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  1. A survey of abstract algebraic logic.J. M. Font, R. Jansana & D. Pigozzi - 2003 - Studia Logica 74 (1-2):13 - 97.
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  • On the complexity of the Leibniz hierarchy.Tommaso Moraschini - 2019 - Annals of Pure and Applied Logic 170 (7):805-824.
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  • The Suszko operator. Part I.Janusz Czelakowski - 2003 - Studia Logica 74 (1-2):181 - 231.
    The paper is conceived as a first study on the Suszko operator. The purpose of this paper is to indicate the existence of close relations holding between the properties of the Suszko operator and the structural properties of the model class for various sentential logics. The emphasis is put on generality both of the results and methods of tackling the problems that arise in the theory of this operator. The attempt is made here to develop the theory for non-protoalgebraic logics.
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  • The equational definability of truth predicates.James Raftery - 2006 - Reports on Mathematical Logic.
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  • Characterizing equivalential and algebraizable logics by the Leibniz operator.Burghard Herrmann - 1997 - Studia Logica 58 (2):305-323.
    In [14] we used the term finitely algebraizable for algebraizable logics in the sense of Blok and Pigozzi [2] and we introduced possibly infinitely algebraizable, for short, p.i.-algebraizable logics. In the present paper, we characterize the hierarchy of protoalgebraic, equivalential, finitely equivalential, p.i.-algebraizable, and finitely algebraizable logics by properties of the Leibniz operator. A Beth-style definability result yields that finitely equivalential and finitely algebraizable as well as equivalential and p.i.-algebraizable logics can be distinguished by injectivity of the Leibniz operator. Thus, (...)
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  • The Poset of All Logics III: Finitely Presentable Logics.Ramon Jansana & Tommaso Moraschini - 2020 - Studia Logica 109 (3):539-580.
    A logic in a finite language is said to be finitely presentable if it is axiomatized by finitely many finite rules. It is proved that binary non-indexed products of logics that are both finitely presentable and finitely equivalential are essentially finitely presentable. This result does not extend to binary non-indexed products of arbitrary finitely presentable logics, as shown by a counterexample. Finitely presentable logics are then exploited to introduce finitely presentable Leibniz classes, and to draw a parallel between the Leibniz (...)
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  • The Poset of All Logics II: Leibniz Classes and Hierarchy.R. Jansana & T. Moraschini - 2023 - Journal of Symbolic Logic 88 (1):324-362.
    A Leibniz class is a class of logics closed under the formation of term-equivalent logics, compatible expansions, and non-indexed products of sets of logics. We study the complete lattice of all Leibniz classes, called the Leibniz hierarchy. In particular, it is proved that the classes of truth-equational and assertional logics are meet-prime in the Leibniz hierarchy, while the classes of protoalgebraic and equivalential logics are meet-reducible. However, the last two classes are shown to be determined by Leibniz conditions consisting of (...)
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  • (2 other versions)Foreword. [REVIEW]J. Font, R. Jansana & D. Pigozzi - 2003 - Studia Logica 74 (1-2):3-12.
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  • Reduced products of logical matrices.Janusz Czelakowski - 1980 - Studia Logica 39 (1):19 - 43.
    The class Matr(C) of all matrices for a prepositional logic (, C) is investigated. The paper contains general results with no special reference to particular logics. The main theorem (Th. (5.1)) which gives the algebraic characterization of the class Matr(C) states the following. Assume C to be the consequence operation on a prepositional language induced by a class K of matrices. Let m be a regular cardinal not less than the cardinality of C. Then Matr (C) is the least class (...)
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  • Equivalential and algebraizable logics.Burghard Herrmann - 1996 - Studia Logica 57 (2-3):419 - 436.
    The notion of an algebraizable logic in the sense of Blok and Pigozzi [3] is generalized to that of a possibly infinitely algebraizable, for short, p.i.-algebraizable logic by admitting infinite sets of equivalence formulas and defining equations. An example of the new class is given. Many ideas of this paper have been present in [3] and [4]. By a consequent matrix semantics approach the theory of algebraizable and p.i.-algebraizable logics is developed in a different way. It is related to the (...)
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  • (3 other versions)Equivalential logics.Janusz Czelakowski - 1981 - Studia Logica 40 (3):227-236.
    The class of equivalential logics comprises all implicative logics in the sense of Rasiowa [9], Suszko's logic SCI and many others. Roughly speaking, a logic is equivalential iff the greatest strict congruences in its matrices are determined by polynomials. The present paper is the first part of the survey in which systematic investigations into this class of logics are undertaken. Using results given in [3] and general theorems from the theory of quasi-varieties of models [5] we give a characterization of (...)
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  • Protoalgebraic logics.W. J. Blok & Don Pigozzi - 1986 - Studia Logica 45 (4):337 - 369.
    There exist important deductive systems, such as the non-normal modal logics, that are not proper subjects of classical algebraic logic in the sense that their metatheory cannot be reduced to the equational metatheory of any particular class of algebras. Nevertheless, most of these systems are amenable to the methods of universal algebra when applied to the matrix models of the system. In the present paper we consider a wide class of deductive systems of this kind called protoalgebraic logics. These include (...)
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  • Admissible Rules and the Leibniz Hierarchy.James G. Raftery - 2016 - Notre Dame Journal of Formal Logic 57 (4):569-606.
    This paper provides a semantic analysis of admissible rules and associated completeness conditions for arbitrary deductive systems, using the framework of abstract algebraic logic. Algebraizability is not assumed, so the meaning and significance of the principal notions vary with the level of the Leibniz hierarchy at which they are presented. As a case study of the resulting theory, the nonalgebraizable fragments of relevance logic are considered.
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  • A logical and algebraic characterization of adjunctions between generalized quasi-varieties.Tommaso Moraschini - 2018 - Journal of Symbolic Logic 83 (3):899-919.
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  • A study of truth predicates in matrix semantics.Tommaso Moraschini - 2018 - Review of Symbolic Logic 11 (4):780-804.
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  • Logics of varieties, logics of semilattices and conjunction.J. M. Font & T. Moraschini - 2014 - Logic Journal of the IGPL 22 (6):818-843.
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  • Algebraizability and Beth's Theorem for equivalential logics.Burghard Herrmann - 1993 - Bulletin of the Section of Logic 22:85-88.
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