Reasoning in a rational extension of SROEL

In this work we define a rational extension SROEL(∩,×)^R T of the low complexity description logic SROEL(∩,×), which underlies the OWL EL ontology language. The logic is extended with a typicality operator T, whose semantics is based on Lehmann and Magidor's ranked models and allows for the definition of defeasible inclusions.We consider both rational entailment and minimal entailment. We show that deciding instance checking under minimal entailment is a CONP-hard problem while, under rational entailment, instance checking can be computed in polynomial time. In particular, we develop a Datalog materialization calculus for instance checking under rational entailment.