Postulates for Conditional Belief Revision

Abstract

In this paper, we present a scheme of postulates for revising epistemic states by conditional beliefs. These postulates are supported mainly by following the specific, non-classical nature of conditionals, and the aim of preserving conditional beliefs is achieved by studying specific interactions between conditionals, represented properly by two relations. Because one of the postulates claims propositional belief revision to be a special case of conditional belief revision, our framework also covers the work of Darwiche and Pearl [Darwiche and Pearl, 1997], and we show that all postulates presented there may be derived from our postulates. We state representation theorems for the principal postulates, and finally, we present a conditional belief operator obeying all of the postulates by using ordinal conditional functions as representations of epistemic states.