Diversity of reason: Equivalence relations over description logic explanations

Given the high expressivity of modern ontology languages, such as OWL, there is the possibility for great diversity in the logical content of ontologies. Informally, this can be seen by the constant evolution of reasoners to deal with new sorts of content and the range of optimisations reasoners need in order to be competitive. More formally, the fact that many naturally occurring entailments have multiple justifications (i.e., minimal entailing subsets) indicates that ontologies often overdetermine their consequences, indicating a diversity in supporting reasons. However, the multiplicity of justifications might be due mostly to diverse material, not formal, grounds for an entailment. That is, the logical form of these multiple reasons could be less diverse than their numbers suggest. In the present paper, we introduce and explore several equivalence relations over justifications for entailments of OWL ontologies. These equivalence relations range from strict isomorphism to a looser notions which cover similarities between justifications containing different concept expressions or possibly different numbers of axioms. We survey a corpus of ontologies from the bio-medical domain and find that large numbers of justifications can often be reduced to a significantly smaller set of justifications which are isomorphic with respect to one of the given definitions.