Reasoning in expressive description logics with fixpoints based on automata on infinite trees

In the last years, the investigation on Description Logics (DLs) has been driven by the goal of applying them in several areas, such as, software engineering, information systems, databases, information integration, and intelligent access to the web. The modeling requirements arising in the above areas have stimulated the need for very rich languages, including fixpoint constructs to represent recursive structures. We study a DL comprising the most general form of fixpoint constructs on concepts, all classical concept forming constructs, plus inverse roles, n-ary relations, qualified number restrictions, and inclusion assertions. We establish the EXPTIME decidability of such logic by presenting a decision procedure based on a reduction to nonemptiness of alternating automata on infinite trees. We observe that this is the first decidability result for a logic combining inverse roles, number restrictions, and general fixpoints.