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Logic Journal of IGPL 2004 12(4):313-333; doi:10.1093/jigpal/12.4.313
© 2004 by Oxford University Press
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Categorical Abstract Algebraic Logic: Categorical Algebraization of Equational Logic

George Voutsadakis *

School of Mathematics and Computer Science, Lake Superior State University, 650 W. Easterday Avenue, Sault Sainte Marie, MI 49783, USA. E-mail: gvoutsad{at}lssu.edu

This paper deals with the algebraization of multi-signature equational logic in the context of the modern theory of categorical abstract algebraic logic. Two are the novelties compared to traditional treatments: First, interpretations between different algebraic types are handled in the object language rather than the metalanguage. Second, rather than constructing the type of the algebraizing class of algebras explicitly in an ad-hoc universal algebraic way, the whole clone is naturally constructed using categorical algebraic techniques.

Key Words: algebraic logic, equivalent deductive systems, algebraizable logics, institutions, equivalent institutions, algebraizable institutions, algebraic theories, monads, triples, adjunctions, equational logic, clone algebras, substitution algebras

Received 25 April 2002. Revised 11 August 2004.

* Partially supported by National Science Foundation grant CCR - 9593168.


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