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

Decidability of an Expressive Description Logic with Rational Grading