An Introduction to Description Logics and Query Rewriting

  • Roman Kontchakov
  • Michael Zakharyaschev
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8714)


This chapter gives an overview of the description logics underlying the OWL 2 Web Ontology Language and its three tractable profiles, OWL2 RL, OWL2EL and OWL 2QL. We consider the syntax and semantics of these description logics as well as main reasoning tasks and their computational complexity.We also discuss the semantical foundations for first-order and datalog rewritings of conjunctive queries over knowledge bases given in the OWL2 profiles, and outline the architecture of the ontology-based data access system Ontop.


Description Logic Canonical Model Conjunctive Query Datalog Program Concept Inclusion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley (1995)Google Scholar
  2. Arora, S., Barak, B.: Computational Complexity: A Modern Approach, 1st edn. Cambridge University Press, New York (2009)CrossRefzbMATHGoogle Scholar
  3. Artale, A., Calvanese, D., Kontchakov, R., Zakharyaschev, M.: The DL-Lite family and relations. Journal of Artificial Intelligence Research (JAIR) 36, 1–69 (2009)MathSciNetzbMATHGoogle Scholar
  4. Baader, F., Brandt, S., Lutz, C.: Pushing the EL envelope. In: Kaelbling, L.P., Saffiotti, A. (eds.) Proceedings of the 19th Int. Joint Conf. on Artificial Intelligence, IJCAI-2005, pp. 364–369. Professional Book Center (2005)Google Scholar
  5. Baader, F., Brandt, S., Lutz, C.: Pushing the EL envelope further. In: Clark, K., Patel-Schneider, P.F. (eds.) Proceedings of the OWLED 2008 DC Workshop on OWL: Experiences and Directions (2008)Google Scholar
  6. Baget, J.-F., Leclère, M., Mugnier, M.-L., Salvat, E.: On rules with existential variables: Walking the decidability line. Artificial Intelligence 175(9–10), 1620–1654 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  7. Brandt, S.: Polynomial time reasoning in a description logic with existential restrictions, GCI axioms, and—what else? In: Proc. of the 16th European Conf. on Artificial Intelligence, ECAI-2004, pp. 298–302. IOS Press (2004)Google Scholar
  8. Calì, A., Gottlob, G., Kifer, M.: Taming the infinite chase: Query answering under expressive relational constraints. J. of Artificial Intelligence Research 48, 115–174 (2013)MathSciNetzbMATHGoogle Scholar
  9. Calì, A., Gottlob, G., Lukasiewicz, T.: A general datalog-based framework for tractable query answering over ontologies. J. of Web Semantics 14, 57–83 (2012)CrossRefGoogle Scholar
  10. Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: DL-Lite: Tractable description logics for ontologies. In: Proc. of AAAI, pp. 602–607. AAAI Press / The MIT Press (2005)Google Scholar
  11. Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Data complexity of query answering in description logics. In: Proc. of the 10th Int. Conf. on the Principles of Knowledge Representation and Reasoning, KR 2006, pp. 260–270 (2006)Google Scholar
  12. Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Tractable reasoning and efficient query answering in description logics: The DL-Lite family. J. of Automated Reasoning 39(3), 385–429 (2007)Google Scholar
  13. Ceri, S., Gottlob, G., Tanca, L.: What you always wanted to know about datalog (and never dared to ask). IEEE Trans. Knowl. Data Eng. 1(1), 146–166 (1989)CrossRefGoogle Scholar
  14. Chagrov, A., Zakharyaschev, M.: Modal Logic. Oxford Logic Guides, vol. 35. Clarendon Press, Oxford (1997)zbMATHGoogle Scholar
  15. Chakravarthy, U.S., Fishman, D.H., Minker, J.: Semantic query optimization in expert systems and database systems. Benjamin-Cummings Publishing Co., Inc. (1986)Google Scholar
