ASP for Minimal Entailment in a Rational Extension of SROEL

Abstract: In this paper we exploit Answer Set Programming (ASP) for reasoning in a rational extension SROEL-R-T of the low complexity description logic SROEL, which underlies the OWL EL ontology language. In the extended language, a typicality operator T is allowed to define concepts T(C) (typical C's) under a rational semantics. It has been proven that instance checking under rational entailment has a polynomial complexity. To strengthen rational entailment, in this paper we consider a minimal model semantics. We show that, for arbitrary SROEL-R-T knowledge bases, instance checking under minimal entailment is \Pi^P_2-complete. Relying on a Small Model result, where models correspond to answer sets of a suitable ASP encoding, we exploit Answer Set Preferences (and, in particular, the asprin framework) for reasoning under minimal entailment. The paper is under consideration for acceptance in Theory and Practice of Logic Programming.