Journal of Logic, Language and Information

, Volume 17, Issue 3, pp 345–381

Highly Constrained Unification Grammars

Article

Abstract

Unification grammars are widely accepted as an expressive means for describing the structure of natural languages. In general, the recognition problem is undecidable for unification grammars. Even with restricted variants of the formalism, off-line parsable grammars, the problem is computationally hard. We present two natural constraints on unification grammars which limit their expressivity and allow for efficient processing. We first show that non-reentrant unification grammars generate exactly the class of context-free languages. We then relax the constraint and show that one-reentrant unification grammars generate exactly the class of mildly context-sensitive languages. We thus relate the commonly used and linguistically motivated formalism of unification grammars to more restricted, computationally tractable classes of languages.

Keywords

Unification grammars Linear indexed grammars Mildly context- sensitive languages Generative capacity 

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References

  1. Barton G.E. Jr., Berwick R.C., Ristad E.S. (1987) The complexity of LFG. In: Barton G.E. Jr., Berwick R.C., Ristad E.S. (eds) Computational complexity and natural language Chap. 3 Computational models of cognition and perception. MIT Press, Cambridge, MA, pp 89–102Google Scholar
  2. Carpenter, B. (1992). The logic of typed feature structures. Cambridge tracts in theoretical computer science. Cambridge University Press.Google Scholar
  3. Feinstein, D., & Wintner, S. (2006). Highly constrained unification grammars. In Proceedings of Coling—ACL 2006, pp. 1089–1096, Sydney, Australia, July.Google Scholar
  4. Gazdar G. (1988) Applicability of indexed grammars to natural languages. In: Reyle U., Rohrer C. (eds) Natural language parsing and linguistic theories. Reidel Publishing Company, Dordrecht, pp 69–94Google Scholar
  5. Jaeger E., Francez N., Wintner S. (2005) Unification grammars and off-line parsability. Journal of Logic, Language and Information 14(2): 199–234CrossRefGoogle Scholar
  6. Johnson, M. (1988). Attribute-value logic and the theory of grammar, Vol. 16 of CSLI Lecture Notes. Stanford, California: CSLI.Google Scholar
  7. Joshi, A. K. (2003). Tree-adjoining grammars. In R. Mitkov (Ed.), The Oxford handbook of computational linguistics (Chap. 26, pp. 483–500). Oxford University Press.Google Scholar
  8. Joshi A.K., Levy L., Takahashi M. (1975) Tree adjunct grammars. Journal of Computer and System Sciences 10: 136–163CrossRefGoogle Scholar
  9. Keller, B., & Weir, D. (1995). A tractable extension of linear indexed grammars. In Proceedings of the Seventh Meeting of the European Chapter of the Association for Computational Linguistics, pp. 75–82.Google Scholar
  10. Pollard, C. (1984). Generalized phrase structure grammars, head grammars and natural language. Ph.D. Thesis, Stanford University.Google Scholar
  11. Satta, G. (1994). Tree-adjoining grammar parsing and boolean matrix multiplication. In Proceedings of the 20st Annual Meeting of the Association for Computational Linguistics, (Vol. 20).Google Scholar
  12. Savitch, W. J., Bach, E., Marsh, W., & Safran-Naveh, G. (Eds.) (1987). The formal complexity of natural language, Vol. 33 of Studies in Linguistics and Philosophy. Dordrecht: D. ReidelGoogle Scholar
  13. Shieber, S. M. (1986). An introduction to unification based approaches to grammar. Number 4 in CSLI Lecture Notes. CSLI.Google Scholar
  14. Shieber S.M. (1992) Constraint-based grammar formalisms. MIT Press, Cambridge, MaGoogle Scholar
  15. Steedman M. (2000) The syntactic process. Language, Speech and Communication. The MIT Press, Cambridge, MaGoogle Scholar
  16. Vijay-Shanker K., Weirm D.J. (1993) Parsing some constrained grammar formalisms. Computational Linguistics 19(4): 591–636Google Scholar
  17. Vijay-Shanker K., Weir D.J. (1994) The equivalence of four extensions of context-free grammars. Mathematical Systems Theory 27: 511–545CrossRefGoogle Scholar
  18. Weir D.J. (1992) A geometric hierarchy beyond context-free languages. Theoretical Computer Science 104: 235–261CrossRefGoogle Scholar
  19. Wintner, S. (2006a). Introduction to unification grammars. In Z. Ésik, C. Martín-Vide, & V. Mitrana (Eds.), Recent advances in formal languages and applications, Vol. 25 of Studies in Computational Intelligence (Chap. 13, pp. 321–342). Springer.Google Scholar
  20. Wintner S. (2006b) Unification: Computational issues. In: Brown K. (eds) Encyclopedia of language and linguistics, Vol. 13. 2nd ed., Elsevier, Oxford, pp 238–250Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of HaifaHaifaIsrael

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