ASP for minimal entailment in a rational extension of SROEL

In this paper we exploit Answer Set Programming (ASP) for reasoning in a rational extension SROEL (π ×)^R T of the low complexity description logic SROEL(âŠ", ×), 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(π ×)^R T knowledge bases, instance checking under minimal entailment is Π^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.