Explaining justifications in OWL DL ontologies

Building domain ontologies such as the SNOMED CT requires a significant amount of effort and expertise. Among supporting tools for building such ontologies are tableaux-based reasoners [21, 19] which can help with detecting inconsistencies or computing implicit statements (i.e. entailments) following from ontologies. They do, however, have a downside: it is difficult to explain their reasoning to human ontology developers as they depend on a refutation proof strategy and unintuitive normalising transformations [2]. Therefore, we aim to develop a computational approach to generating explanations for inconsistencies and undesirable entailments in order to support ontology debugging. Recently there has been an increasing interest in justifications for entailments and inconsistencies [11, 20, 7]. A justification for an entailment is a minimal set of axioms, drawn from the ontology, that causes the entailment to arise. For logicians, a justification is a form of explanation [11]. Human domain experts do, however, require further explanations of the semantics of each axiom and the inference process linking axioms to the entailment [18]. This is because they usually lack understanding of OWL and formal logic [4]. Let us give an example. Assuming a justification for an unwanted entailment Animal ≡ > includes three axioms: (1) Old lady ≡ ∀has pet.Cat, (2) Domain(has pet) = Animal, and (3) Old lady v Animal. We may provide an explanation as the following: