Towards Fast Atomic Decomposition using Axiom Dependency Hypergraphs

Atomic decomposition of ontologies has been suggested as a tool to understand the modular structure of ontologies. It consists of a polynomial size representation of potentially exponentially many modules of an ontology. Tractable algorithms for computing the atomic decomposition for locality-based modules have been introduced, albeit leaving room for improvement in terms of running time. In this paper, we consider ontologies formulated in OWL-EL. We introduce a notion of an axiom dependency hypergraph for an ontology, which represents how axioms are included in locality-based modules. We use a standard algorithm from graph theory to compute strongly connected components of the axiom dependency hypergraph and show that such components correspond to atoms of the ontology. An empirical evaluation of the algorithm on large fragments of biomedical ontologies confirms a significant improvement in running time.