Abstract
In this paper, we aim at understanding the derivations of minimalist grammars without the shortest move constraint. This leads us to study the relationship of those derivations with logic. In particular we show that the membership problem of minimalist grammars without the shortest move constraint is as difficult as provability in Multiplicative Exponential Linear Logic. As a byproduct, this result gives us a new representation of those derivations with linear λ-terms. We show how to interpret those terms in a homomorphic way so as to recover the sentence they analyse. As the homorphisms we describe are rather evolved, we turn to a proof-net representation and explain how Monadic Second Order Logic and related techniques allow us both to define those proof-nets and to retrieve the sentence they analyse.
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References
Lecomte, A., Retoré, C.: Towards a minimal logic for minimalist grammars: a tranformational use of lambek calculus. In: Formal Grammar 1999 (1999)
Lecomte, A., Retoré, C.: Extending lambek grammars: a logical account of minimalist grammars. In: Proceedings of the 39th Meeting of the Association for Computational Linguistics, ACL 2001, pp. 354–361 (2001)
Lecomte, A.: A computational approach to minimalism. In: Proceedings of ICON 2003, International Conference on Natural Language. Central Institute of Indian Languages, pp. 20–31 (2003)
Lecomte, A.: Derivations as proofs: a logical approach to minimalism. In: Proceedings of CG 2004 (2004)
Amblard, M.: Calculs de représentations s’emantique et syntaxe générative: les grammaires minimalistes catégorielles. PhD thesis, Université de Bordeaux 1 (2007)
Girard, J.Y.: Linear logic. Theoretical Computer Science 50, 1–102 (1987)
Curry, H.B.: Some logical aspects of grammatical structure. In: Jakobson, R. (ed.) Structure of Language and Its Mathematical Aspects, pp. 56–68. AMS Bookstore (1961)
Muskens, R.: Lambda Grammars and the Syntax-Semantics Interface. In: van Rooy, R., Stokhof, M. (eds.) Proceedings of the Thirteenth Amsterdam Colloquium, Amsterdam, pp. 150–155 (2001)
de Groote, P.: Towards abstract categorial grammars. In: Association for Computational Linguistics, Proceedings 39th Annual Meeting and 10th Conference of the European Chapter, pp. 148–155. Morgan Kaufmann Publishers, San Francisco (2001)
de Groote, P.: Towards a montagovian account of dynamics. In: Proceedings of Semantics in Linguistic Theory, vol. XVI. CLC Publications (2007)
Stabler, E.: Derivational minimalism. In: Retoré, C. (ed.) LACL 1996. LNCS (LNAI), vol. 1328, pp. 68–95. Springer, Heidelberg (1997)
de Groote, P., Guillaume, B., Salvati, S.: Vector addition tree automata. In: de Groote, P., Guillaume, B., Salvati, S. (eds.) 19th IEEE Symposium on Logic in Computer Science, pp. 63–74 (2004)
Gärtner, H.M., Michaelis, J.: Locality conditions and the complexity of minimalist grammars: a preliminary survey. In: Rogers, J. (ed.) Workshop on Model Theoretic Syntax (MTS@10), Dublin, Ireland, pp. 89–100 (2007)
Hopcroft, J.E., Pansiot, J.J.: On the reachability problem for 5-dimensional vector addition systems. Theoretical Computer Science 8(2), 135–159 (1979)
Yoshinaka, R.: Linearization of affine abstract categorial grammars. In: Proceedings of the 11th Conference on Formal Grammar (2006)
Salvati, S.: Encoding second order string acg with deterministic tree walking transducers. In: Wintner, S. (ed.) Proceedings FG 2006: the 11th Conference on Formal Grammars. FG Online Proceedings, pp. 143–156. CSLI Publications, Stanford (2007)
Michaelis, J.: Derivational minimalism is mildly context-sensitive. In: Moortgat, M. (ed.) LACL 1998. LNCS (LNAI), vol. 2014, pp. 179–198. Springer, Heidelberg (2001)
Kobele, G.M.: Generating Copies: An Investigation into Structural Identity in Language and Grammar. PhD thesis, University of California Los Angeles (2006)
Stabler, E.P.: Remnant movement and structural complexity. In: Constraints and Resources in Natural Language, Studies in Logic, Language and Information, pp. 299–326. CSLI, Stanford (1999)
Courcelle, B.: Monadic second-order definable graph transductions: A survey. Theoritical Computer Science 126(1), 53–75 (1994)
Weir, D.J.: Linear context-free rewriting systems and deterministic tree-walking transducers. In: ACL, pp. 136–143 (1992)
Pullum, G.K., Scholz, B.C.: On the distinction between model-theoretic and generative-enumerative syntactic frameworks. In: de Groote, P., Morrill, G., Retoré, C. (eds.) LACL 2001. LNCS (LNAI), vol. 2099, pp. 17–43. Springer, Heidelberg (2001)
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Salvati, S. (2011). Minimalist Grammars in the Light of Logic. 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_5
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DOI: https://doi.org/10.1007/978-3-642-21490-5_5
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