Defeasible Reasoning in SROEL: from Rational Entailment to Rational Closure

TL;DR

This paper extends the description logic SROEL with a typicality operator to enable defeasible reasoning, providing complexity results and a Datalog-based method for efficient rational closure computation.

Contribution

It introduces a rational extension of SROEL with a typicality operator, analyzing complexity and proposing a Datalog calculus for rational closure in polynomial time.

Findings

Instance checking under rational entailment is polynomial-time computable.

Deciding instance checking under minimal entailment is $ ext{Pi}_2^P$-hard.

A Datalog calculus for rational closure is developed and efficient.

Abstract

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 $\Pi^P_2$-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.