Laconic and Precise Justifications in OWL

A justification for an entailment in an OWL ontology is a minimal subset of the ontology that is sufficient for that entailment to hold. Since justifications respect the syntactic form of axioms in an ontology, they are usually neither syntactically nor semantically minimal. This paper presents two new subclasses of justifications—laconic justifications and precise justifications. Laconic justifications only consist of axioms that do not contain any superfluous “parts”. Precise justifications can be derived from laconic justifications and are characterised by the fact that they consist of flat, small axioms, which facilitate the generation of semantically minimal repairs. Formal definitions for both types of justification are presented. In contrast to previous work in this area, these definitions make it clear as to what exactly “parts of axioms” are. In order to demonstrate the practicability of computing laconic, and hence precise justifications, an algorithm is provided and results from an empirical evaluation carried out on several published ontologies are presented. The evaluation showed that laconic/precise justifications can be computed in a reasonable time for entailments in a range of ontologies that vary in size and complexity. It was found that in half of the ontologies sampled there were entailments that had more laconic/precise justifications than regular justifications. More surprisingly it was observed that for some ontologies there were fewer laconic justifications than regular justifications.