Ordering constraints over feature trees

  • Martin Müller
  • Joachim Niehren
  • Andreas Podelski
Session 5a
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1330)


Feature trees have been used to accommodate records in constraint programming and record like structures in computational linguistics. Feature trees model records, and feature constraints yield extensible and modular record descriptions. We introduce the constraint system fFTof ordering constraints interpreted over feature trees. Under the view that feature trees represent symbolic information, the relation ≤ corresponds to the information ordering (“carries less information than”). We present a polynomial algorithm that decides the satisfi ability of conjunctions of positive and negative information ordering constraints over feature trees. Our results include algorithms for the satisfiability problem and the entailment problem of FT in time O(n3). We also show that FT has the independence property and are thus able to handle negative conjuncts via entailment. Furthermore, we reduce the satisfiability problem of Dörre's weaksubsumption constraints to the satisfiability problem of FT. This improves the complexity bound for solving weak subsumption constraints from O(n5) to O(n3).


feature constraints tree orderings weak subsumption satisfiability entailment complexity 


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  1. 1.
    H. Aft-Kaci and A. Podelski. Entailment and Disentailment of Order-Sorted Feature Constraints. In A. Voronkov, editor, 4th International Conference on Logic Programming and Automated Reasoning, LNAI 698, pp. 1–18. Springer, 1993.Google Scholar
  2. 2.
    H. Aft-Kaci and A. Podelski. Towards a Meaning of Life. The Journal of Logic Programming, 16(3 and 4):195–234, July, Aug. 1993.Google Scholar
  3. 3.
    H. Aft-Kaci, A. Podelski, and G. Smolka. A feature-based constraint system for logic programming with entailment. Theoretical Computer Science, 122(1-2):263–283, Jan. 1994.Google Scholar
  4. 4.
    R. Backofen. A Complete Axiomatization of a Theory with Feature and Arity Constraints. The Journal of Logic Programming, 1995. Special Issue on Computational Linguistics and Logic Programming.Google Scholar
  5. 5.
    R. Backofen and G. Smolka. A complete and recursive feature theory. Theoretical Computer Science, 146(1-2):243–268, July 1995.Google Scholar
  6. 6.
    A. Colmerauer. Equations and Inequations on Finite and Infinite Trees. In 2 nd Future Generation Computer Systems, pages 85–99, 1984.Google Scholar
  7. 7.
    J. Dörre. Feature-Logic with Weak Subsumption Constraints. In Constraints, Languages, and Computation, chapter 7, pages 187–203. Academic Press, 1994.Google Scholar
  8. 8.
    J. Dörre. Feature-Logik and Semiunifikation. Dissertationen zur Kfinstlichen Intelligenz, Band 128. Infix-Verlag, St. Augustin, 1996.Google Scholar
  9. 9.
    J. Dörre and W. C. Rounds. On Subsumption and Semiunifikation in Feature Algebras. In 5 th IEEE Symposium on Logic in Computer Science, pages 300–310. IEEE Computer Science Press, 1990.Google Scholar
  10. 10.
    R. Helm, K. Marriott, and M. Odersky. Constraint-based Query Optimization for Spatial Databases. In l0th Annual IEEE Symposium on the Principles of Database Systems, pages 181–191, May 1991.Google Scholar
  11. 11.
    J. Jaffar and M. J. Maher. Constraint logic programming: A survey. Journal of Logic Programming, 19/20:503–582, May–July 1994.Google Scholar
  12. 12.
    R. M. Kaplan and J. Bresnan. Lexical-Functional Grammar: A Formal System for Grammatical Representation. pages 173–381. MIT Press, Cambridge, MA, 1982.Google Scholar
  13. 13.
    M. Kay. Functional Grammar. In C. Chiarello et al., editor, Proc. of the 5 th Annual Meeting of the Berkeley Linguistics Society, pages 142–158, 1979.Google Scholar
  14. 14.
    J. Lassez and K. McAloon. Applications of a Canonical Form for Generalized Linear Constraints. In 5th Future Generation Computer Systems, pages 703–710, Dec. 1988.Google Scholar
  15. 15.
    M. Müller. Ordering Constraints over Feature Trees with Ordered Sorts. In P Lopez, S. Manandhar, and W. Nutt, eds., Computational Logic and Natural Language Understanding, Lecture Notes in Artificial Intelligence, to appear, 1997.Google Scholar
  16. 16.
    M. Müller and J. Niehren.Entailment for Set Constraints is not Feasible.Technical report, Programming Systems Lab, Universität des Saarlandes, 1997. Available at /conp97.htm1.Google Scholar
  17. 17.
    M. Müller, J. Niehren, and A. Podelski. Inclusion Constraints over Non-Empty Sets of Trees. In International Joint Conference on Theory and Practice of Software Development (TAPSOFT), LNCS, Springer, 1997.Google Scholar
  18. 18.
    C. Pollard and I. Sag. Head-Driven Phrase Structure Grammar. Studies in Contemporary Linguistics. Cambridge University Press, Cambridge, England, 1994.Google Scholar
  19. 19.
    W. C. Rounds. Feature Logics. In J. v. Benthem and A. ter Meulen, editors, Handbook of Logic and Language. Elsevier Science Publishers B.V (North Holland), 1997.Google Scholar
  20. 20.
    S. Shieber. An Introduction to Unification-based Approaches to Grammar. CSLI Lecture Notes No. 4. Center for the Study of Language and Information, 1986.Google Scholar
  21. 21.
    S. Shieber. Parsing and Type Inference for Natural and Computer Languages. SRI Internationax[l Technical Note 460, Stanford University, Mar. 1989.Google Scholar
  22. 22.
    G. Smolka. Feature constraint logics for unification grammars. Journal of Logic Programming, 12:51–87,1992.Google Scholar
  23. 23.
    G. Smolka. The Oz Programming Model. In J. van Leeuwen, editor, Computer Science Today, LNCS, vol. 1000, pages 324–343. Springer-Verlag, Berlin, Germany, 1995.Google Scholar
  24. 24.
    G. Smolka and R. Treinen. Records for Logic Programming. The Journal of Logic Programming, 18(3):229–258, Apr. 1994.Google Scholar
  25. 25.
    R. Treinen. Feature constraints with first-class features. Mathematical Foundations of Computer Science, LNCS, vol. 711, pages 734–743, Springer-Verlag, 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Martin Müller
    • 1
  • Joachim Niehren
    • 1
  • Andreas Podelski
    • 2
  1. 1.Universität des SaarlandesGermany
  2. 2.Max-Planck-Institut für InformatikSaarbrückenGermany

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