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Describing Lambda Terms in Context Unification

  • Conference paper
Logical Aspects of Computational Linguistics (LACL 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3492))

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Abstract

The constraint language for lambda structures (CLLS) is a description language for lambda terms. CLLS provides parallelism constraints to talk about the tree structure of lambda terms, and lambda binding constraints to specify variable binding. Parallelism constraints alone have the same expressiveness as context unification. In this paper, we show that lambda binding constraints can also be expressed in context unification when permitting tree regular constraints.

A previous version of the paper was presented at ICoS4. This research has been partially supported, on the one hand, by the Mostrare project of INRIA Futurs and the LIFL at the Universities of Lille 1 and 3, and on the other hand, by the spanish projects: TIN2004-07672-C03-01 and TIN2004-04343.

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References

  1. Backofen, R., Rogers, J., Vijay-Shanker, K.: A first-order axiomatization of the theory of finite trees. Journal of Logic, Language, and Information 4, 5–39 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bodirsky, M., Erk, K., Koller, A., Niehren, J.: Underspecified beta reduction. In: ACL, pp. 74–81 (2001)

    Google Scholar 

  3. Comon, H.: Completion of rewrite systems with membership constraints. Symbolic Computation 25, 397–453 (1998); Extends on a paper at ICALP 1992

    Article  MATH  MathSciNet  Google Scholar 

  4. Duchier, D., Gardent, C.: Tree descriptions, constraints and incrementality. In: Computing Meaning. Linguistics and Philosophy, pp. 205–227 (2001)

    Google Scholar 

  5. Egg, M., Koller, A., Niehren, J.: The constraint language for lambda structures. Logic, Language, and Information 10, 457–485 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  6. Erk, K., Koller, A., Niehren, J.: Processing underspecified semantic representations in the constraint language for lambda structures. Journal of Research on Language and Computation 1(1), 127–169 (2002)

    Article  MathSciNet  Google Scholar 

  7. Erk, K., Niehren, J.: Parallelism constraints. In: Bachmair, L. (ed.) RTA 2000. LNCS, vol. 1833, pp. 110–126 (2000)

    Google Scholar 

  8. Erk, K., Niehren, J.: Well-nested parallelism constraints for ellipsis resolution. In: EACL, pp. 115–122 (2003)

    Google Scholar 

  9. Levy, J.: Linear second-order unification. In: RTA 1996. LNCS, vol. 1103, pp. 332–346 (1996)

    Google Scholar 

  10. Levy, J., Veanes, M.: On the undecidability of second-order unification. Information and Computation 159, 125–150 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  11. Levy, J., Villaret, M.: Linear second-order unification and context unification with tree-regular constraints. In: RTA, pp. 156–171 (2000)

    Google Scholar 

  12. Levy, J., Villaret, M.: Context unification and traversal equations. In: Middeldorp, A. (ed.) RTA 2001. LNCS, vol. 2051, pp. 169–184. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  13. Marcus, M.P., Hindle, D., Fleck, M.M.: D-theory: Talking about talking about trees. In: Proceedings of the 21st ACL, pp. 129–136 (1983)

    Google Scholar 

  14. Niehren, J., Koller, A.: Dominance constraints in context unification. In: Moortgat, M. (ed.) LACL 1998. LNCS (LNAI), vol. 2014, p. 199. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  15. Niehren, J., Thater, S.: Bridging the gap between underspecification formalisms: Minimal recursion semantics as dominance constraints. In: 41st Meeting of the Association of Computational Linguistics, July 2003, pp. 367–374 (2003)

    Google Scholar 

  16. Niehren, J., Villaret, M.: Parallelism and tree regular constraints. In: Baaz, M., Voronkov, A. (eds.) LPAR 2002. LNCS (LNAI), vol. 2514, pp. 311–326. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  17. Pinkal, M.: Radical underspecification. In: Proceedings of the 10th Amsterdam Colloquium, pp. 587–606 (1996)

    Google Scholar 

  18. Schmidt-Schauß, M.: A decision algorithm for distributive unification. Theoretical Computer Science 208, 111–148 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  19. Schmidt-Schauß, M., Schulz, K.U.: Solvability of context equations with two context variables is decidable. In: Ganzinger, H. (ed.) CADE 1999. LNCS (LNAI), vol. 1632, pp. 67–81. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  20. Schmidt-Schauß, M., Schulz, K.U.: Decidability of bounded higher-order unification. In: Bradfield, J.C. (ed.) CSL 2002 and EACSL 2002. LNCS, vol. 2471, p. 522. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  21. Shieber, S., Pereira, F., Dalrymple, M.: Interaction of scope and ellipsis. Linguistics & Philosophy 19, 527–552 (1996)

    Article  Google Scholar 

  22. 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 (1967)

    Article  MathSciNet  Google Scholar 

  23. Vijay-Shanker, K.: Using descriptions of trees in a tree adjoining grammar. Computational Linguistics 18, 481–518 (1992)

    Google Scholar 

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Author information

Authors and Affiliations

  1. INRIA Futurs, Lille, France

    Joachim Niehren

  2. IMA, Universitat de Girona, Girona, Spain

    Mateu Villaret

Authors
  1. Joachim Niehren
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  2. Mateu Villaret
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Editor information

Editors and Affiliations

  1. LPL-CNRS, Université de Provence, 29 Avenue Robert Schuman, P.O. Box, 13621, Aix-en-Provence, France

    Philippe Blache

  2. Linguistics Dept., UCLA, Box 951543, 90095-1542, Los Angeles, CA, USA

    Edward Stabler

  3. ERSS, Université Bordeaux 3, CNRS, Domaine Universitaire, 33607, Pessac Cedex, France

    Joan Busquets

  4. LaBRI, Université Bordeaux 1, CNRS, 351, Cours de la Libération, 33405, Talence Cedex, France

    Richard Moot

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Niehren, J., Villaret, M. (2005). Describing Lambda Terms in Context Unification. In: Blache, P., Stabler, E., Busquets, J., Moot, R. (eds) Logical Aspects of Computational Linguistics. LACL 2005. Lecture Notes in Computer Science(), vol 3492. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11422532_15

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  • DOI: https://doi.org/10.1007/11422532_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25783-7

  • Online ISBN: 978-3-540-31953-5

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