The Complexity of Conjunctive Query Answering in Expressive Description Logics

Authors:
Carsten Lutz
Affiliations:
Institut für Theoretische Informatik, TU Dresden, Germany
Venue:
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Year:
2008

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Abstract

Conjunctive query answering plays a prominent role in applications of description logics (DLs) that involve instance data, but its exact complexity was a long-standing open problem. We determine the complexity of conjunctive query answering in expressive DLs between $\mathcal{ALC}$ and $\mathcal{SHIQ}$, and thus settle the problem. In a nutshell, we show that conjunctive query answering is 2ExpTime-complete in the presence of inverse roles, and only ExpTime-complete without them.