# ASP for Minimal Entailment in a Rational Extension of SROEL

arXiv: https://arxiv.org/abs/1608.02450 · HTML: https://mlsanity.com/paper/1608.02450/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Aug 2016.

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

- [A Rational Entailment for Expressive Description Logics via Description Logic Programs](https://mlsanity.com/paper/2107.06075/) (2021)
- [A framework for Conditional Reasoning in Answer Set Programming](https://mlsanity.com/paper/2506.03997/) (2025)

## Abstract (arXiv)

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 PiP2-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.