Skip to main content

Logics for Unranked Trees: An Overview

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3580))

Abstract

Labeled unranked trees are used as a model of XML documents, and logical languages for them have been studied actively over the past several years. Such logics have different purposes: some are better suited for extracting data, some for expressing navigational properties, and some make it easy to relate complex properties of trees to the existence of tree automata for those properties. Furthermore, logics differ significantly in their model-checking properties, their automata models, and their behavior on ordered and unordered trees. In this paper we present a survey of logics for unranked trees.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley, Reading (1995)

    MATH  Google Scholar 

  2. Arnold, A., Niwinski, D.: Rudiments of μ-calculus. Elsevier, Amsterdam (2001)

    Google Scholar 

  3. Barceló, P., Libkin, L.: Temporal logics over unranked trees. In: LICS 2005 (2005)

    Google Scholar 

  4. Benedikt, M., Libkin, L., Schwentick, T., Segoufin, L.: Definable relations and first-order query languages over strings. J. ACM 50, 694–751 (2003)

    Article  MathSciNet  Google Scholar 

  5. Blackburn, P.: Structures, languages and translations: the structural approach to feature logic. In: Constraints, Language and Computation, AP, pp. 1–27 (1994)

    Google Scholar 

  6. Blumensath, A., Grädel, E.: Automatic structures. In: LICS 2000, pp. 51–62 (2000)

    Google Scholar 

  7. Bojanczyk, M., David, C., Muscholl, A., Schwentick, T., Segoufin, L.: Two-variable logic on words with data (2005)

    Google Scholar 

  8. Bouyer, P., Petit, A., Thérien, D.: An algebraic characterization of data and timed languages. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, pp. 248–261. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  9. Brüggemann-Klein, A., Murata, M., Wood, D.: Regular tree and regular hedge languages over unranked alphabets: Version 1, HKUST Tech. Report (2001)

    Google Scholar 

  10. Büchi, J.R.: Weak second-order arithmetic and finite automata. Zeit. Math. Logik Grundl. Math. 6, 66–92 (1960)

    Article  MATH  Google Scholar 

  11. Calcagno, C., Cardelli, L., Gordon, A.: Deciding validity in a spatial logic for trees. J. Funct. Progr. (to appear)

    Google Scholar 

  12. Cardelli, L.: Describing semistructured data. SIGMOD Record 30, 80–85 (2001)

    Article  Google Scholar 

  13. Cardelli, L., Ghelli, G.: A query language based on the ambient logic. In: Sands, D. (ed.) ESOP 2001. LNCS, vol. 2028, pp. 1–22. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  14. Cardelli, L., Gordon, A.: Anytime, anywhere: Modal logics for mobile ambients. In: POPL 2000, pp. 365–377 (2000)

    Google Scholar 

  15. Carpenter, B.: The Logic of Typed Feature Structures, Cambridge (1992)

    Google Scholar 

  16. Clarke, E., Grumberg, O., Peled, D.: Model Checking. The MIT Press, Cambridge (1999)

    Google Scholar 

  17. Clark, J., DeRose, S.: XML Path Language (XPath). W3C Recommendation (November 1999), http://www.w3.org/TR/xpath

  18. Comon, H., et al.: Tree Automata: Techniques and Applications (October 2002), Available at http://www.grappa.univ-lille3.fr/tata

  19. Courcelle, B.: The monadic second-order logic of graphs I: Recognizable sets of finite graphs. Inf. &Comput. 85, 12–75 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  20. Courcelle, B.: The monadic second-order logic of graphs V: On closing the gap between definability and recognizability. TCS 80, 153–202 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  21. Dal-Zilio, S., Lugiez, D., Meyssonnier, C.: A logic you can count on. In: POPL 2004, pp. 135–146 (2004)

    Google Scholar 

  22. Emerson, E.A., Jutla, C.: Tree automata, mu-calculus and determinacy. In: FOCS 1991, pp. 368–377 (1991)

    Google Scholar 

  23. Frick, M., Grohe, M.: The complexity of first-order and monadic second-order logic revisited. In: LICS 2002, pp. 215–224 (2002)

    Google Scholar 

  24. Frick, M., Grohe, M., Koch, C.: Query evaluation on compressed trees. In: LICS 2003, pp. 188–197 (2003)

    Google Scholar 

  25. Gottlob, G., Koch, C.: Monadic datalog and the expressive power of languages for web information extraction. J. ACM 51, 74–113 (2004)

    Article  MathSciNet  Google Scholar 

  26. Gottlob, G., Koch, C., Pichler, R., Segoufin, L.: The complexity of XPath query evaluation and XML typing. J. ACM (2005) (to appear)

    Google Scholar 

  27. Gottlob, G., Koch, C., Schulz, K.: Conjunctive queries over trees. In: PODS 2004, pp. 189–200 (2004)

    Google Scholar 

  28. Gottlob, G., Leone, N., Scarcello, F.: The complexity of acyclic conjunctive queries. J. ACM 48, 431–498 (2001)

    Article  MathSciNet  Google Scholar 

  29. Grohe, M., Schweikardt, N.: Comparing the succinctness of monadic query languages over finite trees. In: Baaz, M., Makowsky, J.A. (eds.) CSL 2003. LNCS, vol. 2803, pp. 226–240. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  30. Grohe, M., Schwentick, T., Segoufin, L.: When is the evaluation of conjunctive queries tractable? In: STOC 2001, pp. 657–666 (2001)

