Advertisement

Theory of Computing Systems

, Volume 61, Issue 2, pp 464–493 | Cite as

Bounds in Ontology-Based Data Access via Circuit Complexity

  • Vladimir V. Podolskii
Article

Abstract

Ontology-based data access is an approach to organizing access to a database augmented with a logical theory. In this approach query answering proceeds through a reformulation of a given query into a new one that can be answered without any use of theory. Thus the problem reduces to the standard database setting. However, the size of the query may increase substantially during the reformulation. In this survey we review a recently developed framework on proving lower and upper bounds on the size of this reformulation by employing methods and results from Boolean Circuit Complexity. The survey does not assume from the reader any prior knowledge on ontology-based data access.

Keywords

Ontology-based data access Boolean circuits 

Notes

Acknowledgments

The author is grateful to Michael Zakharyaschev, Mikhail Vyalyi, Evgeny Zolin, Stanislav Kikot and the anonymous reviewer for helpful comments on the preliminary version of this survey.

References

  1. 1.
    Afrati, F., Cosmadakis, S., Yannakakis, M.: On datalog vs polynomial time. J. Comput. Syst. Sci. 51(2), 177–196 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Ajtai, M.: \({{\Sigma }_{1}^{1}}\)-formulae on finite structures. Ann. Pure Appl. Logic 24(1), 1–48 (1983)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Alon, N., Boppana, R.: The monotone circuit complexity of Boolean functions. Combinatorica 7(1), 1–22 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Artale, A., Calvanese, D., Kontchakov, R., Zakharyaschev, M.: The DL-Lite family and relations. J. Artif. Intell. Res. 36, 1–69 (2009)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Baget, J.-F., Leclère, M., Mugnier, M.-L., Salvat, E.: Extending decidable cases for rules with existential variables. In: Proc. of the 21st Int. Joint Conf. on Artificial Intelligence (IJCAI 2009), pages 677–682. IJCAI (2009)Google Scholar
  6. 6.
    Bienvenu, M., Kikot, S., Kontchakov, R., Podolskii, V., Zakharyaschev, M.: Ontology-mediated queries: Combined complexity and succinctness of rewritings via circuit complexity. Manuscript. arXiv:1605.01207 (2016)
  7. 7.
    Bienvenu, M., Kikot, S., Podolskii, V. V.: Tree-like queries in OWL 2 QL: succinctness and complexity results. In: 30th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2015, Kyoto, Japan July 6-10, 2015, pages 317–328 (2015)Google Scholar
  8. 8.
    Calì, A, Gottlob, G., Lukasiewicz, T.: A general datalog-based framework for tractable query answering over ontologies. J. Web Semantics 14, 57–83 (2012)CrossRefGoogle Scholar
  9. 9.
    Calì, A., Gottlob, G., Pieris, A.: Advanced processing for ontological queries. PVLDB 3(1), 554–565 (2010)Google Scholar
  10. 10.
    Calì, A, Gottlob, G., Pieris, A.: Towards more expressive ontology languages: The query answering problem. Artif. Intell. 193, 87–128 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: DL-Lite: Tractable description logics for ontologies. In: Proc. of the 20th Nat. Conf. on Artificial Intelligence (AAAI 2005), pages 602–607. AAAI Press (2005)Google Scholar
  12. 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. Autom. Reason. 39(3), 385–429 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Cover, T.M., Thomas, J.A.: Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing). Wiley-Interscience (2006)Google Scholar
  14. 14.
    Dolby, J., Fokoue, A., Kalyanpur, A., Ma, L., Schonberg, E., Srinivas, K., Sun, X.: Scalable grounded conjunctive query evaluation over large and expressive knowledge bases. In: In Proc. of the 7th Int. Semantic Web Conf. (ISWC 2008), volume 5318 of Lecture Notes in Computer Science, pages 403–418. Springer (2008)Google Scholar
  15. 15.
    Fagin, R., Kolaitis, P.G., Miller, R.J., Popa, L.: Data exchange: semantics and query answering. Theor. Comput. Sci. 336(1), 89–124 (2005). Database TheoryMathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Furst, M., Saxe, J.B., Sipser, M.: Parity, circuits, and the polynomial-time hierarchy. Math. Syst. Theory 17(1), 13–27Google Scholar
  17. 17.
    Gottlob, G., Kikot, S., Kontchakov, R., Podolskii, V. V., Schwentick, T., Zakharyaschev, M.: The price of query rewriting in ontology-based data access. Artif. Intell. 213, 42–59 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Grigni, M., Sipser, M.: Monotone separation of logarithmic space from logarithmic depth. J. Comput. Syst. Sci. 50(3), 433–437 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Håstad, J.: Almost optimal lower bounds for small depth circuits. In: RANDOMNESS AND COMPUTATION, pages 6–20. JAI Press (1989)Google Scholar
