On Computing Solutions to Belief Change Scenarios

Belief change scenarios have been introduced as a framework 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. In this paper, we show how the belief revision and belief contraction operators can be axiomatised by means of quantified Boolean formulas. Basically 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, in this paper 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 alternative characterisation then leads to further insight into the belief change framework. Second, this axiomatisation allows us to identify strict complexity bounds for the considered reasoning tasks. Finally, we obtain an implementation of different forms of belief change by appeal to existing solvers for quantified Boolean formulas. 1School of Computing Science Simon Fraser University Burnaby, B.C., Canada V5A 1S6 E-mail: [email protected] 2Institut für Informatik, Universität Potsdam Postfach 90 03 27, D–14439 Potsdam, Germany. E-mail: [sarsakov, torsten]@cs.uni-potsdam.de 3Institut für Informationssysteme, Abteilung Wissensbasierte Systeme 184/3, Technische Universität Wien, Favoritenstraße 9-11, A–1040 Wien, Austria. E-mail: [tompits, stefan]@kr.tuwien.ac.at Acknowledgements: This work was partially supported by the Austrian Science Fund Project under grant P15068 as well as a Canadian NSERC Research Grant. 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). Copyright c 2003 by the authors