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Categorical Abstract Algebraic Logic: Algebraizable Institutions

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Abstract

The framework developed by Blok and Pigozzi for the algebraizability of deductive systems is extended to cover the algebraizability of multisignature logics with quantifiers. Institutions are used as the supporting structure in place of deductive systems. In particular, the concept of an algebraic institution and that of an algebraizable institution are made precise using the theory of monads from categorical algebra and the notion of equivalence of institutions introduced by Voutsadakis. Several examples of algebraic and algebraizable institutions are provided.

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Authors and Affiliations

  1. Department of Mathematics, Iowa State University, Ames, IA, 50011, U.S.A.

    George Voutsadakis

  2. Department of Mathematics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH, 44106, U.S.A

    George Voutsadakis

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  1. George Voutsadakis
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Voutsadakis, G. Categorical Abstract Algebraic Logic: Algebraizable Institutions. Applied Categorical Structures 10, 531–568 (2002). https://doi.org/10.1023/A:1020990419514

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