A polynomial time subsumption algorithm for EL under rational closure

In this paper we consider Description Logics (DLs) under Rational Closure (RC), a well-known framework for non-monotonic reasoning in DLs. Specifically, we address the concept subsumption decision problem under RC for the DL ELâ?¥, a notable DL representative of the OWL profile OWL EL. Previous subsumption decision procedures for DLs under RC have been defined for more expressive DLs. These procedures, however, do not scale down in the sense that they remain exponential for ELâ?¥, even if the monotonic subsumption decision problem is polynomial. Our main contribution here is to define a polynomial time subsumption procedure for ELâ?¥ under RC. We also adapt it to known extensions of RC for DLs, such as Lexicographic Closure, Defeasible Inheritance-based DLs, and two versions of Relevant Closure. Since the basic language requirement is to have conjunction on the left-hand side of so-called Generalised Concept Inclusions, we show that our procedure can be adapted to any other DL having this feature as well.