The Description Logic ALCNHR+ Extended with Concrete Domains: A Practically Motivated Approach
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Reasoning with concrete domains
IJCAI'99 Proceedings of the 16th international joint conference on Artifical intelligence - Volume 1
Ontology RepresentationDesign Patterns and Ontologies that Make Sense
Proceedings of the 2009 conference on Ontology Representation: Design Patterns and Ontologies that Make Sense
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Description logics are knowledge representation and reasoning formalisms which represent conceptual knowledge on an abstract logical level. Concrete domains are a theoretically well-founded approach to the integration of description logic reasoning with reasoning about concrete objects such as numbers, time intervals or spatial regions. In this paper, the complexity of combined reasoning with description logics and concrete domains is investigated. We extend ALC(D), which is the basic description logic for reasoning with concrete domains, by the operators "feature agreement" and "feature disagreement". For the extended logic, called ALCF(D), an algorithm for deciding the ABox consistency problem is devised. The strategy employed by this algorithm is vital for the efficient implementation of reasoners for description logics incorporating concrete domains. Based on the algorithm, it is proved that the standard reasoning problems for both logics ALC(D) and (D) are PSpace-complete - provided that the satisfiability test of the concrete domain used is in PSpace.