A Polynomial Time Subsumption Algorithm for Nominal Safe $\mathcal{ELO}_\bot$ under Rational Closure

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 decisionproblem under RC for nominal safeELO⊥, a notable and practically important DL represen-tative of the OWL 2 profile OWL 2 EL.Our contribution here is to define a polynomial time subsumption procedure for nominalsafeELO⊥ under RC that relies entirely on a series of classical, monotonicEL⊥ subsumptiontests. Therefore, any existing classical monotonicEL⊥ reasoner can be used as a black boxto implement our method. We then also adapt the method to one of the known extensionsof RC for DLs, namely Defeasible Inheritance-based DLs without losing the computationaltractability.