Decidability of SHIQ with complex role inclusion axioms

Motivated by medical terminology applications, we investigate the decidability of an expressive and prominent description logic (DL), SHIQ, extended with role inclusion axioms of the form R ⊂ S ⊆̇ T. It is well known that a naive such extension leads to undecidability, and thus we restrict our attention to axioms of the form R ⊂ S ⊆̇ R or S ⊂ R ⊆̇ R, which is the most important form of axioms in the applications that motivated this extension. Surprisingly, this extension is still undecidable. However, it turns out that by restricting our attention further to acyclic sets of such axioms, we regain decidability. We present a tableau-based decision procedure for this DL and report on its implementation, which promises to behave well in practice and provides important additional functionality in a medical terminology application. © 2004 Elsevier B.V. All rights reserved.