Decidability of an Expressive Description Logic with Rational Grading

In this paper syntactic objects---concept constructors called part restrictions which realize rational grading are considered in Description Logics (DLs). Being able to convey statements about a rational part of a set of successors, part restrictions essentially enrich the expressive capabilities of DLs. We examine an extension of well-studied DL ALCQIHR+ with part restrictions, and prove that the reasoning in the extended logic is still decidable. The proof uses tableaux technique augmented with indices technique, designed for dealing with part restrictions.