21 found
Sort by:
  1. Josep Maria Font & Tommaso Moraschini (forthcoming). M-Sets and the Representation Problem. Studia Logica:1-31.
    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 (...)
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  2. Josep Maria Font (2014). Erratum toJ. M. Font, The Simplest Protoalgebraic Logic. Mathematical Logic Quarterly 60 (1-2):91-91.
    No categories
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  3. Josep Maria Font (2013). Atoms in a Lattice of Theories. Bulletin of the Section of Logic 42.
    No categories
    Direct download  
     
    My bibliography  
     
    Export citation  
  4. Josep Maria Font (2013). The Simplest Protoalgebraic Logic. Mathematical Logic Quarterly 59 (6):435-451.
    No categories
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  5. Josep Maria Font & Ramon Jansana (2013). Introduction. Studia Logica 101 (4):647-650.
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  6. Josep Maria Font & Ramon Jansana (2011). Leibniz-Linked Pairs of Deductive Systems. 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 (...)
    Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  7. Josep Maria Font (2009). Taking Degrees of Truth Seriously. 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 (...)
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  8. Josep Maria Font, Ramon Jansana & Don Pigozzi (2009). Update to “A Survey of Abstract Algebraic Logic”. Studia Logica 91 (1):125-130.
    Direct download  
     
    My bibliography  
     
    Export citation  
  9. Josep Maria Font (2007). On Substructural Logics Preserving Degrees of Truth. Bulletin of the Section of Logic 36 (3/4):117-129.
    No categories
    Direct download  
     
    My bibliography  
     
    Export citation  
  10. Josep Maria Font (2006). Beyond Rasiowa's Algebraic Approach to Non-Classical Logics. 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 (...)
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  11. Josep Maria Font, Àngel J. Gil, Antoni Torrens & Ventura Verdú (2006). On the Infinite-Valued Łukasiewicz Logic That Preserves Degrees of Truth. 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 (...)
    No categories
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  12. Josep Maria Font, Ramon Jansana & Don Pigozzi (2006). On the Closure Properties of the Class of Full G-Models of a Deductive System. 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 (...)
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  13. Félix Bou, Josep Maria Font & José Luis García Lapresta (2004). On Weakening the Deduction Theorem and Strengthening Modus Ponens. Mathematical Logic Quarterly 50 (3):303-324.
    No categories
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  14. Josep Maria Font, Ramon Jansana & Don Pigozzi (2003). Foreword. Studia Logica 74 (1-2):1-9.
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  15. Josep Maria Font & Petr Hájek (2002). On Łukasiewicz's Four-Valued Modal Logic. 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.
    Direct download (8 more)  
     
    My bibliography  
     
    Export citation  
  16. Josep Maria Font & Ramon Jansana (2001). Leibniz Filters and the Strong Version of a Protoalgebraic Logic. 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 (...)
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  17. Josep Maria Font, Ramon Jansana & Don Pigozzi (2000). Foreword. Studia Logica 65 (1):1-9.
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  18. Josep Maria Font & Miquel Rius (2000). An Abstract Algebraic Logic Approach to Tetravalent Modal Logics. 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 (...)
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  19. Josep Maria Font (1999). On Special Implicative Filters. Mathematical Logic Quarterly 45 (1):117-126.
    No categories
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  20. Josep Maria Font & Ramon Jansana (1995). Full Models for Sentential Logics. Bulletin of the Section of Logic 24 (3):123-131.
    No categories
    Direct download  
     
    My bibliography  
     
    Export citation  
  21. Josep Maria Font & Gonzalo Rodríguez (1994). Algebraic Study of Two Deductive Systems of Relevance Logic. Notre Dame Journal of Formal Logic 35 (3):369-397.
    In this paper two deductive systems (i.e., two consequence relations) 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 (...)
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation