Archive for Mathematical Logic 51 (7-8):831-861 (2012)

Ramon Jansana Ferrer
Universitat de Barcelona
The best known algebraizable logics with a conjunction and an implication have the property that the conjunction defines a meet semi-lattice in the algebras of their algebraic counterpart. This property makes it possible to associate with them a semi-lattice based deductive system as a companion. Moreover, the order of the semi-lattice is also definable using the implication. This makes that the connection between the properties of the logic and the properties of its semi-lattice based companion is strong. We introduce a class of algebraizable deductive systems that includes those systems, and study some of their properties and of their semi-lattice based companions. We also study conditions which, when satisfied by a deductive system in the class, imply that it is strongly algebraizable. This brings some information on the open area of research ofAlgebraic Logic which consists in finding interesting characterizations of classes of algebraizable logics that are strongly algebraizable
Keywords Algebraizable logics  Strongly algebraizable logics  Logics based on semi-lattices  Abstract Algebraic logic
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DOI 10.1007/s00153-012-0301-z
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References found in this work BETA

A Survey of Abstract Algebraic Logic.J. M. Font, R. Jansana & D. Pigozzi - 2003 - Studia Logica 74 (1-2):13 - 97.
Protoalgebraic Logics.Janusz Czelakowski - 2001 - Kluwer Academic Publishers.
Selfextensional Logics with a Conjunction.Ramon Jansana - 2006 - Studia Logica 84 (1):63-104.

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Citations of this work BETA

Selfextensional Logics with a Distributive Nearlattice Term.Luciano J. González - 2019 - Archive for Mathematical Logic 58 (1-2):219-243.
Monotonic modal logics with a conjunction.Paula Menchón & Sergio Celani - forthcoming - Archive for Mathematical Logic:1-21.

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