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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Baader, F., McGuiness, D.L., Nardi, D., Patel-Schneider, P.: The Description Logic Handbook. Cambridge University Press, Cambridge (2003)
Calvanese, D., De Giacomo, G., Lenzerini, M.: On the decidability of query containment under constraints. In: Proc. of PODS 1998, pp. 149–158 (1998)
Calvanese, D., Giacomo, G.D., Lembo, D., Lenzerini, M., Rosati, R.: Data complexity of query answering in description logics. In: Proc. of KR 2006, pp. 260–270. AAAI Press, Menlo Park (2006)
Calvanese, D., Eiter, T., Ortiz, M.: Answering regular path queries in expressive description logics: an automata-theoretic approach. In: Proc. of AAAI 2007. AAAI Press, Menlo Park (2007)
Chandra, A.K., Kozen, D.C., Stockmeyer, L.J.: Alternation. Journal of the ACM 28(1), 114–133 (1981)
Glimm, B., Horrocks, I., Sattler, U.: Conjunctive query entailment for \(\mathcal{SHOQ}\). In: Proc. of DL 2007. CEUR-WS, vol. 250 (2007)
Glimm, B., Lutz, C., Horrocks, I., Sattler, U.: Answering conjunctive queries in the \(\mathcal{SHIQ}\) description logic. JAIR 31, 150–197 (2008)
Horrocks, I., Sattler, U., Tobies, S.: Practical reasoning for expressive description logics. In: Ganzinger, H., McAllester, D., Voronkov, A. (eds.) LPAR 1999. LNCS, vol. 1705, pp. 161–180. Springer, Heidelberg (1999)
Horrocks, I., Sattler, U., Tobies, S.: Reasoning with individuals for the description logic SHIQ. In: McAllester, D. (ed.) CADE 2000. LNCS, vol. 1831, pp. 482–496. Springer, Heidelberg (2000)
Horrocks, I., Tessaris, S.: A conjunctive query language for description logic ABoxes. In: Proc. of AAAI 2000. AAAI Press, Menlo Park (2000)
Hustadt, U., Motik, B., Sattler, U.: Data complexity of reasoning in very expressive description logics. In: Proc. of IJCAI 2005, pp. 466–471. Professional Book Center (2005)
Krötzsch, M., Rudolph, S., Hitzler, P.: Conjunctive queries for a tractable fragment of OWL 1.1. In: Aberer, K., Choi, K.-S., Noy, N., Allemang, D., Lee, K.-I., Nixon, L., Golbeck, J., Mika, P., Maynard, D., Mizoguchi, R., Schreiber, G., Cudré-Mauroux, P. (eds.) ISWC 2007. LNCS, vol. 4825, pp. 310–323. Springer, Heidelberg (2007)
Lutz, C.: The Complexity of Reasoning with Concrete Domains. PhD thesis, LuFG Theoretical Computer Science, RWTH Aachen, Germany (2002)
Lutz, C., Areces, C., Horrocks, I., Sattler, U.: Keys, nominals, and concrete domains. Journal of Artificial Intelligence Research (JAIR) 23, 667–726 (2005)
Lutz, C.: Inverse roles make conjunctive queries hard. In: Proc. of DL 2007, CEUR-WS vol. 250 (2007), http://lat.inf.tu-dresden.de/~clu/papers/
Lutz, C.: Two upper bounds for conjunctive query answering in \(\mathcal{SHIQ}\). In: Proc. of DL 2008, CEUR-WS (2008), http://lat.inf.tu-dresden.de/~clu/papers/
Ortiz, M., Calvanese, D., Eiter, T.: Characterizing data complexity for conjunctive query answering in expressive description logics. In: Proc. of AAAI 2006. AAAI Press, Menlo Park (2006)
Ortiz, M., Šimkus, M., Eiter, T.: Worst-case optimal conjunctive query answering for an expressive description logic without inverses. In: Proc. of AAAI 2008. AAAI Press, Menlo Park (2008)
Ortiz, M., Šimkus, M., Eiter, T.: Conjunctive query answering in \(\mathcal{SH}\) using knots. In: Proc. of DL 2008. CEUR WS (2008)
Schaerf, A.: On the complexity of the instance checking problem in concept languages with existential quantification. JIIS 2, 265–278 (1993)
Rosati, R.: On conjunctive query answering in \(\mathcal{EL}\). In: Proc. of DL 2007. CEUR-WS, vol. 250 (2007)
Tobies, S.: Complexity Results and Practical Algorithms for Logics in Knowledge Representation. PhD thesis, RWTH Aachen (2001)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lutz, C. (2008). The Complexity of Conjunctive Query Answering in Expressive Description Logics. In: Armando, A., Baumgartner, P., Dowek, G. (eds) Automated Reasoning. IJCAR 2008. Lecture Notes in Computer Science(), vol 5195. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71070-7_16
Download citation
DOI: https://doi.org/10.1007/978-3-540-71070-7_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71069-1
Online ISBN: 978-3-540-71070-7
eBook Packages: Computer ScienceComputer Science (R0)