Abstract

Description Logics , a family of formalisms for reasoning about conceptual knowledge, can be extended with concrete domains to allow an adequate representation of “concrete qualities” of real-worlds entities such as their height, temperature, duration, and size. In this paper, we study the complexity of reasoning with the basic DL with concrete domains AℒC and its extension with so-called feature agreements and disagreements AℒCF. We show that, for both logics, the standard reasoning tasks concept satisfiability, concept subsumption, and ABox consistency are PSPACE-complete if the concrete domain D satisfies some natural conditions