A Polynomial Time Subsumption Algorithm for Nominal Safe $\mathcal{ELO}_\bot$ under Rational Closure
This provides an efficient solution for non-monotonic reasoning in a practically important logic, enabling use with existing reasoners, though it is incremental as it builds on known frameworks.
The paper tackles the concept subsumption decision problem under Rational Closure for nominal safe $\mathcal{ELO}_ot$, a Description Logic used in OWL 2 EL, by developing a polynomial-time procedure that uses classical monotonic $\mathcal{EL}_ot$ subsumption tests as a black box.
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.