Implication and Axiomatization of Functional Constraints on Patterns with an Application to the RDF Data Model

  • Jelle Hellings
  • Marc Gyssens
  • Jan Paredaens
  • Yuqing Wu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8367)

Abstract

Akhtar et al. introduced equality-generating constraints and functional constraints as an initial step towards dependency-like integrity constraints for RDF data [1]. Here, we focus on functional constraints. The usefulness of functional constraints is not limited to the RDF data model. Therefore, we study the functional constraints in the more general setting of relations with arbitrary arity. We show that a chase algorithm for functional constraints can be normalized to a more specialized symmetry-preserving chase algorithm. This symmetry-preserving chase algorithm is subsequently used to construct a sound and complete axiomatization for the functional constraints. This axiomatization is in particular applicable in the RDF data model, solving a major open problem of Akhtar et al.

Keywords

functional constraints chase algorithm axiomatization 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Akhtar, W., Cortés-Calabuig, Á., Paredaens, J.: Constraints in RDF. In: Schewe, K.-D., Thalheim, B. (eds.) SDKB 2010. LNCS, vol. 6834, pp. 23–39. Springer, Heidelberg (2011)Google Scholar
  2. 2.
    Codd, E.F.: Relational completeness of data base sublanguages. Technical Report RJ 987, IBM Research Laboratory, San Jose, California (1972)Google Scholar
  3. 3.
    Codd, E.F.: Recent investigations in relational data base systems. Information Processing 74, 1017–1021 (1974)Google Scholar
  4. 4.
    Beeri, C., Vardi, M.: The implication problem for data dependencies. In: Even, S., Kariv, O. (eds.) Automata, Languages and Programming. LNCS, vol. 115, pp. 73–85. Springer, Heidelberg (1981)CrossRefGoogle Scholar
  5. 5.
    Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley (1995)Google Scholar
  6. 6.
    Lausen, G., Meier, M., Schmidt, M.: SPARQLing constraints for RDF. In: Proceedings of the 11th International Conference on Extending Database Technology: Advances in Database Technology, EDBT 2008, pp. 499–509 (2008)Google Scholar
  7. 7.
    Hartmann, S., Link, S.: More functional dependencies for XML. In: Advances in Databases and Information Systems. In: Kalinichenko, L., Manthey, R., Thalheim, B., Wloka, U. (eds.) ADBIS 2003. LNCS, vol. 2798, pp. 355–369. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Buneman, P., Davidson, S., Fan, W., Hara, C., Tan, W.C.: Keys for XML. Computer Networks 39(5), 473–487 (2002)CrossRefGoogle Scholar
  9. 9.
    Hartmann, S., Link, S.: Efficient reasoning about a robust XML key fragment. ACM Transactions on Database Systems 34(2), 10:1–10:33 (2009)Google Scholar
  10. 10.
    Vincent, M.W., Liu, J., Mohania, M.: The implication problem for ‘closest node’ functional dependencies in complete XML documents. Journal of Computer and System Sciences 78(4), 1045–1098 (2012)CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Arenas, M., Libkin, L.: A normal form for XML documents. ACM Transactions on Database Systems 29(1), 195–232 (2004)CrossRefGoogle Scholar
  12. 12.
    Calbimonte, J.P., Porto, F., Keet, C.M.: Functional dependencies in OWL ABOX. In: XXIV Simpósio Brasileiro de Banco de Dados, pp. 16–30 (2009)Google Scholar
  13. 13.
    Yu, Y., Heflin, J.: Extending functional dependency to detect abnormal data in RDF graphs. In: Aroyo, L., Welty, C., Alani, H., Taylor, J., Bernstein, A., Kagal, L., Noy, N., Blomqvist, E. (eds.) ISWC 2011, Part I. LNCS, vol. 7031, pp. 794–809. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  14. 14.
    Cortés-Calabuig, A., Paredaens, J.: Semantics of constraints in RDFS. In: Proceedings of the 6th Alberto Mendelzon International Workshop on Foundations of Data Management, pp. 75–90 (2012)Google Scholar
  15. 15.
    Fagin, R.: Horn clauses and database dependencies. Journal of the ACM 29(4), 952–985 (1982)CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Wijsen, J.: Database repairing using updates. ACM Transactions on Database Systems 30(3), 722–768 (2005)CrossRefGoogle Scholar
  17. 17.
    Fan, W., Geerts, F., Jia, X., Kementsietsidis, A.: Conditional functional dependencies for capturing data inconsistencies. ACM Transactions on Database Systems 33(2), 6:1–6:48 (2008)Google Scholar
  18. 18.
    He, Q., Ling, T.W.: Extending and inferring functional dependencies in schema transformation. In: Proceedings of the Thirteenth ACM International Conference on Information and Knowledge Management, CIKM 2004, pp. 12–21. ACM (2004)Google Scholar
  19. 19.
    Armstrong, W.W.: Dependency structures of data base relationships. Information Processing 74, 580–583 (1974)MathSciNetGoogle Scholar
  20. 20.
    Aho, A.V., Beeri, C., Ullman, J.D.: The theory of joins in relational databases. ACM Transactions on Database Systems 4(3), 297–314 (1979)CrossRefGoogle Scholar
  21. 21.
    Beeri, C., Vardi, M.Y.: A proof procedure for data dependencies. Journal of the ACM 31(4), 718–741 (1984)CrossRefMATHMathSciNetGoogle Scholar
  22. 22.
    Beeri, C., Fagin, R., Howard, J.H.: A complete axiomatization for functional and multivalued dependencies in database relations. In: Proceedings of the 1977 ACM SIGMOD International Conference on Management of Data, SIGMOD 1977, pp. 47–61 (1977)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Jelle Hellings
    • 1
  • Marc Gyssens
    • 1
  • Jan Paredaens
    • 2
  • Yuqing Wu
    • 3
  1. 1.Hasselt University and Transnational University of LimburgBelgium
  2. 2.University of AntwerpBelgium
  3. 3.Indiana UniversityUSA

Personalised recommendations