  16. Chortaras, A., Trivela, D., Stamou, G.: Optimized query rewriting for OWL 2 QL. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 192–206. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  17. Eiter, T., Lutz, C., Ortiz, M., Šimkus, M.: Query answering in description logics: The knots approach. In: Ono, H., Kanazawa, M., de Queiroz, R. (eds.) WoLLIC 2009. LNCS, vol. 5514, pp. 26–36. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  18. Eiter, T., Ortiz, M., Šimkus, M., Tran, T.-K., Xiao, G.: Query rewriting for Horn-SHIQ plus rules. In: Proc. of AAAI 2012. AAAI Press (2012)Google Scholar
  19. Elmasri, R., Navathe, S.: Fundamentals of Database Systems, 6th edn. Addison-Wesley (2010)Google Scholar
  20. Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman (1979)Google Scholar
  21. Gottlob, G., Kikot, S., Kontchakov, R., Podolskii, V.V., Schwentick, T., Zakharyaschev, M.: The price of query rewriting in ontology-based data access. Artificial Intelligence 213, 42–59 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  22. Gottlob, G., Orsi, G., Pieris, A.: Ontological queries: Rewriting and optimization. In: Proc. of ICDE 2011, pp. 2–13. IEEE Computer Society Press (2011)Google Scholar
  23. Grosof, B.N., Horrocks, I., Volz, R., Decker, S.: Description logic programs: Combining logic programs with description logic. In: Proc. of the 12th Int. World Wide Web Conference, WWW 2003, pp. 48–57 (2003)Google Scholar
  24. Horrocks, I., Kutz, O., Sattler, U.: The even more irresistible SROIQ. In: Proc. of the 10th Int. Conf. on Principles of Knowledge Representation and Reasoning, KR 2006, pp. 57–67. AAAI Press (2006)Google Scholar
  25. Horrocks, I., Motik, B., Wang, Z.: The HermiT OWL reasoner. In: Proc. of ORE, CEUR Workshop Proceedings, vol. 858, (2012)Google Scholar
  26. Johnson, D.S., Klug, A.C.: Testing containment of conjunctive queries under functional and inclusion dependencies. J. Comput. Syst. Sci. 28(1), 167–189 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  27. Kikot, S., Kontchakov, R., Podolskii, V., Zakharyaschev, M.: Exponential lower bounds and separation for query rewriting. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) ICALP 2012, Part II. LNCS, vol. 7392, pp. 263–274. Springer, Heidelberg (2012a)CrossRefGoogle Scholar
  28. Kikot, S., Kontchakov, R., Zakharyaschev, M.: Conjunctive query answering with OWL 2 QL. In: Proc. of KR 2012, AAAI Press (2012b)Google Scholar
  29. König, M., Leclère, M., Mugnier, M.-L., Thomazo, M.: A sound and complete backward chaining algorithm for existential rules. In: Krötzsch, M., Straccia, U. (eds.) RR 2012. LNCS, vol. 7497, pp. 122–138. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  30. Kontchakov, R., Lutz, C., Toman, D., Wolter, F., Zakharyaschev, M.: The combined approach to ontology-based data access. In: Proceedings of the 20th Int. Joint Conf. on Artificial Intelligence, IJCAI-2011, pp. 2656–2661. AAAI Press (2011)Google Scholar
  31. Kozen, D.: Theory of Computation. Springer (2006)Google Scholar
  32. Lenzerini, M.: Data integration: A theoretical perspective. In: Proc. of the 21st ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, PODS 2002, pp. 233–246. ACM (2002)Google Scholar
  33. Libkin, L.: Elements Of Finite Model Theory. Springer (2004)Google Scholar
