Incorporating specificity into circumscriptive theories

Abstract

We describe an approach whereby specificity notions are introduced into circumscriptive theories. In this approach, a default theory is initially given as a set of strict and defeasible conditionals. By making use of a theory of default conditionals, here given by System Z, we isolate minimal sets of defaults with specificity conflicts. From the specificity information intrinsic in these sets, a propositional theory is specified. By circumscribing a set of “abnormality” propositions, one obtains a nonmonotonic reasoning system in which specificity information is appropriately handled. This notion of specificity subsumes that of property inheritance, and so in this approach a bird will fly (by default) whereas a penguin will not. This work differs from previous work in specifying priorities in circumscription, in that priorities are obtained from information intrinsic in a set of conditionals, rather than assumed to exist a priori. This paper extends earlier work in hybrid nonmonotonic reasoning systems: First, in this previous work specificity issues were addressed with respect to Default Logic. Second, we here augment the approach to allow strict as well as default knowledge.