ASP for Minimal Entailment in a Rational Extension of SROEL
This work addresses theoretical complexity and practical reasoning challenges for ontology languages in AI, though it appears incremental as it builds on existing rational extensions.
The paper tackles the problem of reasoning under minimal entailment in the rational extension SROEL-R-T of description logic, showing that instance checking under this semantics is Π^P_2-complete and leveraging Answer Set Programming with preferences for implementation.
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 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. The paper is under consideration for acceptance in Theory and Practice of Logic Programming.