Axiomatization of Finite Algebras

Authors:
Jochen Burghardt
Affiliations:
-
Venue:
KI '02 Proceedings of the 25th Annual German Conference on AI: Advances in Artificial Intelligence
Year:
2002

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Abstract

We show that the set of all formulas in n variables valid in a finite class A of finite algebras is always a regular tree language, and compute a finite axiom set for A. We give a rational reconstruction of Barzdins' liquid flow algorithm [BB91]. We show a sufficient condition for the existence of a class A of prototype algebras for a given theory 驴. Such a set allows us to prove 驴 |= 驴 simply by testing whether 驴 holds in A.