Conjunctive query answering for the description logic SHIQ

Authors:
Birte Glimm;Ian Horrocks;Carsten Lutz;Uli Sattler
Affiliations:
School of Computer Science, University of Manchester, UK;School of Computer Science, University of Manchester, UK;Institute for Theoretical Computer Science, TU Dresden, Germany;School of Computer Science, University of Manchester, UK
Venue:
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Year:
2007

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Abstract

Conjunctive queries play an important role as an expressive query language for Description Logics (DLs). Although modern DLs usually provide for transitive roles, it was an open problem whether conjunctive query answering over DL knowledge bases is decidable if transitive roles are admitted in the query. In this paper, we consider conjunctive queries over knowledge bases formulated in the popular DL SHIQ and allow transitive roles in both the query and the knowledge base. We show that query answering is decidable and establish the following complexity bounds: regarding combined complexity, we devise a deterministic algorithm for query answering that needs time single exponential in the size of the KB and double exponential in the size of the query. Regarding data complexity, we prove co-NP-completeness.