Using boundary method for extraction of axiom-based module in EL⁺⁺ ontologies

Modularization is a promising technique to meet the scalability challenge in reasoning with very large ontologies. In this paper, a novel axiom-based module extraction approach by using boundary method is introduced for EL⁺⁺ ontologies. The proposed method is capable of identifying relevant axioms in an ontology based on the notion of boundaries of symbols, with respect to a given reasoning task. We present definitions and propositions relevant to boundary of symbols. Based on the formulization, we proved that axiom-based modules extracted by using boundary method are correct for the reasoning task. A practical algorithm for computing axiom-based modules by using boundary method is given and implemented for EL⁺⁺. Experimental results on real-world ontologies show that axiom-based modules generated by our method are very close to the optimal result, the average size of our module is less than double size of the optimal one; the extraction process has good run-time performance, and it can be accomplished in about one second when the extracted ontology is on the scale of 1 × 10⁴. Therefore, module extraction by using boundary method is suitable for optimizing ontology reasoning.