Revising by an Inconsistent Set of Formulas

Abstract

This paper presents an approach to belief revision in which revision is a function from a belief state and a finite set of formulas to a new belief state. In the interesting case, the set for revision S may be inconsistent but individual members of S are consistent. We argue that S will still contain interesting information regarding revision; in particular, maximum consistent subsets of S will determine candidate formulas for the revision process, and the agent's associated faithful ranking will determine the plausibility of such candidate formulas. Postulates and semantic conditions characterizing this approach are given, and representation results are provided. As a consequence of this approach, we argue that revision by a sequence of formulas, usually considered as a problem of iterated revision, is more appropriately regarded as revision by the possibly-inconsistent set of these formulas. Hence we suggest that revision by a sequence of formulas is foremost a problem of (uniterated) set revision.