Publication year: 2011
Source: Artificial Intelligence, Available online 7 October 2011
James Delgrande, Yi Jin
The area ofbelief revisionstudies how a rational agent may incorporate new information about a domain into its belief corpus. An agent is characterized by a belief stateK, and receives a new item of informationαwhich is to be included among its set of beliefs. Revision then is a function from a belief state and a formula to a new belief state.We propose here a more general framework for belief revision, in which revision is a function from a belief state and a finitesetof formulas to a new belief state. In particular, we distinguish revision by the setfrom the set. This seemingly innocuous change has significant ramifications with respect toiterated belief revision. A 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.This problem is avoided here in that, in revising by a set of formulasS, the resulting belief state contains not just the information that members ofSare believed to be true, but also the counterfactual supposition that if some members ofSwere later believed to be false, then the remaining members would nonetheless still be believed to be true. Thus if some members ofSwere in fact later believed to be false, then the other elements ofSwould still be believed to be true. Hence, we provide a more nuanced approach to belief revision. The general approach, which we callparallel belief revision, is independent of extant approaches to iterated revision. We present first a basic approach to parallel belief revision. Following this we combine the basic approach with an approach due to Jin and Thielscher for iterated revision. Postulates and semantic conditions characterizing these approaches are given, and representation results provided. We conclude with a discussion of the possible ramifications of this approach in belief revision in general.