    Google Scholar 

  31. Hafer, T., Thomas, W.: Computation tree logic CTL* and path quantifiers in the monadic theory of the binary tree. In: Ottmann, T. (ed.) ICALP 1987. LNCS, vol. 267, pp. 269–279. Springer, Heidelberg (1987)

    Google Scholar 

  32. Janin, D., Lenzi, G.: Relating levels of the mu-calculus hierarchy and levels of the monadic hierarchy. In: LICS 2001, pp. 347–356 (2001)

    Google Scholar 

  33. Kamp, H.W.: Tense Logic and the Theory of Linear Order. PhD Thesis, UCLA (1968)

    Google Scholar 

  34. Keller, B.: Feature Logics, Infinitary Descriptions and Grammar. CSLI Press (1993)

    Google Scholar 

  35. Kupferman, O., Pnueli, A.: Once and for all. In: LICS 1995, pp. 25–35 (1995)

    Google Scholar 

  36. Libkin, L.: Elements of Finite Model Theory. Springer, Heidelberg (2004)

    MATH  Google Scholar 

  37. Libkin, L., Neven, F.: Logical definability and query languages over unranked trees. In: LICS 2003, pp. 178–187 (2003)

    Google Scholar 

  38. Marx, M.: Conditional XPath, the first order complete XPath dialect. In: PODS 2004, pp. 13–22 (2004)

    Google Scholar 

  39. Marx, M., de Rijke, M.: Semantic characterizations of XPath. In: TDM Workshop on XML Databases and Information Retrieval (2004)

    Google Scholar 

  40. Moller, F., Rabinovich, A.: Counting on CTL*: on the expressive power of monadic path logic. Information and Computation 184, 147–159 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  41. Neven, F.: Design and Analysis of Query Languages for Structured Documents. PhD Thesis, U. Limburg (1999)

    Google Scholar 

  42. Neven, F.: Automata, logic, and XML. In: Bradfield, J.C. (ed.) CSL 2002 and EACSL 2002. LNCS, vol. 2471, pp. 2–26. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  43. Neven, F., Schwentick, T.: Expressive and efficient pattern languages for tree-structured data. In: PODS 2000, pp. 145–156 (2000), Corrigendum at http://www.mathematik.uni-marburg.de/~tick/

  44. Neven, F., Schwentick, T.: Query automata over finite trees. Theor. Comput. Sci. 275, 633–674 (2002)

    Google Scholar 

  45. Neven, F., Schwentick, T.: Towards regular languages over infinite alphabets. In: Sgall, J., Pultr, A., Kolman, P. (eds.) MFCS 2001. LNCS, vol. 2136, pp. 560–572. Springer, Heidelberg (2001)

    Google Scholar 

  46. Niehren, J., Podelski, A.: Feature automata and recognizable sets of feature trees. In: Gaudel, M.-C., Jouannaud, J.-P. (eds.) CAAP 1993, FASE 1993, and TAPSOFT 1993. LNCS, vol. 668, pp. 356–375. Springer, Heidelberg (1993)

    Google Scholar 

  47. Niwinski, D.: Fixed points vs. infinite generation. In: LICS 1988, pp. 402–409 (1988)

    Google Scholar 

  48. Potthoff, A., Thomas, W.: Regular tree languages without unary symbols are star-free. In: FCT 1993, pp. 396–405 (1993)

    Google Scholar 

  49. Rabin, M.: Decidability of second-order theories and automata on infinite trees. Trans. AMS 141, 1–35 (1969)

    MATH  MathSciNet  Google Scholar 

  50. Rounds, W.C., Kasper, R.: A logical semantics for feature structures. In: 24th Annual Meeting of the Assoc. for Computational Linguistics, pp. 257–266 (1986)

    Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  52. Segoufin, L., Vianu, V.: Validating streaming XML documents. In: PODS 2002, pp. 53–64 (2002)

    Google Scholar 

  53. Seidl, H., Schwentick, T., Muscholl, A.: Numerical document queries. In: PODS 2003, pp. 155–166 (2003)

    Google Scholar 

  54. Seidl, H., Schwentick, T., Muscholl, A., Habermehl, P.: Counting in trees for free. In: ICALP 2004, pp. 1136–1149 (2004)

    Google Scholar 

  55. Stockmeyer, L., Meyer, A.: Cosmological lower bound on the circuit complexity of a small problem in logic. Journal of the ACM 49, 753–784 (2002)

    Article  MathSciNet  Google Scholar 

  56. Thatcher, J.W.: Characterizing derivation trees of context-free grammars through a generalization of finite automata theory. JCSS 1, 317–322 (1967)

    MATH  MathSciNet  Google Scholar 

  57. Thatcher, J.W., Wright, J.B.: Generalized finite automata theory with an application to a decision problem of second-order logic. Mathematical Systems Theory 2(1), 57–81 (1968)

    Article  MathSciNet  Google Scholar 

  58. Thomas, W.: Languages, automata, and logic. In: Handbook of Formal Languages, vol. 3, Springer, Heidelberg (1997)

    Google Scholar 

  59. Vardi, M.Y.: Reasoning about the past with two-way automata. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 628–641. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  60. Walukiewicz, I.: Monadic second-order logic on tree-like structures. TCS 275, 311–346 (2002)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Libkin, L. (2005). Logics for Unranked Trees: An Overview. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds) Automata, Languages and Programming. ICALP 2005. Lecture Notes in Computer Science, vol 3580. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11523468_4

Download citation

  • DOI: https://doi.org/10.1007/11523468_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-27580-0

  • Online ISBN: 978-3-540-31691-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics