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Proof-Nets, Hybrid Logics and Minimalist Representations

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Grammars

Abstract

In this paper, we aim at giving a logical account of the representationalist view of minimalist grammars by referring to the notion of Proof-Net in Linear Logic. We propose, at the same time, a hybrid logic which mixes one logic (Lambek calculus) for building up elementary proofs and another one for combining the proofs so obtained. Because the first logic is non-commutative and the second one is commutative, this brings us a way to combine commutativity and non-commutativity in the same framework. The dynamic of cut-elimination in proof-nets is used to formalise the move-operation. Otherwise, we advocate a proof-net formalism which allows us to consider formulae as nodes to which it is possible to assign weights which determine the final phonological interpretation.

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References

  • Chomsky, N. The Minimalist Program, The MIT Press, Cambridge, MA, 1996.

    Google Scholar 

  • Cornell, T. Derivational and Representational Views of Minimalist Transformational Grammar. In A. Lecomte, F. Lamarche and G. Perrier, editors, Logical Aspects of Computational Linguistics, 1998.

  • Joshi, A. and S. Kulick, Partial Proof Trees, Resource Sensitive Logics and Syntactic Constraints. In Retoré (1997), 21–42, 1997.

  • Lamarche, F. Proof-Nets for Intuitionistic Linear Logic: Essential Nets. Technical report, Imperial College, London, 1995.

    Google Scholar 

  • Moortgat, M. Categorial Type Logics. In J. van Benthem and A. ter Meulen, editors, Handbook of Logic and Language, Elsevier, Amsterdam, chapt. 2, 93–178, 1997.

    Google Scholar 

  • Retoré, C. PerfectMatchings and Series-ParallelGraphs:Multiplicative Proof-Nets as BR-Graphs. In J. Girard, M. Okada and A. Scedrov, editors, Linear'96, vol. 3 of Electronic Notes in Theoretical Computer Sciences, 1996.

  • Retoré, C. (editor). Logical Aspects of Computational Linguistics, Vol. 1328 of LNCS/LNAI. Springer, Berlin, 1997.

    Google Scholar 

  • Stabler, E. Derivational Minimalism. In Retoré (1997), 68–95, 1997.

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Authors and Affiliations

  1. LORIA-Calligramme, 615 Rue du Jardin Botanique, BP 101, 54602, Villers-les-Nancy, France

    Alain Lecomte

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  1. Alain Lecomte
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Lecomte, A. Proof-Nets, Hybrid Logics and Minimalist Representations. Grammars 3, 243–257 (2000). https://doi.org/10.1023/A:1009957126407

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  • DOI: https://doi.org/10.1023/A:1009957126407

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