  34. Lloyd, J., Shepherdson, J.: Partial Evaluation in Logic Programming. The Journal of Logic Programming 11(3-4), 217–242 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  35. Lutz, C., Seylan, İ., Toman, D., Wolter, F.: The combined approach to OBDA: Taming role hierarchies using filters. In: Alani, H., et al. (eds.) ISWC 2013, Part I. LNCS, vol. 8218, pp. 314–330. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  36. Lutz, C., Toman, D., Wolter, F.: Conjunctive query answering in the description logic EL using a relational database system. In: Proceedings of the 21st Int. Joint Conf. on Artificial Intelligence, IJCAI 2009, pp. 2070–2075 (2009)Google Scholar
  37. Lutz, C., Wolter, F.: Conservative extensions of the lightweight description logic EL. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 84–99. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  38. Motik, B.: On the properties of metamodeling in OWL. J. Log. Comput. 17(4), 617–637 (2007)Google Scholar
  39. Papadimitriou, C.: Computational Complexity. Addison-Wesley (1994)Google Scholar
  40. Pérez-Urbina, H., Motik, B., Horrocks, I.: A comparison of query rewriting techniques for DL-Lite. In: Proc. of DL 2009, vol. 477, CEUR-WS (2009)Google Scholar
  41. Pérez-Urbina, H., Rodríguez-Díaz, E., Grove, M., Konstantinidis, G., Sirin, E.: Evaluation of query rewriting approaches for OWL 2. In: Proc. of SSWS+HPCSW 2012, vol. 943, CEUR-WS (2012)Google Scholar
  42. Poggi, A., Lembo, D., Calvanese, D., De Giacomo, G., Lenzerini, M., Rosati, R.: Linking data to ontologies. J. on Data Semantics, X:133–X:173 (2008)Google Scholar
  43. Rodríguez-Muro, M., Calvanese, D.: Dependencies: Making ontology based data access work. In: Proc. of AMW 2011, vol. 749, (2011)Google Scholar
  44. Rodríguez-Muro, M., Kontchakov, R., Zakharyaschev, M.: Ontology-based data access: Ontop of databases. In: Alani, H., et al. (eds.) ISWC 2013, Part I. LNCS, vol. 8218, pp. 558–573. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  45. Rosati, R.: Prexto: Query rewriting under extensional constraints in DL-Lite. In: Simperl, E., Cimiano, P., Polleres, A., Corcho, O., Presutti, V. (eds.) ESWC 2012. LNCS, vol. 7295, pp. 360–374. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  46. Rosati, R., Almatelli, A.: Improving query answering over DL-Lite ontologies. In: Proc. of KR 2010. AAAI Press (2010)Google Scholar
  47. Schaerf, A.: On the complexity of the instance checking problem in concept languages with existential quantification. J. of Intelligent Information Systems 2, 265–278 (1993)MathSciNetCrossRefGoogle Scholar
  48. Sirin, E., Parsia, B., Cuenca Grau, B., Kalyanpur, A., Katz, Y.: Pellet: A practical OWL-DL reasoner. J. of Web Semantics 5(2), 51–53 (2007)CrossRefGoogle Scholar
  49. Steigmiller, A., Liebig, T., Glimm, B.: Konclude: System description. J. of Web Semantics (2014)Google Scholar
  50. ter Horst, H.J.: Completeness, decidability and complexity of entailment for RDF Schema and a semantic extension involving the OWL vocabulary. J. of Web Semantics 3(2-3), 79–115 (2005)CrossRefGoogle Scholar
  51. Tobies, S.: Complexity results and practical algorithms for logics in knowledge representation. PhD thesis, LuFG Theoretical Computer Science, RWTH-Aachen, Germany (2001)Google Scholar
  52. Tsarkov, D., Horrocks, I.: FaCT++ description logic reasoner: System description. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 292–297. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  53. Vardi, M.: The complexity of relational query languages (extended abstract). In: Proc. of the 14th ACM SIGACT Symp. on Theory of Computing, STOC 1982, pp. 137–146 (1982)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Roman Kontchakov
    • 1
  • Michael Zakharyaschev
    • 1
  1. 1.Department of Computer Science and Information SystemsBirkbeck, University of LondonU.K.

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