On the measure of conflicts: A MUS-Decomposition Based Framework

TL;DR

This paper introduces a novel MUS-decomposition framework for measuring inconsistency in knowledge bases, emphasizing decomposability, and enabling parallel inconsistency checking, with theoretical and experimental validation.

Contribution

It proposes an intuitive MUS-decomposition approach, including a distributable variant, and analyzes its properties and computational complexity for inconsistency measurement.

Findings

Distributable MUS-decomposition allows parallel inconsistency checking.

The proposed measure satisfies key rational properties.

Feasibility demonstrated through preliminary experiments.

Abstract

Measuring inconsistency is viewed as an important issue related to handling inconsistencies. Good measures are supposed to satisfy a set of rational properties. However, defining sound properties is sometimes problematic. In this paper, we emphasize one such property, named Decomposability, rarely discussed in the literature due to its modeling difficulties. To this end, we propose an independent decomposition which is more intuitive than existing proposals. To analyze inconsistency in a more fine-grained way, we introduce a graph representation of a knowledge base and various MUSdecompositions. One particular MUS-decomposition, named distributable MUS-decomposition leads to an interesting partition of inconsistencies in a knowledge base such that multiple experts can check inconsistencies in parallel, which is impossible under existing measures. Such particular MUSdecomposition results in an inconsistency measure that satisfies a number of desired properties. Moreover, we give an upper bound complexity of the measure that can be computed using 0/1 linear programming or Min Cost Satisfiability problems, and conduct preliminary experiments to show its feasibility.