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XPath and Modal Logics of Finite DAG‘s

  • Conference paper
Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 2003)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2796))

Abstract

XPath, CTL and the modal logics proposed by Blackburn et al, Palm and Kracht are variable free formalisms to describe and reason about (finite) trees. XPath expressions evaluated at the root of a tree correspond to existential positive modal formulas. The models of XPath expressions are finite ordered trees, or in the presence of XML’s ID/IDREF mechanism graphs. The ID/IDREF mechanism can be seen as a device for naming nodes. Naming devices have been studied in hybrid logic by nominals. We add nominals to the modal logic of Palm and interpret the language on directed acyclic graphs. We give an algorithm which decides the consequence problem of this logic in exponential time. This yields a complexity result for query containment of the corresponding extension of XPath.

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References

  1. Abiteboul, S., Buneman, P., Suciu, D.: Data on the web. Morgan Kaufman, San Francisco (2000)

    Google Scholar 

  2. Alechina, N., Demri, S., de Rijke, M.: A modal perspective on path constraints. Journal of Logic and Computation 13, 1–18 (2003)

    Article  Google Scholar 

  3. 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) (to appear)

    Chapter  Google Scholar 

  4. Blackburn, P.: Representation, reasoning, and relational structures: a hybrid logic manifesto. Logic Journal of the IGPL 8(3), 339–365 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2001)

    MATH  Google Scholar 

  6. Blackburn, P., Gaiffe, B., Marx, M.: Variable free reasoning on finite trees. In: Proceedings of Mathematics of Language (MOL–8), Bloomington (2003)

    Google Scholar 

  7. Clark, J.: XML Path Language (XPath), http://www.w3.org/TR/xpath

  8. World-Wide Web Consortium. Xml path language (xpath): Version 2.0, http://www.w3.org/TR/xpath20/

  9. Deutsch, A., Tannen, V.: Containment of regular path expressions under integrity constraints. In: Knowledge Representation Meets Databases (2001)

    Google Scholar 

  10. Doner, J.: Tree acceptors and some of their applications. J. Comput. Syst. Sci. 4, 405–451 (1970)

    Article  MathSciNet  Google Scholar 

  11. Emerson, E., Halpern, J.: ”Sometimes and Not Never”; revisited: on branching versus linear time temporal logic. Journal of the ACM (JACM) 33(1), 151–178 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  12. Fisher, M., Ladner, R.: Propositional dynamic logic of regular programs. J. Comput. Syst. Sci. 18(2), 194–211 (1979)

    Article  Google Scholar 

  13. Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. MIT Press, Cambridge (2000)

    MATH  Google Scholar 

  14. Kracht, M.: Syntactic codes and grammar refinement. Journal of Logic, Language and Information 4, 41–60 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  15. Kracht, M.: Inessential features. In: Retoré, C. (ed.) LACL 1996. LNCS (LNAI), vol. 1328, pp. 43–62. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  16. Marx, M.: XPath and modal logic of finite trees. In: Proceedings of M4M 2003, Nancy (2003)

    Google Scholar 

  17. Miklau, G., Suciu, D.: Containment and equivalence for an XPath fragment. In: Proc. PODS 2002, pp. 65–76 (2002)

    Google Scholar 

  18. Neven, F., Schwentick, T.: XPath containment in the presence of disjunction, DTDs, and variables. In: Calvanese, D., Lenzerini, M., Motwani, R. (eds.) ICDT 2003. LNCS, vol. 2572, pp. 312–326. Springer, Heidelberg (2002)

    Google Scholar 

  19. Palm, A.: Transforming tree constraints into formal grammars. PhD thesis, Universität Passau (1997)

    Google Scholar 

  20. Palm, A.: Propositional tense logic for trees. In: Sixth Meeting on Mathematics of Language. University of Central Florida, Orlando, Florida (1999)

    Google Scholar 

  21. Pratt, V.: Models of program logics. In: Proceedings of the 20th IEEE symposium on Foundations of Computer Science, pp. 115–122 (1979)

    Google Scholar 

  22. Rabin, M.: Decidability of second order theories and automata on infinite trees. Transactions of the American Mathematical Society 141, 1–35 (1969)

    MATH  MathSciNet  Google Scholar 

  23. Reinhardt, K.: The complexity of translating logic to finite automata. In: Grädel, E., Thomas, W., Wilke, T. (eds.) Automata, Logics, and Infinite Games. LNCS, vol. 2500, pp. 231–238. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  24. Schlingloff, B.-H.: Expressive completeness of temporal logic of trees. Journal of Applied Non–Classical Logics 2(2), 157–180 (1992)

    MATH  MathSciNet  Google Scholar 

  25. Wood, P.: On the equivalence of XML patterns. In: Palamidessi, C., Moniz Pereira, L., Lloyd, J.W., Dahl, V., Furbach, U., Kerber, M., Lau, K.-K., Sagiv, Y., Stuckey, P.J. (eds.) CL 2000. LNCS (LNAI), vol. 1861, pp. 1152–1166. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. ILLC, Universiteit van Amsterdam, The Netherlands

    Maarten Marx

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  1. Maarten Marx
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Editors and Affiliations

  1. Dipartimento di Informatica e Automazione, Università di Roma Tre, via Vasca Navale 79, 00146, Roma, Italia

    Marta Cialdea Mayer

  2. Dipartimento di Informatica e Sistemistica (DIS), Sapienza, University of Rome “Sapienza”, via Ariosto 25, 00185, Roma

    Fiora Pirri

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Marx, M. (2003). XPath and Modal Logics of Finite DAG‘s. In: Cialdea Mayer, M., Pirri, F. (eds) Automated Reasoning with Analytic Tableaux and Related Methods . TABLEAUX 2003. Lecture Notes in Computer Science(), vol 2796. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45206-5_13

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  • DOI: https://doi.org/10.1007/978-3-540-45206-5_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40787-4

  • Online ISBN: 978-3-540-45206-5

  • eBook Packages: Springer Book Archive

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