The Complexity of Conjunctive Query Answering in Expressive Description Logics

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 ALC and 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.

• Type: Conference
• Year: 2008
• Where: CADE
• Authors: Carsten Lutz
• Keywords: Automated Reasoning, CADE 2008, Conjunctive Query Answering, Long-standing Open Problem, Prominent Role