On the measure of conflicts: an argumentation-based framework

An important issue in the management of knowledge-based systems is the handling of inconsistency. This problem has recently been attracting a lot of attention from Artificial Intelligence community. When inconsistency occurs in a knowledge base, there are mainly two ways to deal with it; we either resolve it or accept inconsistency and cope with it. This paper tackles the problem of evaluating the amount of contradiction in propositional knowledge bases, and provides a new measure of conflict based on deductive argumentation theory. Measuring the degree of conflict of a knowledge base can help us to deal with inconsistencies. Several semantic- and syntax-based approaches have been proposed separately. Given the pivotal role of argumentation in representing and handling inconsistency, in this paper, we use logical argumentation as a way to compute the inconsistency measure for propositional formulae. We show using the complete argumentation tree that our family of inconsistency measures is able to localise the conflict of a formula following its context and allows us to distinguish between formulae. We extend our measure to quantify the degree of inconsistency of a set of formulae and give a general formulation of the inconsistency using some logical properties. We also provide a general formulation of our method in order to quantify the conflict of the whole knowledge base. Finally, we address the problem of restoring consistency using inconsistency measures.