Abstract
Stabler proposes an implementation of the Chomskyan Minimalist Program [1] with Minimalist Grammars (MG) [2]. This framework inherits a long linguistic tradition. But the semantic calculus is more easily added if one uses the Curry-Howard isomorphism. Minimalist Categorial Grammars (MCG), based on an extension of the Lambek calculus, the mixed logic, were introduced to provide a theoretically-motivated syntax-semantics interface [3]. In this article, we give full definitions of MG with algebraic tree descriptions and of MCG, and take the first steps towards giving a proof of inclusion of their generated languages.
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
Chomsky, N.: The Minimalist Program. MIT Press, Cambridge (1995)
Stabler, E.: Derivational minimalism. In: Retoré, C. (ed.) LACL 1996. LNCS (LNAI), vol. 1328, pp. 68–95. Springer, Heidelberg (1997)
Amblard, M.: Calcul de représentations sémantiques et suntaxe générative: les grammaires minimalistes catégorielles. Ph.D. thesis, université de Bordeaux 1 (Septembre 2007)
Muskens, R.: Language, Lambdas, and Logic. In: Kruijff, G.J., Oehrle, R. (eds.) Resource Sensitivity in Binding and Anaphora. Studies in Linguistics and Philosophy, pp. 23–54. Kluwer, Dordrecht (2003)
de Groote, P.: Towards abstract categorial grammars. Association for Computational Linguistics. In: Proceedings of the Conference on 39th Annual Meeting and 10th Conference of the European Chapter, Proceedings of the Conference (2001)
Mansfield, L., Martin, S., Pollard, C., Worth, C.: Phenogrammatical labelling in convergent grammar: the case of wrap (2009) (unpublished)
Berwick, R., Epstein, S.: On the convergence of ’minimalist’ syntax and categorial grammars (1996)
Retoré, C., Stabler, E.: Reseach on Language and Computation, vol. 2(1). Christian Retoré and Edward Stabler (2004)
Lecomte, A.: Rebuilding the minimalist program on a logical ground. Journal of Research on Language and Computation 2(1), 27–55 (2004)
Cornell, T.: Lambek calculus for transformational grammars. Journal of Research on Language and Computation 2(1), 105–126 (2004)
Lecomte, A., Retoré, C.: Towards a logic for minimalist. In: Formal Grammar (1999)
Lecomte, A., Retoré, C.: Extending Lambek grammars: a logical account of minimalist grammars. In: Proceedings of the 39th Annual Meeting of the Association for Computational Linguistics, ACL 2001, pp. 354–361. ACL, Toulouse (2001), http://www.labri.fr/perso/retore
Lecomte, A.: Categorial grammar for minimalism. In: Language and Grammar: Studies in Mathematical Linguistics and Natural Language CSLI Lecture Notes, vol. (168), pp. 163–188 (2005)
Amblard, M., Lecomte, A., Retoré, C.: Syntax and semantics interacting in a minimalist theory. In: Prospect and Advance in the Syntax/Semantic Interface, pp. 17–22 (October 2003)
Amblard, M., Lecomte, A., Retoré, C.: Synchronization syntax semantic for a minimalism theory. Journée Sémantique et Modélisation (Mars 2004)
Huet, G.P.: The zipper. J. Funct. Program 7(5), 549–554 (1997)
Levy, J.J., Cori, R.: Algorithmes et Programmation. Ecole Polytechnique
Chomsky, N.: Conditions on transformations. In: Kiparsky, S.A.P. (ed.) A Festschrift for Morris Halle, pp. 232–286. Holt, Rinehart and Winston (1973)
Vermaat, W.: Controlling movement: Minimalism in a deductive perspective. Master’s thesis, Universiteit Utrecht (1999)
Stabler, E.: Remnant movement and structural complexity. In: Constraints and Resources in Natural Language Syntax and Semantics pp. 299–326 (1999)
Koopman, H., Szabolcsi, A.: A verbal Complex. MIT Press, Cambridge (2000)
Kayne, R.S.: Overt vs covert movment. Syntax 1,2, 128–191 (1998)
Howard, W.A.: The formulae-as-types notion of construction. In: Hindley, J., Seldin, J. (eds.) To H.B. Curry: Essays on Combinatory Logic, λ-calculus and Formalism, pp. 479–490. Academic Press, London (1980)
de Groote, P.: Partially commutative linear logic: sequent calculus and phase semantics. In: Abrusci, V.M., Casadio, C. (eds.) Third Roma Workshop: Proofs and Linguistics Categories – Applications of Logic to the Analysis and Implementation of Natural Language, pp. 199–208. CLUEB, Bologna (1996)
Amblard, M., Retore, C.: Natural deduction and normalisation for partially commutative linear logic and lambek calculus with product. In: Computation and Logic in the Real World, CiE 2007 Quaderni del Dipartimento di Scienze Matematiche e Informatiche ”Roberto Magari” (June 2007))
Kobele, G.: Generating Copies: An Investigation into Structural Identity in Language and Grammar. Ph.D. thesis, University of California, Los Angeles (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Amblard, M. (2011). Minimalist Grammars and Minimalist Categorial Grammars: Toward Inclusion of Generated Languages. In: Pogodalla, S., Quatrini, M., Retoré, C. (eds) Logic and Grammar. Lecture Notes in Computer Science(), vol 6700. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21490-5_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-21490-5_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21489-9
Online ISBN: 978-3-642-21490-5
eBook Packages: Computer ScienceComputer Science (R0)