# Defeasible Reasoning in SROEL: from Rational Entailment to Rational Closure

arXiv: https://arxiv.org/abs/1803.08885 · HTML: https://mlsanity.com/paper/1803.08885/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2018.

## Built on by (most cited first, 2 of 2)

- [Weighted Conditional EL{^}bot Knowledge Bases with Integer Weights: an ASP Approach](https://mlsanity.com/paper/2109.08286/) (2021)
- [A framework for Conditional Reasoning in Answer Set Programming](https://mlsanity.com/paper/2506.03997/) (2025)

## Abstract (arXiv)

In this work we study a rational extension SROELR 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 PiP2-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.