Circumscription implies predicate completion (sometimes)

Abstract

Predicate completion is an approach to closed world reasoning which assumes that the given sufficient conditions on a predicate are also necessary. Circumscription is a formal device characterizing minimal reasoning i.e. reasoning in minimal models, and is realized by an axiom schema. The basic result of this paper is that for first order theories which are Horn in a predicate P, the circumscription of P logically implies P's completion axiom.