Forgetting and Conflict Resolving in Disjunctive Logic Programming
Abstract: We establish a declarative theory of forgetting for disjunctive logic programs. The suitability of this theory is justified by a number of desirable properties. In particular, one of our results shows that our notion of forgetting is completely captured by the classical forgetting. A transformation-based algorithm is also developed for computing the result of forgetting. We also provide an analysis of computational complexity. As an application of our approach, a fairly general framework for resolving conflicts in inconsistent knowledge bases represented by disjunctive logic programs is defined. The basic idea of our framework is to weaken the preferences of each agent by forgetting certain knowledge that causes inconsistency. In particular, we show how to use the notion of forgetting to provide an elegant solution for preference elicitation in disjunctive logic programming.
A new result we obtained recently shows that our notion of forgetting in ASP is unique in the sense of classical forgetting.
Theorem Let P be a logic program without strong negation and p an atom in P. Then X is an answer set of forget(P,p) if and only if X is a minimal model of forget(lcomp(P), p). Here lcomp(P) is the completion with loop of P and thus forget(lcomp(P), p) is the classical forgetting.
Note. X is an answer set of a disjunctive program P iff X is a model of lcomp(P). (see Lin&Zhao AAAI02, AIJ04; Lee&Lifschitz ICLP03 for details)