Categorical Abstract Algebraic Logic: Algebraizable Institutions

cal Abstract Algebraic Logic: Algebraizable Institutions To Don Pigozzi this work is dedicated GEORGE VOUTSADAKIS Department of Mathematics, Iowa State University, Ames, IA 50011 U.S.A. and Department of Mathematics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106 U.S.A. (Received: 6 April 2000; acepted: 26 April 2002) 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. Mathematics Subject Classifications (2000): Primary: 03Gxx, 18Cxx; Seconda...

• Type: Journal
• Year: 2002
• Where: ACS
• Authors: George Voutsadakis
• Keywords: ACS 2002, ACS 2007, Algebraic Logic, Algebraizable Institutions, Logics