Inconsistency Measurement based on Variables in Minimal Unsatisfiable Subsets

Measuring inconsistency degrees of knowledge bases (KBs) provides important context information for facilitating inconsistency handling. Several semantic and syntax based measures have been proposed separately. In this paper, we propose a new way to define inconsistency measurements by combining semantic and syntax based approaches. It is based on counting the variables of minimal unsatisfiable subsets (MUSes) and minimal correction subsets (MCSes), which leads to two equivalent inconsistency degrees, named IDMUS and IDMCS. We give the theoretical and experimental comparisons between them and two purely semantic-based inconsistency degrees: 4-valued and the Quasi Classical semantics based inconsistency degrees. Moreover, the computational complexities related to our new inconsistency measurements are studied. As it turns out that computing the exact inconsistency degrees is intractable in general, we then propose and evaluate an anytime algorithm to make IDMUS and IDMCS usable in knowledge management applications. In particular, as most of syntax based measures tend to be difficult to compute in reality due to the exponential number of MUSes, our new inconsistency measures are practical because the numbers of variables in MUSes are often limited or easily to be approximated. We evaluate our approach on the DC benchmark. Our encouraging experimental results show that these new inconsistency measurements or their approximations are efficient to handle large knowledge bases and to better distinguish inconsistent knowledge bases.