On Computing Belief Change Operations using Quantified Boolean Formulas

In this paper, we show how an approach to belief revision and belief contraction can be axiomatised by means of quantified Boolean formulas. Specifically, we consider the approach of belief change scenarios, a general framework that has been introduced for expressing different forms of belief change. The essential idea is that for a belief change scenario (K, R, C), the set of formulas K, representing the knowledge base, is modified so that the sets of formulas R and C are respectively true in, and consistent with the result. By restricting the form of a belief change scenario, one obtains specific belief change operators including belief revision, contraction, update, and merging. For both the general approach and for specific operators, we give a quantified Boolean formula such that satisfying truth assignments to the free variables correspond to belief change extensions in the original approach. Hence, we reduce the problem of determining the results of a belief change operation to that of satisfiability. This approach has several benefits. First, it furnishes an axiomatic specification of belief change with respect to belief change scenarios. This then leads to further insight into the belief change framework. A preliminary version of this paper appeared in the Proceedings of the Sixth European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2001). This work was partially supported by the Austrian Science Fund Project under grants Z29-N04 and P15068-INF, as well as a Canadian NSERC Research Grant. Affiliated with the School of Computing Science at Simon Fraser University, Burnaby, Canada.