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 decision problem under RC for nominal safe
$\mathcal{ELO}_\bot$, 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 $\mathcal{ELO}_\bot$ under RC that relies entirely on a series
of classical, monotonic $\mathcal{EL}_\bot$ subsumption tests. Therefore, any
existing classical monotonic $\mathcal{EL}_\bot$ 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.
