Axiom Dependency Hypergraphs for Fast Atomic Decomposition of Ontologies

In this paper we use directed hypergraphs to represent the locality-based dependencies between the axioms of an OWL ontology. We define a notion of an axiom dependency hypergraph, where axioms are represented as nodes and dependencies between axioms as hyperedges connecting possibly several nodes with one node. We show that a locality-based module of an ontology corresponds to a connected component in the hypergraph, and an atom of an ontology to a strongly connected component. Collapsing the strongly connected components into single nodes yields a condensed axiom dependency hypergraph, which contains the atomic decomposition of the ontology. To condense the axiom dependency hypergraph we exploit linear time graph algorithms on its graph fragment. This optimization can significantly reduce the time needed to compute the atomic decomposition of an ontology. We provide an experimental evaluation for computing the atomic decomposition of large biomedical ontologies, and for computing syntactic locality-based modules using the condensed axiom dependency hypergraph.