A Polynomial Time Subsumption Algorithm for Nominal Safe ${\mathcal{E}\mathcal{L}\mathcal{O}}_{\perp }$ under Rational Closure

Abstract

Description Logics (DLs) under Rational Closure (RC) is a well-known framework for non-monotonic reasoning in DLs. In this paper, we address the concept subsumption decision problem under RC for nominal safe ${\mathcal{E}\mathcal{L}\mathcal{O}}_{\perp }$, a notable and practically important DL representative of the OWL 2 profile OWL 2 EL. Our contribution here is to define a polynomial time subsumption procedure for nominal safe ${\mathcal{E}\mathcal{L}\mathcal{O}}_{\perp }$ under RC that relies entirely on a series of classical, monotonic ${\mathcal{E}\mathcal{L}}_{\perp }$ subsumption tests. Therefore, any existing classical monotonic ${\mathcal{E}\mathcal{L}}_{\perp }$ reasoner can be used as a black box to implement our method. We then also adapt the method to one of the known extensions of RC for DLs, namely Defeasible Inheritance-based DLs without losing the computational tractability.