A faithful representation of non-associative lambek grammars in abstract categorial grammars

被引：1
作者：
Retoré C. [1 ]
Salvati S. [1 ]
机构：
[1] INRIA Bordeaux Sud-Ouest, LaBRI (Université de Bordeauxet C.N.R.S.), 33405 Talence cedex, 351, cours de la Libération
来源：
Journal of Logic, Language and Information | 2010年 / 19卷 / 2期
关键词：
Categorial grammar; Formal language theory; Lambda calculus;
D O I：
10.1007/s10849-009-9111-z
中图分类号：
学科分类号：
摘要：
This paper solves a natural but still open question: can abstract categorial grammars (ACGs) respresent usual categorial grammars? Despite their name and their claim to be a unifying framework, up to now there was no faithful representation of usual categorial grammars in ACGs. This paper shows that Non-Associative Lambek grammars as well as their derivations can be defined using ACGs of order two. To conclude, the outcome of such a representation are discussed. © 2010 Springer Science+Business Media B.V.
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页码：185 / 200
页数：15
相关论文
共 16 条
  • [1] Barendregt H.P., The Lambda Calculus: Its Syntax and Semantics, Vol. 103. Studies in Logic and the Foundations of Mathematics (Revised Edition), (1984)
  • [2] Buszkowski W., Mathematical linguistics and proof theory, Handbook of logic and language, pp. 683-736, (1997)
  • [3] Capelletti M., Parsing with structure-preserving categorial grammars, (2007)
  • [4] de Groote P., Towards abstract categorial grammars, Proceedings 39th Annual Meeting and 10th Conference of the European Chapter, pp. 148-155, (2001)
  • [5] de Groote P., Pogodalla S., On the expressive power of abstract categorial grammars: Representing context-free formalisms, Journal of Logic, Language and Information, 13, 4, pp. 421-438, (2004)
  • [6] Engelfriet J., Maneth S., The equivalence problem for deterministic MSO tree transducers is decidable, Information Processing Letters, 100, 5, pp. 206-212, (2006)
  • [7] Girard J.Y., Taylor P., Lafont Y., Proofs and Types, (1989)
  • [8] Huet G., Résolution d'équations dans des langages d'ordre 1, 2,...,ω, Thèse de doctorat d'état ès sciences mathématiques, (1976)
  • [9] Kandulski M., Derived tree languages of nonassociative Lambek categorial grammars with product, Fundamenta Informaticae, 55, 3-4, pp. 349-362, (2003)
  • [10] Lambek J., On the calculus of syntactic types, Studies of Language and its Mathematical Aspects, Proceedings of the 12th Symposium of Applied Mathematics, pp. 166-178, (1961)
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