Axiomatizing the Least Fixed Point Operation and Binary Supremum

Authors:
Zoltán Ésik
Affiliations:
-
Venue:
Proceedings of the 14th Annual Conference of the EACSL on Computer Science Logic
Year:
2000

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Abstract

The equational properties of the least fixed point operation on (ω-)continuous functions on (ω-)complete partially ordered sets are captured by the axioms of iteration algebras, or iteration theories. We show that the equational laws of the binary supremum operation in conjunction with the least fixed point operation on (ω-)continuous functions on (ω-)complete semilattices have a finite axiomatization over the equations of iteration algebras. As a byproduct of this relative axiomatizability result, we obtain complete infinite equational, and finite implicational axiomatizations.