Parallel Belief Revision

A recalcitrant problem in approaches to iterated belief revision is that, after first revising by a formula and then by a formula that is inconsistent with the first formula, all information in the original formula is lost. As noted by various researchers, this phenomenon is made explicit in the second postulate (C2) of the well-known Darwiche-Pearl framework, and so this postulate has been a point of criticism of this and related approaches. In contrast, we argue that the true culprit of this problem arises from a basic assumption of the AGM framework, that new information is represented by a single formula. We propose a more general framework for belief revision (called parallel belief revision) in which individual items of new information are represented by a set of formulas. In this framework, if one revises by a set of formulas, and then by the negation of some members of this set, then other members of the set are still believed after the revision. Hence the aforecited problem is discharged. We present first a basic approach to parallel belief revision, and next an approach that combines the basic approach with that of Jin and Thielscher. Postulates and semantic conditions characterizing these approaches are given, and representation results provided.