Default logics for plausible reasoning with controversial axioms

Using a variant of Lehmann's Default Logics and Probabilistic Description Logics we recently presented a framework that invalidates those unwanted inferences that cause concept unsatisfiability without the need to remove explicitly stated axioms. The solutions of this methods were shown to outperform classical ontology repair w.r.t. the number of inferences invalidated. However, conflicts may still exist in the knowledge base and can make reasoning ambiguous. Furthermore, solutions with a minimal number of inferences invalidated do not necessarily minimize the number of conflicts. In this paper we provide an overview over finding solutions that have a minimal number of conflicts while invalidating as few inferences as possible. Specifically, we propose to evaluate solutions w.r.t. the quantity of information they convey by recurring to the notion of entropy and discuss a possible approach towards computing the entropy w.r.t. an ABox