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  1. Selfextensional Logics with a Distributive Nearlattice Term.Luciano J. González - 2019 - Archive for Mathematical Logic 58 (1-2):219-243.
    We define when a ternary term m of an algebraic language \ is called a distributive nearlattice term -term) of a sentential logic \. Distributive nearlattices are ternary algebras generalising Tarski algebras and distributive lattices. We characterise the selfextensional logics with a \-term through the interpretation of the DN-term in the algebras of the algebraic counterpart of the logics. We prove that the canonical class of algebras associated with a selfextensional logic with a \-term is a variety, and we obtain (...)
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  • Symmetric Operators on Modal Pseudocomplemented De Morgan Algebras.Aldo Figallo-Orellano, Alicia Ziliani & Martín Figallo - 2017 - Logic Journal of the IGPL 25 (4):496-511.
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  • Extension Properties and Subdirect Representation in Abstract Algebraic Logic.Tomáš Lávička & Carles Noguera - 2018 - Studia Logica 106 (6):1065-1095.
    This paper continues the investigation, started in Lávička and Noguera : 521–551, 2017), of infinitary propositional logics from the perspective of their algebraic completeness and filter extension properties in abstract algebraic logic. If follows from the Lindenbaum Lemma used in standard proofs of algebraic completeness that, in every finitary logic, intersection-prime theories form a basis of the closure system of all theories. In this article we consider the open problem of whether these properties can be transferred to lattices of filters (...)
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  • 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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  • On Gentzen Relations Associated with Finite-Valued Logics Preserving Degrees of Truth.Angel J. Gil - 2013 - Studia Logica 101 (4):749-781.
    When considering m-sequents, it is always possible to obtain an m-sequent calculus VL for every m-valued logic (defined from an arbitrary finite algebra L of cardinality m) following for instance the works of the Vienna Group for Multiple-valued Logics. The Gentzen relations associated with the calculi VL are always finitely equivalential but might not be algebraizable. In this paper we associate an algebraizable 2-Gentzen relation with every sequent calculus VL in a uniform way, provided the original algebra L has a (...)
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  • 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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  • Compatibility Operators in Abstract Algebraic Logic.Hugo Albuquerque, Josep Maria Font & Ramon Jansana - 2016 - Journal of Symbolic Logic 81 (2):417-462.
  • On the Set of Intermediate Logics Between the Truth- and Degree-Preserving Łukasiewicz Logics.Marcelo E. Coniglio, Francesc Esteva & Lluís Godo - 2016 - Logic Journal of the IGPL 24 (3):288-320.