Believability in default logic entails logical consequence from circumscription (sometimes)

Abstract

There have been a number of efforts, recently, towards developing default logic and circumscription, two important formalisms for non-monotonic reasoning. In this paper, we shall propose a partial translation of default logic to circumscription. We limit ourselves to an open default of the form, a(x):Mβ(x)/γ(x), whose justification β(x) contains no positive occurrences of a predicate. We show, under certain conditions, for a given default theory, any consistent extension is a logical consequence of the resulting circumscription.