Reasoning with Concrete Domains

Abstract

Description logics are formalisms for the representation of and reasoning about conceptual knowledge on an abstract level. Concrete domains allow the integration of description logic reasoning with reasoning about concrete objects such as numbers, time intervals, or spatial regions. The importance of this combined approach, especially for building real-world applications, is widely accepted. However, the complexity of reasoning with concrete domains has never been formally analyzed and efficient algorithms have not been developed. This paper closes the gap by providing a tight bound for the complexity of reasoning with concrete domains and presenting optimal algorithms. 1 Introduction Description logics are knowledge representation and reasoning formalisms dealing with conceptual knowledge on an abstract logical level. However, for a variety of applications, it is essential to integrate the abstract knowledge with knowledge of a more concrete nature. Examples of such "co...