---
title: "Decidability of SHIQ with Complex Role Inclusion Axioms"
authors:
  - "Ian Horrocks"
  - "Ulrike Sattler"
doi: ""
url: "https://ijcai.org/proceedings/2003/51"
pdf: "https://ijcai.org/proceedings/2003/0051.pdf"
venue: "Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence"
year: 2003
pages: "343-347"
track: ""
keywords:
---

# Decidability of SHIQ with Complex Role Inclusion Axioms

Ian Horrocks, Ulrike Sattler

*Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence*, pages 343-347.

## Abstract

Motivated by medical terminology applications, we investigate the decidability of the well known expressive DL, SHIQ, extended with role inclusion axioms (RIAs) of the form R o S ~ P. We show that this extension is undecidable even when RIAs are restricted to the forms R o S ~ R or So R ~ R, but that decidability can be regained by further restricting RIAs to be acyclic. We present a tableau algorithm for this DL and report on its implementation, which behaves well in practise and provides important additional functionality in a medical terminology application.