Knowledge Base Compilation for Inconsistency Measures

Abstract

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.

MaxSAT-Based Inconsistency Measurement

“…However, when dealing with knowledge bases consisting of propositional logic formulas, a natural choice of the declarative paradigm as a basis for developing increasingly effective algorithmic approaches to inconsistency measurement would seem to be SAT, building on the extraordinary success of SAT solvers [29] as "realworld NP oracles" as a key to efficiently find solutions of various decision and optimization problems. First SAT-based approaches have been recently proposed for inconsistency measurement [23,24,21]. However, for the various inconsistency measures we consider in this work, they have been shown to be outperformed by the ASP-based approaches.…”