Abstract Algebraic Logic

Authors:
Don Pigozzi
Affiliations:
-
Venue:
AMAST '98 Proceedings of the 7th International Conference on Algebraic Methodology and Software Technology
Year:
1999

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Abstract

The classical method of associating a class of algebras with a logical system is that of Lindenbaum and Tarski. It can be applied to any system with a biconditional ↔ that is compositional in the sense that it defines a congruence relation on the absolutely free algebra of formulas. The method has been abstacted to provide effective criteria for the algebraizability of a large class of formal systems. One consequence of this work is a uniform method of providing a formal system with algebraic semantics. The main features of the theory of abstract algebraic logic and one of its potential applications are surveyed.