Towards Service Description Logics
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
Extending Datatype Support in Web Ontology Reasoning
On the Move to Meaningful Internet Systems, 2002 - DOA/CoopIS/ODBASE 2002 Confederated International Conferences DOA, CoopIS and ODBASE 2002
NEXPTIME-Complete Description Logics with Concrete Domains
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
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Description Logics (DLs) are well-suited for the representation of abstract conceptual knowledge. Concrete knowledge such as knowledge about numbers, time intervals, and spatial regions can be incorporated into DLs by using so-called concrete domains. The basic Description Logics providing concrete domains is ALC(D) which was introduced by Baader and Hanschke. Reasoning with ALC(D) concepts is known to be PSpace-complete if reasoning with the concrete domain D is in PSpace. In this paper, we consider the following three extensions of ALC(D) and examine the computational complexity of the resulting formalism: acyclic TBoxes inverse roles, and a role-forming predicate constructor. As lower bounds, we show that there exists a concrete domain P for which reasoning is in PTime such that reasoning with ALC(P) and any of the above extensions (separately) is NExpTime-hard. This is rather surprising since acyclic TBoxes and inverse roles are known to ``usually'''' not increase the complexity of reasoning. As a corresponding upper bound, we show that reasoning with ALC(D) and all of the above extensions (together) is in NExpTime if reasoning with the concrete domain D is in NP. For proving the lower bound, we introduce a NExpTime-complete variant of the Post Correspondence Problem and reduce it to the three logics under consideration. The upper bound is proved by giving a tableau algorithm.