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Josep Maria Font [24]Josep M. Font [11]
  1.  82
    Taking Degrees of Truth Seriously.Josep Maria Font - 2009 - Studia Logica 91 (3):383-406.
    This is a contribution to the discussion on the role of truth degrees in manyvalued logics from the perspective of abstract algebraic logic. It starts with some thoughts on the so-called Suszko’s Thesis (that every logic is two-valued) and on the conception of semantics that underlies it, which includes the truth-preserving notion of consequence. The alternative usage of truth values in order to define logics that preserve degrees of truth is presented and discussed. Some recent works studying these in the (...)
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  2.  47
    Note on Algebraic Models for Relevance Logic.Josep M. Font & Gonzalo Rodríguez - 1990 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (6):535-540.
  3.  76
    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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  4.  63
    Update to “A Survey of Abstract Algebraic Logic”.Josep Maria Font, Ramon Jansana & Don Pigozzi - 2009 - Studia Logica 91 (1):125-130.
    A definition and some inaccurate cross-references in the paper A Survey ofAlgebraic Logic, which might confuse some readers, are clarified and corrected; a short discussion of the main one is included. We also update a dozen of bibliographic references.
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  5.  34
    Leibniz Filters and the Strong Version of a Protoalgebraic Logic.Josep Maria Font & Ramon Jansana - 2001 - Archive for Mathematical Logic 40 (6):437-465.
    A filter of a sentential logic ? is Leibniz when it is the smallest one among all the ?-filters on the same algebra having the same Leibniz congruence. This paper studies these filters and the sentential logic ?+ defined by the class of all ?-matrices whose filter is Leibniz, which is called the strong version of ?, in the context of protoalgebraic logics with theorems. Topics studied include an enhanced Correspondence Theorem, characterizations of the weak algebraizability of ?+ and of (...)
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  6.  59
    Algebraic Study of Two Deductive Systems of Relevance Logic.Josep Maria Font & Gonzalo Rodríguez - 1994 - Notre Dame Journal of Formal Logic 35 (3):369-397.
    In this paper two deductive systems associated with relevance logic are studied from an algebraic point of view. One is defined by the familiar, Hilbert-style, formalization of R; the other one is a weak version of it, called WR, which appears as the semantic entailment of the Meyer-Routley-Fine semantics, and which has already been suggested by Wójcicki for other reasons. This weaker consequence is first defined indirectly, using R, but we prove that the first one turns out to be an (...)
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  7.  82
    M-Sets and the Representation Problem.Josep Maria Font & Tommaso Moraschini - 2015 - Studia Logica 103 (1):21-51.
    The “representation problem” in abstract algebraic logic is that of finding necessary and sufficient conditions for a structure, on a well defined abstract framework, to have the following property: that for every structural closure operator on it, every structural embedding of the expanded lattice of its closed sets into that of the closed sets of another structural closure operator on another similar structure is induced by a structural transformer between the base structures. This question arose from Blok and Jónsson abstract (...)
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  8.  53
    On Łukasiewicz's Four-Valued Modal Logic.Josep Maria Font & Petr Hájek - 2002 - Studia Logica 70 (2):157-182.
    ukasiewicz''s four-valued modal logic is surveyed and analyzed, together with ukasiewicz''s motivations to develop it. A faithful interpretation of it in classical (non-modal) two-valued logic is presented, and some consequences are drawn concerning its classification and its algebraic behaviour. Some counter-intuitive aspects of this logic are discussed in the light of the presented results, ukasiewicz''s own texts, and related literature.
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  9.  63
    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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  10.  44
    On the Closure Properties of the Class of Full G-Models of a Deductive System.Josep Maria Font, Ramon Jansana & Don Pigozzi - 2006 - Studia Logica 83 (1-3):215-278.
    In this paper we consider the structure of the class FGModS of full generalized models of a deductive system S from a universal-algebraic point of view, and the structure of the set of all the full generalized models of S on a fixed algebra A from the lattice-theoretical point of view; this set is represented by the lattice FACSs A of all algebraic closed-set systems C on A such that (A, C) ε FGModS. We relate some properties of these structures (...)
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  11.  12
    Modality and Possibility in Some Intuitionistic Modal Logics.Josep M. Font - 1986 - Notre Dame Journal of Formal Logic 27 (4):533-546.
  12.  43
    An Abstract Algebraic Logic Approach to Tetravalent Modal Logics.Josep Maria Font & Miquel Rius - 2000 - Journal of Symbolic Logic 65 (2):481-518.
    This paper contains a joint study of two sentential logics that combine a many-valued character, namely tetravalence, with a modal character; one of them is normal and the other one quasinormal. The method is to study their algebraic counterparts and their abstract models with the tools of Abstract Algebraic Logic, and particularly with those of Brown and Suszko's theory of abstract logics as recently developed by Font and Jansana in their "A General Algebraic Semantics for Sentential Logics". The logics studied (...)
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  13.  30
    Compatibility Operators in Abstract Algebraic Logic.Hugo Albuquerque, Josep Maria Font & Ramon Jansana - 2016 - Journal of Symbolic Logic 81 (2):417-462.
    This paper presents a unified framework that explains and extends the already successful applications of the Leibniz operator, the Suszko operator, and the Tarski operator in recent developments in abstract algebraic logic. To this end, we refine Czelakowski’s notion of an S-compatibility operator, and introduce the notion of coherent family of S-compatibility operators, for a sentential logic S. The notion of coherence is a restricted property of commutativity with inverse images by surjective homomorphisms, which is satisfied by both the Leibniz (...)
