Abstract
We study query answering in Description Logics (DLs). In particular, we consider conjunctive queries, unions of conjunctive queries, and their extensions with safe negation or inequality, which correspond to well-known classes of relational algebra queries. We provide a set of decidability, undecidability and complexity results for answering queries of the above languages over various classes of Description Logics knowledge bases. In general, such results show that extending standard reasoning tasks in DLs to answering relational queries is unfeasible in many DLs, even in inexpressive ones. In particular: (i) answering even simple conjunctive queries is undecidable in some very expressive DLs in which standard DL reasoning is decidable; (ii) in DLs where answering (unions of) conjunctive queries is decidable, adding the possibility of expressing safe negation or inequality leads in general to undecidability of query answering, even in DLs of very limited expressiveness. We also highlight the negative consequences of these results for the integration of ontologies and rules. We believe that these results have important implications for ontology-based information access, in particular for the design of query languages for ontologies.
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References
Abiteboul, S., Duschka, O.: Complexity of answering queries using materialized views (unpublished, manuscript, 1999) available at: ftp://ftp.inria.fr/INRIA/Projects/gemo/gemo/GemoReport-383.pdf
Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison Wesley Publ.Co, Reading (1995)
Baader, F., Brandt, S., Lutz, C.: Pushing the \(\mathcal{EL}\) envelope. In: Proc. of IJCAI 2005, pp. 364–369 (2005)
Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P.F. (eds.): The Description Logic Handbook: Theory, Implementation and Applications. Cambridge University Press, Cambridge (2003)
Berger, R.: The undecidability of the dominoe problem. Mem. Amer. Math. Soc. 66, 1–72 (1966)
Borgida, A.: On the relative expressiveness of description logics and predicate logics. Artificial Intelligence 82(1–2), 353–367 (1996)
Borgida, A., Lenzerini, M., Rosati, R.: Description logics for data bases. In: Baader, et al. (eds.) [5] ch.16, pp. 462–484
Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: DL-Lite: Tractable description logics for ontologies. In: Proc. of AAAI 2005, pp. 602–607 (2005)
Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Data complexity of query answering in description logics. In: Proc. of KR 2006 (2006)
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., Lenzerini, M., Nardi, D.: Unifying class-based representation formalisms. J. of Artificial Intelligence Research 11, 199–240 (1999)
Calvanese, D., Rosati, R.: Answering recursive queries under keys and foreign keys is undecidable. In: Proc. of KRDB 2003. CEUR Electronic Workshop Proceedings (2003), http://ceur-ws.org/Vol-79/
Glimm, B., Horrocks, I., Sattler, U.: Conjunctive query answering for description logics with transitive roles. In: Proc. of DL 2006, CEUR Electronic Workshop Proceedings (2006), http://ceur-ws.org/Vol-189
Grädel, E., Kolaitis, P.G., Vardi, M.Y.: On the decision problem for two-variable first-order logic. Bulletin of Symbolic Logic 3(1), 53–69 (1997)
Grau, B.C.: A possible simplification of the semantic web architecture. In: Proc. of the 13th Int. World Wide Web Conf (WWW 2004), pp. 704–713 (2004)
Horrocks, I., Tessaris, S.: Querying the Semantic Web: a formal approach. In: Horrocks, I., Hendler, J. (eds.) ISWC 2002. LNCS, vol. 2342, pp. 177–191. Springer, Heidelberg (2002)
Imielinski, T., L. Jr., W.: Incomplete information in relational databases. J. of the ACM 31(4), 761–791 (1984)
Lenzerini, M.: Data integration: A theoretical perspective. In: Proc. of PODS 2002, pp. 233–246 (2002)
Levy, A.Y., Rousset, M.-C.: Combining Horn rules and description logics in CARIN. Artificial Intelligence 104(1–2), 165–209 (1998)
Motik, B.: Reasoning in Description Logics using Resolution and Deductive Databases. PhD thesis, University of Karlsruhe (2005)
Ortiz, M.M., Calvanese, D., Eiter, T.: Characterizing data complexity for conjunctive query answering in expressive description logics. In: Proc. of AAAI 2006 (2006)
Ortiz, M.M., Calvanese, D., Eiter, T.: Data complexity of answering unions of conjunctive queries in \(\mathcal{SHIQ}\). In: Proc. of DL 2006, CEUR Electronic Workshop Proceedings (2006), http://ceur-ws.org/Vol-189
Patel-Schneider, P.F., Hayes, P.J., Horrocks, I., van Harmelen, F.: OWL web ontology language; semantics and abstract syntax. W3C candidate recommendation (November 2002), http://www.w3.org/tr/owl-semantics/
Rosati, R.: On the decidability and finite controllability of query processing in databases with incomplete information. In: Proc. of PODS 2006, pp. 356–365 (2006)
Sirin, E., Parsia, B.: Optimizations for answering conjunctive abox queries: First results. In: Proc. of DL 2006, CEUR Electronic Workshop Proceedings (2006), http://ceur-ws.org/Vol-189
Tessaris, S.: Questions and Answers: Reasoning and Querying in Description Logic. PhD thesis, University of Manchester, Department of Computer Science (April 2001)
Trahktenbrot, B.: Impossibility of an algorithm for the decision problem in finite classes. Transactions of the American Mathematical Society 3, 1–5 (1963)
van der Meyden, R.: The complexity of querying indefinite data about linearly ordered domains. J. of Computer and System Sciences 54(1), 113–135 (1997)
Vardi, M.Y.: The complexity of relational query languages. In: Proc. of STOC 1982, pp. 137–146 (1982)
Vardi, M.Y.: On the integrity of databases with incomplete information. In: Proc. of PODS 1982, pp. 252–266 (1982)
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Rosati, R. (2006). The Limits of Querying Ontologies. In: Schwentick, T., Suciu, D. (eds) Database Theory – ICDT 2007. ICDT 2007. Lecture Notes in Computer Science, vol 4353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11965893_12
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DOI: https://doi.org/10.1007/11965893_12
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