In this paper we exploit Answer Set Programming (ASP) for reasoning in a rational extension SROEL (⊓,×)
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(⊓,×)
T knowledge bases, instance checking under minimal entailment is Π
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.