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Algebraizable logics with a strong conjunction and their semi-lattice based companions

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Abstract

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 of Abstract Algebraic Logic which consists in finding interesting characterizations of classes of algebraizable logics that are strongly algebraizable.

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Authors and Affiliations

  1. Department of Lògica, Història i Filosofia de la Ciència, Universitat de Barcelona, Montalegre 6, 08001, Barcelona, Spain

    Ramon Jansana

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  1. Ramon Jansana
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Correspondence to Ramon Jansana.

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The research for the paper has been partially supported by 2009SGR-1433 research grant of the research funding agency AGAUR of the Generalitat de Catalunya, MTM2008-01139 research grant of the Spanish Ministry of Education and Science and by the MTM2011–25747 research grant of the Spanish Ministry of Science and Innovation.

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Jansana, R. Algebraizable logics with a strong conjunction and their semi-lattice based companions. Arch. Math. Logic 51, 831–861 (2012). https://doi.org/10.1007/s00153-012-0301-z

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  • DOI: https://doi.org/10.1007/s00153-012-0301-z

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