  20. 20.
    Heymans, S., Ma, L., Anicic, D., Ma, Z., Steinmetz, N., Pan, Y., Mei, J., Fokoue, A., Kalyanpur, A., Kershenbaum, A., Schonberg, E., Srinivas, K., Feier, C., Hench, G., Wetzstein, B., Keller, U.: Ontology reasoning with large data repositories (2008)Google Scholar
  21. 21.
    Immerman, N.: Nondeterministic space is closed under complementation. In: Proceedings: Third Annual Structure in Complexity Theory Conference, Georgetown University, Washington, D. C., USA, June 14-17 1988 pages 112–115 (1988)Google Scholar
  22. 22.
    Jukna, S.: Boolean Function Complexity: Advances and Frontiers. Springer (2012)Google Scholar
  23. 23.
    Karchmer, M., Wigderson, A.: Monotone circuits for connectivity require super-logarithmic depth. In: Proc. of the 20th Annual ACM Symposium on Theory of Computing (STOC’88), pages 539–550. ACM (1988)Google Scholar
  24. 24.
    Kikot, S., Kontchakov, R., Podolskii, V.V., Zakharyaschev, M.: Exponential lower bounds and separation for query rewriting. In: Automata, Languages, and Programming - 39th International Colloquium, ICALP 2012, Warwick, UK, July 9-13, 2012, Proceedings, Part II pages 263–274 (2012)Google Scholar
  25. 25.
    Kikot, S., Kontchakov, R., Podolskii, V.V., Zakharyaschev, M.: On the succinctness of query rewriting over shallow ontologies. In: Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), CSL-LICS ’14, Vienna, Austria, July 14 - 18, 2014, pages 57 (2014)Google Scholar
  26. 26.
    Kikot, S., Kontchakov, R., Zakharyaschev, M.: On (in)tractability of OBDA with OWL 2 QL. In: Proceedings of the 24th International Workshop on Description Logics (DL 2011), Barcelona, Spain, July, 13-16, 2011, pp. 224–234Google Scholar
  27. 27.
    Kolaitis, P.G.: Schema mappings, data exchange, and metadata management. In: Proceedings of the Twenty-fourth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, PODS ’05, pages 61–75, New York, NY, USA, 2005. ACMGoogle Scholar
  28. 28.
    Kontchakov, R., Zakharyaschev, M.: An introduction to description logics and query rewriting. In: Koubarakis, M., Stamou, G., Stoilos, G., Horrocks, I., Kolaitis, P., Lausen, G., Weikum, G. (eds.) Reasoning Web. Reasoning on the Web in the Big Data Era, volume 8714 of Lecture Notes in Computer Science, pages 195–244. Springer International Publishing (2014)Google Scholar
  29. 29.
    Kowalski, R.A.: The early years of logic programming. Commun. ACM 31(1), 38–43 (1988)CrossRefGoogle Scholar
  30. 30.
    Lenzerini, M.: Data integration: A theoretical perspective. In: Proceedings of the Twenty-first ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, PODS ’02, pages 233–246, New York, NY, USA, 2002. ACMGoogle Scholar
  31. 31.
    Motik, B., Cuenca Grau, B., Horrocks, I., Wu, Z., Fokoue, A., Lutz, C.: OWL 2 Web Ontology Language profiles. W3C Recommendation, vol. 11. http://www.w3.org/TR/owl2-profiles/. (2012)
  32. 32.
    Podolskii, V.V.: Circuit complexity meets ontology-based data access. In: Computer Science - Theory and Applications - 10th International Computer Science Symposium in Russia, CSR 2015, Listvyanka, Russia, July 13-17, 2015, Proceedings, pages 7–26 (2015)Google Scholar
  33. 33.
    Poggi, A., Lembo, D., Calvanese, D., De Giacomo, G., Lenzerini, M., Rosati, R.: Linking data to ontologies. J. Data Semantics, 133–173 (2008)Google Scholar
  34. 34.
    Razborov, A.: Lower bounds for the monotone complexity of some Boolean functions. Dokl. Akad. Nauk SSSR 281(4), 798–801 (1985)MathSciNetzbMATHGoogle Scholar
  35. 35.
    Razborov, A.: Lower bounds for deterministic and nondeterministic branching programs. In: Proc. of the 8th Int. Symposium on Fundamentals of Computation Theory (FCT’91), volume 529 of Lecture Notes in Computer Science, pages 47–60. Springer (1991)Google Scholar
  36. 36.
    Szelepcsényi, R.: The moethod of focing for nondeterministic automata. Bulletin of the EATCS 33, 96–99 (1987)zbMATHGoogle Scholar
  37. 37.
    Ullman, J.D.: Principles of Database and Knowledge-base Systems, vol. I. Computer Science Press, Inc., New York (1988)Google Scholar
  38. 38.
    Vollmer, H.: Introduction to Circuit Complexity: A Uniform Approach. Springer (1999)Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteMoscowRussia

Personalised recommendations