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  14.  19
    On Substructural Logics Preserving Degrees of Truth.Josep Maria Font - 2007 - Bulletin of the Section of Logic 36 (3/4):117-129.
  15.  40
    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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  16.  43
    Beyond Rasiowa's Algebraic Approach to Non-Classical Logics.Josep Maria Font - 2006 - Studia Logica 82 (2):179-209.
    This paper reviews the impact of Rasiowa's well-known book on the evolution of algebraic logic during the last thirty or forty years. It starts with some comments on the importance and influence of this book, highlighting some of the reasons for this influence, and some of its key points, mathematically speaking, concerning the general theory of algebraic logic, a theory nowadays called Abstract Algebraic Logic. Then, a consideration of the diverse ways in which these key points can be generalized allows (...)
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  17.  19
    The Strong Version of a Sentential Logic.Hugo Albuquerque, Josep Maria Font & Ramon Jansana - 2017 - Studia Logica 105 (4):703-760.
    This paper explores a notion of “the strong version” of a sentential logic S, initially defined in terms of the notion of a Leibniz filter, and shown to coincide with the logic determined by the matrices of S whose filter is the least S-filter in the algebra of the matrix. The paper makes a general study of this notion, which appears to unify under an abstract framework the relationships between many pairs of logics in the literature. The paradigmatic examples are (...)
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  18.  13
    The Simplest Protoalgebraic Logic.Josep Maria Font - 2013 - Mathematical Logic Quarterly 59 (6):435-451.
  19.  36
    Leibniz-Linked Pairs of Deductive Systems.Josep Maria Font & Ramon Jansana - 2011 - Studia Logica 99 (1-3):171-202.
    A pair of deductive systems (S,S’) is Leibniz-linked when S’ is an extension of S and on every algebra there is a map sending each filter of S to a filter of S’ with the same Leibniz congruence. We study this generalization to arbitrary deductive systems of the notion of the strong version of a protoalgebraic deductive system, studied in earlier papers, and of some results recently found for particular non-protoalgebraic deductive systems. The necessary examples and counterexamples found in the (...)
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  20.  19
    Note on a Six-Valued Extension of Three-Valued Logic.Josep M. Font & Massoud Moussavi - 1993 - Journal of Applied Non-Classical Logics 3 (2):173-187.
    ABSTRACT In this paper we introduce a set of six logical values, arising in the application of three-valued logics to time intervals, find its algebraic structure, and use it to define a six-valued logic. We then prove, by using algebraic properties of the class of De Morgan algebras, that this semantically defined logic can be axiomatized as Belnap's ?useful? four-valued logic. Other directions of research suggested by the construction of this set of six logical values are described.
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  21. Atoms in a Lattice of Theories.Josep Maria Font - 2013 - Bulletin of the Section of Logic 42 (1/2).
  22.  14
    On Special Implicative Filters.Josep Maria Font - 1999 - Mathematical Logic Quarterly 45 (1):117-126.
    In her well-known book, Rasiowa states without proof that in implicative algebras there is a one-to-one correspondence between kernels of epimorphisms and the so-called special implicative filters, and that in the logic whose algebraic counterpart is the class of implicative algebras the deductive filters coincide with the special implicative filters. We show that neither claim is true, and how to repair the situation by redefining some of the notions involved. We answer other questions concerning special implicative filters, taking the theory (...)
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  23.  25
    On Weakening the Deduction Theorem and Strengthening Modus Ponens.Félix Bou, Josep Maria Font & José Luis García Lapresta - 2004 - Mathematical Logic Quarterly 50 (3):303-324.
    This paper studies, with techniques ofAlgebraic Logic, the effects of putting a bound on the cardinality of the set of side formulas in the Deduction Theorem, viewed as a Gentzen-style rule, and of adding additional assumptions inside the formulas present in Modus Ponens, viewed as a Hilbert-style rule. As a result, a denumerable collection of new Gentzen systems and two new sentential logics have been isolated. These logics are weaker than the positive implicative logic. We have determined their algebraic models (...)
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  24.  28
    Foreword.Josep Maria Font, Ramon Jansana & Don Pigozzi - 2003 - Studia Logica 74 (1-2):1-9.
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  25.  7
    Correction to “Some Remarks on Heyting Matrices”.Josep M. Font - 1988 - Mathematical Logic Quarterly 34 (3):287-288.
  26.  27
    Correction to “Some Remarks on Heyting Matrices”.Josep M. Font - 1988 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 34 (3):287-288.
  27.  9
    Erratum to J. M. Font, The Simplest Protoalgebraic Logic.Josep Maria Font - 2014 - Mathematical Logic Quarterly 60 (1-2):91-91.
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  28.  26
    Foreword.Josep Maria Font, Ramon Jansana & Don Pigozzi - 2000 - Studia Logica 65 (1):1-9.
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  29.  21
    Full Models for Sentential Logics.Josep Maria Font & Ramon Jansana - 1995 - Bulletin of the Section of Logic 24 (3):123-131.
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  30.  28
    Introduction.Josep Maria Font & Ramon Jansana - 2013 - Studia Logica 101 (4):647-650.
  31.  13
    Intuitionistic Implication in Some Non-Classical Modal Logics of Type S4.Josep M. Font - 1983 - Bulletin of the Section of Logic 12 (1):2-5.
  32.  43
    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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