-selfextensional and does not satisfy the deduction theorem. In addition, there exists no Gentzen calculus fully adequate (...)
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  2.  34
    Algebraic Logic for Classical Conjunction and Disjunction.Josep M. Font & Ventura Verdú - 1991 - Studia Logica 50 (3-4):391 - 419.
    In this paper we study the relations between the fragment L of classical logic having just conjunction and disjunction and the variety D of distributive lattices, within the context of Algebraic Logic. We prove that these relations cannot be fully expressed either with the tools of Blok and Pigozzi's theory of algebraizable logics or with the use of reduced matrices for L. However, these relations can be naturally formulated when we introduce a new notion of model of a sequent calculus. (...)
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  3.  19
    A First Approach to Abstract Modal Logics.Josep M. Font & Ventura Verdú - 1989 - Journal of Symbolic Logic 54 (3):1042-1062.
    The object of this paper is to make a study of four systems of modal logic (S4, S5, and their intuitionistic analogues IM4 and IM5) with the techniques of the theory of abstract logics set up by Suszko, Bloom, Brown, Verdú and others. The abstract concepts corresponding to such systems are defined as generalizations of the logics naturally associated to their algebraic models (topological Boolean or Heyting algebras, general or semisimple). By considering new suitably defined connectives and by distinguishing between (...)
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  4.  33
    On a Contraction-Less Intuitionistic Propositional Logic with Conjunction and Fusion.Romà J. Adillon & Ventura Verdú - 2000 - Studia Logica 65 (1):11-30.
    In this paper we prove the equivalence between the Gentzen system G LJ*\c , obtained by deleting the contraction rule from the sequent calculus LJ* (which is a redundant version of LJ), the deductive system IPC*\c and the equational system associated with the variety RL of residuated lattices. This means that the variety RL is the equivalent algebraic semantics for both systems G LJ*\c in the sense of [18] and [4], respectively. The equivalence between G LJ*\c and IPC*\c is a (...)
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  5.  15
    Logics Projectively Generated From [ℳ] = by a Set of Homomorphisms.Ventura Verdú - 1987 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (3):235-241.
  6.  5
    Logics Projectively Generated From [ℳ︁] = (ℱ4, [{1}]) by a Set of Homomorphisms.Ventura Verdú - 1987 - Mathematical Logic Quarterly 33 (3):235-241.
  7.  17
    Some Algebraic Structures Determined by Closure Operators.Ventura Verdú - 1985 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 31 (14-18):275-278.
  8.  3
    A Finite Hilbert‐Style Axiomatization of the Implication‐Less Fragment of the Intuitionistic Propositional Calculus.Jordi Rebagliato & Ventura Verdú - 1994 - Mathematical Logic Quarterly 40 (1):61-68.
    In this paper we obtain a finite Hilbert-style axiomatization of the implicationless fragment of the intuitionistic propositional calculus. As a consequence we obtain finite axiomatizations of all structural closure operators on the algebra of {–}-formulas containing this fragment.
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  9.  29
    On a Substructural Gentzen System, its Equivalent Variety Semantics and its External Deductive System.R. Adillon & Ventura Verdú - 2002 - Bulletin of the Section of Logic 31 (3):125-134.
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  10.  9
    A Strong Completeness Theorem for the Gentzen Systems Associated with Finite Algebras.Àngel J. Gil, Jordi Rebagliato & Ventura Verdú - 1999 - Journal of Applied Non-Classical Logics 9 (1):9-36.
  11.  4
    Some Algebraic Structures Determined by Closure Operators.Ventura Verdú - 1985 - Mathematical Logic Quarterly 31 (14‐18):275-278.
  12.  14
    Lukasiewicz Logic and Wajsberg Algebras.Antonio J. Rodriguez, Antoni Torrens & Ventura Verdú - 1990 - Bulletin of the Section of Logic 19 (2):51-55.
  13.  19
    On Two Fragments with Negation and Without Implication of the Logic of Residuated Lattices.Félix Bou, Àngel García-Cerdaña & Ventura Verdú - 2006 - Archive for Mathematical Logic 45 (5):615-647.
    The logic of (commutative integral bounded) residuated lattices is known under different names in the literature: monoidal logic [26], intuitionistic logic without contraction [1], H BCK [36] (nowadays called by Ono), etc. In this paper we study the -fragment and the -fragment of the logical systems associated with residuated lattices, both from the perspective of Gentzen systems and from that of deductive systems. We stress that our notion of fragment considers the full consequence relation admitting hypotheses. It results that this (...)
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  14.  14
    A Gentzen System Equivalent to the BCK-Logic'.R. Adillon & Ventura Verdú - 1996 - Bulletin of the Section of Logic 25 (2):73-79.
  15.  24
    The Lattice of Distributive Closure Operators Over an Algebra.Josep M. Font & Ventura Verdú - 1993 - Studia Logica 52 (1):1 - 13.
    In our previous paper Algebraic Logic for Classical Conjunction and Disjunction we studied some relations between the fragmentL of classical logic having just conjunction and disjunction and the varietyD of distributive lattices, within the context of Algebraic Logic. The central tool in that study was a class of closure operators which we calleddistributive, and one of its main results was that for any algebraA of type (2,2) there is an isomorphism between the lattices of allD-congruences ofA and of all distributive (...)
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