NONMONOTONIC REASONING, CONDITIONAL OBJECTS AND POSSIBILITY THEORY

This short paper relates the conditional object-based and possibility theory-based approaches for reasoning with conditional statements perv aded with exceptions, to other methods in nonmonotonic reasoning which have been independently proposed: namely, Lehmann's preferential and rational closure entailments which obey normative postulates, the infi nitesimal probability approach, and the conditional (modal) logics-bas ed approach. All these methods are shown to be equivalent with respect to their capabilities for reasoning with conditional knowledge althou gh they are based on different modeling frameworks. It thus provides a unified understanding of nonmonotonic consequence relations. More par ticularly, conditional objects, a purely qualitative counterpart to co nditional probabilities, offer a very simple semantics, based on a 3-v alued calculus, for the preferential entailment, while in the purely o rdinal setting of possibility theory both the preferential and the rat ional closure entailments can be represented. (C) 1997 Elsevier Scienc e B.V.