On the measure of conflicts: an argumentation-based framework

Abstract

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.

Keywords:

• Deductive argumentation
• inconsistency measures
• propositional logic

Acknowledgements

This work is a revised and extended version of the conference paper (Raddaoui, 2015). The author is very grateful to the anonymous reviewers for making a number of important suggestions for improving the paper.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

This paper is a revised and extended version of the conference paper.