The Impact of Transitive Closure on the Boolean Expressiveness of Navigational Query Languages on Graphs

  • George H. L. Fletcher
  • Marc Gyssens
  • Dirk Leinders
  • Jan Van den Bussche
  • Dirk Van Gucht
  • Stijn Vansummeren
  • Yuqing Wu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7153)


Several established and novel applications motivate us to study the expressive power of navigational query languages on graphs, which represent binary relations. Our basic language has only the operators union and composition, together with the identity relation. Richer languages can be obtained by adding other features such as other set operators, projection and coprojection, converse, and the diversity relation. In this paper, we show that, when evaluated at the level of boolean queries with an unlabeled input graph (i.e., a single relation), adding transitive closure to the languages with coprojection adds expressive power, while this is not the case for the basic language to which none, one, or both of projection and the diversity relation are added. In combination with earlier work [10], these results yield a complete understanding of the impact of transitive closure on the languages under consideration.


Source Node Directed Acyclic Graph Sink Node Target Node Transitive Closure 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
  2. 2.
    Abiteboul, S., Buneman, P., Suciu, D.: Data on the Web: From Relations to Semistructured Data and XML. Morgan Kaufmann (1999)Google Scholar
  3. 3.
    Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison Wesley, Reading (1995)zbMATHGoogle Scholar
  4. 4.
    Aho, A.V., Ullman, J.D.: The universality of data retrieval languages. In: Conference Record of the Sixth Annual ACM Symposium on Principles of Programming Languages, San Antonio, Texas, pp. 110–120 (January 1979)Google Scholar
  5. 5.
    Angles, R., Gutiérrez, C.: Survey of graph database models. ACM Comput. Surv. 40(1), 1–39 (2008)CrossRefGoogle Scholar
  6. 6.
    Baader, F., Calvanese, D., McGuiness, D., Nardi, D., Patel-Schneider, P. (eds.): The Description Logic Handbook. Cambridge University Press (2003)Google Scholar
  7. 7.
    Benedikt, M., Fan, W., Kuper, G.M.: Structural Properties of XPath Fragments. In: Calvanese, D., Lenzerini, M., Motwani, R. (eds.) ICDT 2003. LNCS, vol. 2572, pp. 79–95. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  8. 8.
    Bizer, C., Heath, T., Berners-Lee, T.: Linked data - the story so far. Int. J. Semantic Web Inf. Syst. 5(3), 1–22 (2009)CrossRefGoogle Scholar
  9. 9.
    Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press (2001)Google Scholar
  10. 10.
    Fletcher, G.H.L., Gyssens, M., Leinders, D., Van den Bussche, J., Van Gucht, D., Vansummeren, S., Wu, Y.: Relative expressive power of navigational querying on graphs. In: Milo, T. (ed.) ICDT, pp. 197–207. ACM (2011)Google Scholar
  11. 11.
    Florescu, D., Levy, A., Mendelzon, A.: Database techniques for the World-Wide Web: A survey. SIGMOD Record 27(3), 59–74 (1998)CrossRefGoogle Scholar
  12. 12.
    Franklin, M.J., Halevy, A.Y., Maier, D.: From databases to dataspaces: a new abstraction for information management. SIGMOD Record 34(4), 27–33 (2005)CrossRefGoogle Scholar
  13. 13.
    Gyssens, M., Paredaens, J., Van Gucht, D., Fletcher, G.H.L.: Structural characterizations of the semantics of XPath as navigation tool on a document. In: Vansummeren, S. (ed.) PODS, pp. 318–327. ACM (2006)Google Scholar
  14. 14.
    Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. MIT Press (2000)Google Scholar
  15. 15.
    Heath, T., Bizer, C.: Linked Data: Evolving the Web into a Global Data Space, 1st edn. Synthesis Lectures on the Semantic Web: Theory and Technology, vol. 1. Morgan & Claypool Publishers (February 2011)Google Scholar
  16. 16.
    Libkin, L.: Elements of Finite Model Theory. Springer, Berlin (2004)CrossRefzbMATHGoogle Scholar
  17. 17.
    Maddux, R.D.: Relation Algebras. Elsevier, Amsterdam (2006)zbMATHGoogle Scholar
  18. 18.
    Mamoulis, N.: Efficient processing of joins on set-valued attributes. In: Proceedings ACM SIGMOD International Conference on Management of Data, pp. 157–168 (2003)Google Scholar
  19. 19.
    Marx, M., Venema, Y.: Multi-Dimensional Modal Logic. Springer, Heidelberg (1997)CrossRefzbMATHGoogle Scholar
  20. 20.
    Marx, M.: Conditional XPath. ACM Trans. Database Syst. 30(4), 929–959 (2005)CrossRefGoogle Scholar
  21. 21.
    Marx, M., de Rijke, M.: Semantic characterizations of navigational XPath. SIGMOD Record 34(2), 41–46 (2005)CrossRefGoogle Scholar
  22. 22.
    Pratt, V.R.: Origins of the calculus of binary relations. In: Proceedings 7th Annual IEEE Symposium on Logic in Computer Science, pp. 248–254 (1992)Google Scholar
  23. 23.
    Tarski, A.: On the calculus of relations. J. of Symbolic Logic 6(3), 73–89 (1941)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Tarski, A., Givant, S.: A Formalization of Set Theory without Variables. American Mathematical Society (1987)Google Scholar
  25. 25.
    Wu, Y., Van Gucht, D., Gyssens, M., Paredaens, J.: A study of a positive fragment of Path queries: Expressiveness, normal form and minimization. Comput. J. 54(7), 1091–1118 (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • George H. L. Fletcher
    • 1
  • Marc Gyssens
    • 2
  • Dirk Leinders
    • 2
  • Jan Van den Bussche
    • 2
  • Dirk Van Gucht
    • 3
  • Stijn Vansummeren
    • 4
  • Yuqing Wu
    • 3
  1. 1.Eindhoven University of TechnologyThe Netherlands
  2. 2.School for Information TechnologyHasselt University and Transnational University of LimburgBelgium
  3. 3.Indiana UniversityUSA
  4. 4.Université Libre de BruxellesBelgium

Personalised recommendations