Consequence−Based Reasoning beyond Horn Ontologies

Abstract

Consequence-based ontology reasoning procedures have so far been known only for Horn ontology languages. A difficulty in extending such procedures is that non-Horn axioms seem to require reasoning by case, which causes non-determinism in tableau-based procedures. In this paper we present a consequence-based procedure for ALCH that overcomes this difficulty by using rules similar to ordered resolution to deal with disjunctive axioms in a deterministic way; it retains all the favourable attributes of existing consequence-based procedures, such as goal-directed ``one pass'' classification, optimal worst-case complexity, and ``pay-as-you-go'' behaviour. Our preliminary empirical evaluation suggests that the procedure scales well to non-Horn ontologies.