Ontology Materialization by Abstraction Refinement in Horn SHOIF

Abstraction refinement is a recently introduced technique which allows for reducing materialization of an ontology with a large ABox to materialization of a smaller (compressed) ‘abstraction’ of this ontology. Although this approach is sound for the very expressive language SROIQ, so far it was proved to be complete only for Horn ALCHOI ontologies. In this paper we propose an extension of this method that is now complete for Horn SHOIF ontologies. Supporting functional roles, in particular, is nontrivial due to the sophisticated interaction with nominals and inverse roles. Additionally, we show how to compute not only the concept-materialization but also the roleand equalitymaterialization. To show completeness we use a tailored set of materialization rules that loosely decouple the ABox from the TBox, which is intrinsically interesting as reasoning with nominals in general requires both ABox and TBox.