The Description Logic ALCN H R + Extended with Concrete Domains: A Practically Motivated Approach Volker Haarslev, Ralf M¨ oller and Michael Wessel University of Hamburg, Computer Science Department Vogt-K¨ olln-Str. 30, 22527 Hamburg, Germany Abstract. In this paper the description logic ALCNH R +(D) - is in- troduced. Prominent language features beyond conjunction, full nega- tion, and quantifiers are number restrictions, role hierarchies, transitively closed roles, generalized concept inclusions, and concrete domains. As in other languages based on concrete domains (e.g. ALC(D)) a so-called ex- istential predicate restriction is provided. However, compared to ALC(D) only features and no feature chains are allowed in this operator. This re- sults in a limited expressivity w.r.t. concrete domains but is required to ensure the decidability of the language. We show that the results can be exploited for building practical description logic systems for solving e.g. configuration problems. 1 Introduction In the field of knowledge representation, description logics (DLs) have been proven to be a sound basis for solving application problems. An application domain where DLs have been successfully applied is configuration (see [9] for an early publication). The main notions for domain modeling are concepts (unary predicates) and roles (binary predicates). Furthermore, a set of axioms (also called TBox) is used for modeling the terminology of an application. Knowledge about specific individuals and their interrelationships is modeled with a set of additional axioms (so-called ABox). Experiences with description logics in applications indicate that negation, existential and universal restrictions, transitive roles, role hierarchies, and num- ber restrictions are required to solve practical modeling problems without re- sorting to ad hoc extensions. A description logic which provides these language constructs is, for instance, ALCNH R + [5]. The optimized DL knowledge rep- resentation system RACE [4] provides an optimized implementation for ABox reasoning in ALCNH R +. With the optimized implementation of RACE, practi- cal systems based on description logics can be built. However, it is well-known that, in addition to the language constructs mentioned above, reasoning about objects from other domains (so-called concrete domains, e.g. for the reals) is very important for practical applications as well. In [1] the description logic ALC (D) is investigated and it is shown that, provided a decision procedure for the concrete