First Order Paths in Ordered Trees

  • Maarten Marx
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3363)


We give two sufficient conditions on XPath like languages for having first order expressivity, meaning that every first order definable set of paths in an ordered node-labeled tree is definable in that XPath language. They are phrased in terms of expansions of navigational (sometimes called “Core”) XPath. Adding either complementation, or the more elegant conditional paths is sufficient. A conditional path is an axis relation of the form (one_step_axis::n[F]) + , denoting the transitive closure of the relation expressed by one_step_axis::n[F]. As neither is expressible in navigational XPath we also give characterizations in terms of first order logic of the answer sets and the sets of paths navigational XPath can define. The first in terms of a suitable two variable fragment, the second in terms of unions of conjunctive queries.


Temporal Logic Free Variable Transitive Closure Order Logic Conjunctive Query 
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  1. 1.
    Benedikt, M., Fan, W., Kuper, G.: 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
  2. 2.
    Blackburn, P., Meyer-Viol, W., de Rijke, M.: A proof system for finite trees. In: Kleine Büning, H. (ed.) CSL 1995. LNCS, vol. 1092, pp. 86–105. Springer, Heidelberg (1996)Google Scholar
  3. 3.
    World-Wide Web Consortium. XML path language (XPath): Version 1.0,
  4. 4.
    Etessami, K., Vardi, M., Wilke, Th.: First-order logic with two variables and unary temporal logic. In: Proc. LICS 1997, pp. 228–235 (1997)Google Scholar
  5. 5.
    Gottlob, G., Koch, C., Pichler, R.: Efficient algorithms for processing XPath queries. In: VLDB 2002 (2002)Google Scholar
  6. 6.
    Gottlob, G., Koch, C., Schulz, K.: Conjunctive queries over trees. In: Proceedings of PODS, pp. 189–200 (2004)Google Scholar
  7. 7.
    Halevy, A., Rousset, M.: Combining horn rules and description logics in CARIN. Artificial Intelligence 104, 165–209 (1998)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Hodkinson, I., Simon, A.: The k-variable property is stronger than H-dimension k. Journal of Philosophical Logic 26, 81–101 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Immerman, N., Kozen, D.: Definability with bounded number of bound variables. In: Proceedings of the Symposium of Logic in Computer Science, Washington, pp. 236–244. Computer Society Press, Rockville (1987)Google Scholar
  10. 10.
    Kamp, J.A.W.: Tense Logic and the Theory of Linear Order. PhD thesis, University of California, Los Angeles (1968)Google Scholar
  11. 11.
    Marx, M.: Conditional XPath, the first order complete XPath dialect. In: Proceedings of PODS 2004, pp. 13–22 (2004)Google Scholar
  12. 12.
    Marx, M.: XPath with conditional axis relations. In: Bertino, E., Christodoulakis, S., Plexousakis, D., Christophides, V., Koubarakis, M., Böhm, K., Ferrari, E. (eds.) EDBT 2004. LNCS, vol. 2992, pp. 477–494. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  13. 13.
    Marx, M., de Rijke, M.: Semantic characterizations of XPath. In: TDM 2004 workshop on XML Databases and Information Retrieval, Twente, The Netherlands, June 21 (2004)Google Scholar
  14. 14.
    Palm, A.: Propositional tense logic for trees. In: Sixth Meeting on Mathematics of Language. University of Central Florida, Orlando (1999)Google Scholar
  15. 15.
    Rogers, J.: A Descriptive Approach to Language Theoretic Complexity. CSLI Press (1998)Google Scholar
  16. 16.
    Tarski, A., Givant, S.: A Formalization of Set Theory without Variables, vol. 41. AMS Colloquium publications, Providence (1987)zbMATHGoogle Scholar
  17. 17.
    Vardi, M.: Why is modal logic so robustly decidable? In: DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 31, pp. 149–184. American Math. Society, Providence (1997)Google Scholar
  18. 18.
    Wadler, P.: Two semantics for XPath. Technical report, Bell Labs (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Maarten Marx
    • 1
  1. 1.Informatics InstituteUniversity of Amsterdam 

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