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**1 - 2**of**2**### Axiom Dependency Hypergraphs for Fast Modularisation and Atomic Decomposition

"... Abstract. 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 hyper-edges connecting possibly sever ..."

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Abstract. 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 hyper-edges connecting possibly several nodes with one node. We show that a locality-based module of an ontology corresponds to a connected compo-nent in the hypergraph, and an atom of an ontology to a strongly con-nected 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 ax-iom 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. 1

### IOS Press HyS: Fast Atomic Decomposition and Module Extraction of OWL-EL ontologies

"... Abstract. In this paper, we present HyS, an application for fast atomic decomposition and module extraction of OWL-EL ontologies. HyS computes a hypergraph representation of the modular structure of an ontology. This hypergraph representation contains the atomic decomposition of the input ontology, ..."

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Abstract. In this paper, we present HyS, an application for fast atomic decomposition and module extraction of OWL-EL ontologies. HyS computes a hypergraph representation of the modular structure of an ontology. This hypergraph representation contains the atomic decomposition of the input ontology, and it allows to extract modules for a given signature. We provide an experimental evaluation of HyS with a selection of large and prominent biomedical ontologies, most of which are available in the NCBO Bioportal.