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Conjunctive queries play an important role as an expressive query languagefor Description Logics (DLs). Although modern DLs usually provide fortransitive roles, conjunctive query answering over DL knowledge bases is onlypoorly understood if transitive roles are admitted in the query. In this paper,we consider unions of conjunctive queries over knowledge bases formulated inthe prominent DL SHIQ and allow transitive roles in both the query and theknowledge base. We show decidability of query answering in this setting andestablish two tight complexity bounds: regarding combined complexity, we provethat there is a deterministic algorithm for query answering that needs timesingle exponential in the size of the KB and double exponential in the size ofthe query, which is optimal. Regarding data complexity, we prove containment inco-NP.

Conjunctive Query Answering for the Description Logic SHIQ