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.
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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)
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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
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DOI: https://doi.org/10.1007/978-3-642-22256-6_5
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