论文信息 - Categorical Abstract Algebraic Logic: Algebraizable Institutions

Categorical Abstract Algebraic Logic: Algebraizable Institutions

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.

GEORGE VOUTSADAKIS | G. Voutsadakis

[1] José Luiz Fiadeiro,et al. Structuring Theories on Consequence , 1988, ADT.

[2] W. Blok. Algebraic Semantics for Universal Horn Logic Without Equality , 1992 .

[3] J. Czelakowski. Equivalential logics (II) , 1981 .

[4] Norman Feldman. Axiomatization of Polynomial Substitution Algebras , 1982, J. Symb. Log..

[5] Joseph A. Goguen,et al. Institutions: abstract model theory for specification and programming , 1992, JACM.

[6] G. Voutsadakis. Categorical Abstract Algebraic Logic , 1998 .

[7] A. Tarski,et al. Cylindric Algebras. Part II , 1988 .

[8] J. Czelakowski,et al. Amalgamation and Interpolation in Abstract Algebraic Logic , 2003 .

[9] Willem J. Blok,et al. Protoalgebraic logics , 1986, Stud Logica.

[10] M. Barr,et al. Toposes, Triples and Theories , 1984 .

[11] Alexej P. Pynko,et al. Definitional Equivalence and Algebraizability of Generalized Logical Systems , 1999, Ann. Pure Appl. Log..

[12] B. Herrmann. Equivalential and algebraizable logics , 1996 .

[13] George Voutsadakis,et al. Categorical Abstract Algebraic Logic: Equivalent Institutions , 2003, Stud Logica.

[14] Burghard Herrmann. Characterizing equivalential and algebraizable logics by the Leibniz operator , 1996, Stud Logica.