Abstract
The notion of k-valued categorial grammars where a word is associated to at most k types is often used in the field of lexicalized grammars as a fruitful constraint for obtaining several properties like the existence of learning algorithms. This principle is relevant only when the classes of k-valued grammars correspond to a real hierarchy of languages. Such a property had been shown earlier for classical categorial grammars.
This paper establishes the relevance of this notion when categorial grammars are enriched with iterated types.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bar-Hillel, Y.: A quasi arithmetical notation for syntactic description. Language 29, 47–58 (1953)
Béchet, D., Dikovsky, A., Foret, A.: Two models of learning iterated dependencies. In: Proc. of the 15th Conference on Formal Grammar (FG 2010), Copenhagen, Denmark. LNCS (2010) (to appear), http://www.angl.hu-berlin.de/FG10/fg10_list_of_papers
Béchet, D., Dikovsky, A., Foret, A., Moreau, E.: On learning discontinuous dependencies from positive data. In: Proc. of the 9th Intern. Conf. Formal Grammar (FG 2004), Nancy, France, pp. 1–16 (2004)
Béchet, D., Foret, A.: k-valued non-associative lambek grammars (Without product) form a strict hierarchy of languages. In: Blache, P., Stabler, E.P., Busquets, J.V., Moot, R. (eds.) LACL 2005. LNCS (LNAI), vol. 3492, pp. 1–17. Springer, Heidelberg (2005)
Dekhtyar, M., Dikovsky, A.: Generalized categorial dependency grammars. In: Avron, A., Dershowitz, N., Rabinovich, A. (eds.) Pillars of Computer Science. LNCS, vol. 4800, pp. 230–255. Springer, Heidelberg (2008)
Dikovsky, A.: Dependencies as categories. In: Recent Advances in Dependency Grammars (COLING 2004) Workshop, pp. 90–97 (2004)
Gold, E.: Language identification in the limit. Information and control 10, 447–474 (1967)
Joshi, A.K., Shabes, Y.: Tree-adjoining grammars and lexicalized grammars. In: Tree Automata and LGS, Elsevier Science, Amsterdam (1992)
Kanazawa, M.: Learnable Classes of Categorial Grammars. In: Studies in Logic, Language and Information, Center for the Study of Language and Information (CSLI) and The European association for Logic, Language and Information (FOLLI), Stanford, California (1998)
Karlov, B.: On properties of generalized categorial dependency grammars. In: Proc. of the 12th National Conference on Artificial Intelligence, Russia, vol. 1, pp. 283–290 (2010)
Lambek, J.: The mathematics of sentence structure. American mathematical monthly 65 (1958)
Mel’čuk, I.: Dependency Syntax. SUNY Press, Albany (1988)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Béchet, D., Dikovsky, A., Foret, A. (2011). Categorial Grammars with Iterated Types form a Strict Hierarchy of k-Valued Languages. In: Bouchou-Markhoff, B., Caron, P., Champarnaud, JM., Maurel, D. (eds) Implementation and Application of Automata. CIAA 2011. Lecture Notes in Computer Science, vol 6807. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22256-6_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-22256-6_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22255-9
Online ISBN: 978-3-642-22256-6
eBook Packages: Computer ScienceComputer Science (R0)