Finding justifications for an entailment in an OWL ontology is an important reasoning service in the development and maintenance of OWL ontologies. In this paper, we consider the problem of finding all the justifications of an entailment in description logic EL+, which underpins OWL 2 EL. Our method for computing all the justifications utilizes the classification result of an EL+ ontology by an OWL EL reasoner. We first give an algorithm for finding all the justifications of an entailment by constructing an explanation dependency graph from the entailment and the classification result. We then propose some pruning strategies to optimize this algorithm. We implement a prototype system by using the multi-core technology. The experimental results show that in many cases, our optimized algorithm outperforms an existing algorithm for finding all the justifications for an entailment in EL+ that is optimized with the module extraction technology.
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