Tableau-based decision procedures have been successfully used for solving a wide variety of problems. For some applications, nonetheless, it is desirable not only to obtain a Boolean answer, but also to detect the causes for such a result. In this report, a method for finding explanations on tableau-based procedures is explored, generalizing previous results on the field. The importance and use of the method is shown by means of examples.

Motivated by medical terminology applications, we investigate the decidability of an expressive and prominent DL, SHIQ, extended with role inclusion axioms of the form RoS⊑T. It is well-known that a naive such extension leads to undecidability, and thus we restrict our attention to axioms of the form RoS⊑R or SoR⊑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 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 behaves well in practise and provides important additional functionality in a medical terminology application.