Defeasible Reasoning in SROEL: from Rational Entailment to Rational Closure
This work addresses defeasible reasoning for ontology languages like OWL EL, providing efficient algorithms for rational entailment, but it is incremental as it builds on existing ranked models and logics.
The authors tackled the problem of defeasible reasoning in description logics by extending SROEL with a typicality operator, showing that instance checking under minimal entailment is Π^P_2-hard, while under rational entailment it can be computed in polynomial time.
In this work we study a rational extension $SROEL^R T$ of the low complexity description logic SROEL, which underlies the OWL EL ontology language. The extension involves 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 in general $Π^P_2$-hard, while, under rational entailment, instance checking can be computed in polynomial time. We develop a Datalog calculus for instance checking under rational entailment and exploit it, with stratified negation, for computing the rational closure of simple KBs in polynomial time.