Conditional entailment: Bridging two approaches to default reasoning

Abstract

In recent years, two conceptually different interpretations of default expressions have been advanced: extensional interpretations, in which defaults are regarded as prescriptions for extending one's set of beliefs, and conditional interpretations, in which defaults are regarded as beliefs whose validity is bound to a particular context. The two interpretations possess virtues and limitations that are practically orthogonal to each other. The conditional interpretations successfully resolve arguments of different "specificity" (e.g., "penguins don't fly in spite of being birds") but fail to capture arguments of "irrelevance" (e.g., concluding "red birds fly" from "birds fly"). The opposite is true for the extensional interpretations. This paper develops a new account of defaults, called conditional entailment, which combines the benefits of the two interpretations. Like prioritized circumscriptions, conditional entailment resolves arguments by enforcing priorities among defaults. However, instead of having to be specified by the user, these priorities are extracted automatically from the knowledge base. Similarly, conditional entailment possesses a sound and complete proof theory, based on interacting arguments and amenable to implementation in conventional ATMSs. © 1992.