Definability for Downward and Vertical XPath on Data Trees

  • Sergio Abriola
  • María Emilia Descotte
  • Santiago Figueira
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8652)

Abstract

We study the expressive power of the downward and vertical fragments of XPath equipped with (in)equality tests over data trees. We give necessary and sufficient conditions for a class of pointed data trees to be definable by a set of formulas or by a single formula of each of the studied logics. To do so, we introduce a notion of saturation, and show that over saturated data trees bisimulation coincides with logical equivalence.

Keywords

XPath data tree bisimulation definability first-order logic ultraproduct saturation 

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References

  1. 1.
    Areces, C., Carreiro, F., Figueira, S.: Characterization, definability and separation via saturated models. In: Theoretical Computer Science (to appear, 2014)Google Scholar
  2. 2.
    Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge Tracts in Theoretical Computer Science, vol. 53. Cambridge University Press (2001)Google Scholar
  3. 3.
    Bojańczyk, M., Muscholl, A., Schwentick, T., Segoufin, L.: Two-variable logic on data trees and XML reasoning. Journal of the ACM 56(3), 1–48 (2009)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Chang, C.C., Keisler, H.J.: Model theory. Studies in logic and the foundations of mathematics. North-Holland (1990)Google Scholar
  5. 5.
    Clark, J., DeRose, S.: XML path language (XPath). Website (1999), W3C Recommendation, http://www.w3.org/TR/xpath
  6. 6.
    De Rijke, M.: Modal model theory. Annals of Pure and Applied Logic (1995)Google Scholar
  7. 7.
    De Rijke, M., Sturm, H.: Global definability in basic modal logic. Essays on Non-Classical Logic 1, 111 (2001)CrossRefGoogle Scholar
  8. 8.
    Figueira, D., Figueira, S., Areces, C.: Basic model theory of XPath on data trees. In: ICDT, pp. 50–60 (2014)Google Scholar
  9. 9.
    Gottlob, G., Koch, C., Pichler, R.: Efficient algorithms for processing XPath queries. ACM Transactions on Database Systems 30(2), 444–491 (2005)CrossRefMathSciNetGoogle Scholar
  10. 10.
    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: PODS, pp. 318–327. ACM (2006)Google Scholar
  11. 11.
    Kurtonina, N., de Rijke, M.: Bisimulations for temporal logic. Journal of Logic, Language and Information 6, 403–425 (1997)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Kurtonina, N., de Rijke, M.: Simulating without negation. Journal of Logic and Computation 7, 503–524 (1997)Google Scholar
  13. 13.
    Marx, M., de Rijke, B.: Semantic characterizations of navigational XPath. SIGMOD Record 34(2), 41–46 (2005)CrossRefGoogle Scholar
  14. 14.
    ten Cate, B.: The expressivity of XPath with transitive closure. In: Vansummeren, S. (ed.) PODS, pp. 328–337. ACM (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Sergio Abriola
    • 1
  • María Emilia Descotte
    • 1
  • Santiago Figueira
    • 1
    • 2
  1. 1.University of BuenosAiresArgentina
  2. 2.CONICETArgentina

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