Abstract
Categorial Dependency Grammars (CDG) is a class of simple and expressive categorial grammars defining projective and discontinuous dependency structures in a strongly compositional way. They are more expressive than CF-grammars, are polynomial time recognizable and different from the mildly context sensitive grammars. CDG languages are proved to be closed under all AFL operations, but iteration. In this paper, we explain the connection between the iteration closure and the iterated dependencies (optional repeatable dependencies, inevitable in dependency syntax) and show that the CDG extended by a natural multimodal rule define an AFL, but the membership problem in this extended family is NP-complete.
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References
Bar-Hillel, Y., Gaifman, H., Shamir, E.: On categorial and phrase structure grammars. Bull. Res. Council Israel 9F, 1–16 (1960)
Béchet, D., Dikovsky, A.J., Foret, A.: Dependency Structure Grammars. In: Blache, P., Stabler, E.P., Busquets, J.V., Moot, R. (eds.) LACL 2005. LNCS (LNAI), vol. 3492, pp. 18–34. 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)
Dekhtyar, M., Dikovsky, A.: Categorial dependency grammars. In: Moortgat, M., Prince, V. (eds.) Proc. of Intern. Conf. on Categorial Grammars, Montpellier, pp. 76–91 (2004)
Dikovsky, A.: Multimodal categorial dependency grammars. In: Proc. of the 12th Conference on Formal Grammar, Dublin, Ireland, pp. 1–12 (2007)
Dikovsky, A.: Dependencies as categories. In: Duchier, D., Kruijff, G.-J.M. (eds.) Recent Advances in Dependency Grammars (COLING 2004) Workshop, pp. 90–97 (2004)
Duchier, D., Debusmann, R.: Topological dependency trees: A constraint-based account of linear precedence. In: Proc. of the 39th Intern. Conf. (ACL 2001), pp. 180–187. ACL & Morgan Kaufman (2001)
Hudson, R.A.: Word Grammar. Basil Blackwell, Oxford-New York (1984)
Joshi, A.K., Shanker, V.K., Weir, D.J.: The convergence of mildly context-sensitive grammar formalisms. In: Sells, P., Shieber, S., Wasow, T. (eds.) Foundational Issues in Natural Language Processing, pp. 31–81. MIT Press, Cambridge (1991)
Karlov, B.N.: Normal forms and automata for categorial dependency grammars. In: Vestnik Tverskogo Gosudarstvennogo Universiteta (Annals of Tver State University). Applied Mathematics, vol. 35 (95), pp. 23–43 (2008) (in Russ.)
Lambek, J.: On the calculus of syntactic types. In: Jakobson, R. (ed.) Structure of Languages and its Mathematical Aspects, pp. 166–178. American Mathematical Society, Providence (1961)
Mel’čuk, I.: Dependency Syntax. SUNY Press, Albany (1988)
Moortgat, M., Morrill, G.V.: Heads and phrases. Type calculus for dependency and constituent structure. Ms OTS, Utrecht (1991)
Morrill, G.V.: Type Logical Grammar. Categorial Logic of Signs. Kluwer, Dordrecht (1994)
Sleator, D., Temperly, D.: Parsing English with a Link Grammar. In: Proc. IWPT 1993, pp. 277–291 (1993)
Steedman, M., Baldridge, J.: Combinatory categorial grammar. In: Brown, K. (ed.) Encyclopedia of Language and Linguistics, vol. 2, pp. 610–622. Elsevier, Oxford (2006)
Tesnière, L.: Éléments de syntaxe structurale. Librairie C. Klincksieck, Paris (1959)
Vijay-Shanker, K., Weir, D.J.: The equivalence of four extensions of context-free grammars. Mathematical Systems Theory 27, 511–545 (1994)
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Dekhtyar, M., Dikovsky, A., Karlov, B. (2012). Iterated Dependencies and Kleene Iteration. In: de Groote, P., Nederhof, MJ. (eds) Formal Grammar. FG FG 2010 2011. Lecture Notes in Computer Science, vol 7395. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32024-8_5
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DOI: https://doi.org/10.1007/978-3-642-32024-8_5
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