Knowledge base compilation for inconsistency measures

Measuring conflicts is recognized as an important issue for handling inconsistencies. Indeed, an inconsistency measure can be employed to support the knowledge engineer in building a consistent knowledge base or repairing an inconsistent one. Good measures are supposed to satisfy a set of rational properties. However, defining sound properties is sometimes problematic. In (Jabbour et al., 2014c), the authors proposed a new prime implicates based approach to identify the variables involved in the contradiction, and a refinement of the notion of minimal inconsistent subsets (MUSes) in propositional knowledge bases. In this article, we establish a bridge between the conflicting variables in knowledge bases and the three valued semantics by compiling each formula of the base into its prime implicates. We then extend hitting sets for MUSes to hitting sets of the set of deduced MUSes (DMUSes) based on prime implicates representation. This leads to an interesting family of inconsistency metrics.