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Parsing Pregroup Grammars and Lambek Calculus Using Partial Composition

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Abstract

The paper presents a way to transform pregroup grammars into contextfree grammars using functional composition. The same technique can also be used for the proof-nets of multiplicative cyclic linear logic and for Lambek calculus allowing empty premises.

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References

  1. Abrusci Michele, (December 1991). ‘Phase semantics and sequent calculus for pure non-commutative classical linear logic’. Journal of Symbolic Logic 56(4):1403–1451

    Article  Google Scholar 

  2. Béchet Denis, (1998). ‘Minimality of the correctness criterion for multiplicative proof nets’. Mathematical Structures in Computer Science 8:543–558

    Article  Google Scholar 

  3. Béchet, Denis, ‘Incremental parsing of Lambek calculus using proof-net interfaces’, in ACL/SIGPARSE (ed.), Proceedings of the Eigth International Workshop on Parsing Technologies, Nancy, France, April 2003, INRIA, April 2003, pp. 31–42.

  4. Buszkowski, Wojciech, ‘Lambek grammars based on pregroups’, in Philippe de Groote, Glyn Morill, and Christian Retoré (eds.), Logical aspects of computational linguistics: 4th International Conference, LACL 2001, Le Croisic, France, June 2001, volume 2099, Springer-Verlag, 2001.

  5. Buszkowski, Wojciech, and Katarzyna Moroz, ‘PTIME transformation of pregroup grammar into cfg and pda’, 37th Poznań Linguistic Meeting (PLM), Poznań, 2006.

  6. Danos Vincent, Laurent Regnier, (1989). ‘The structure of multiplicatives’. Archive for Mathematical Logic 28:181–203

    Article  Google Scholar 

  7. de Groote, Philippe, ‘A dynamic programming approach to categorial deduction’, Conference on Automated Deduction, CADE‘99, Lecture Notes in Artificial Intelligence, Springer-Verlag, July 1999.

  8. Girard Jean-Yves, (1987). ‘Linear logic’. Theoretical Computer Science 50(1):1–102

    Article  Google Scholar 

  9. Lambek Joachim, (1958). ‘The mathematics of sentence structure’. American Mathematical Monthly 65:154–170

    Article  Google Scholar 

  10. Lambek, Joachim, ‘Type grammars revisited’, in Alain Lecomte, François Lamarche and Guy Perrier (eds.), Logical aspects of computational linguistics: Second International Conference, LACL ’97, Nancy, France, September 22–24, 1997; selected papers, volume 1582, Springer-Verlag, 1999.

  11. Lambek, Joachim, ‘Mathematics and the mind’, in V.M. Abrusci and C. Casadio (eds.), New Perspectives in Logic and Formal Linguisitics, Proceedings Vth ROMA Workshop, Bulzoni Editore, 2001.

  12. Lecomte, Alain, and Christian Retoré, ‘Words as modules and modules as partial proof nets in a lexicalised grammar’, in Michele Abrusci and Claudia Casadio (eds.), Third Roma Workshop: Proofs and Linguistics Categories — Applications of Logic to the analysis and implementation of Natural Language, Bologna:CLUEB, 1996, pp. 187–198.

  13. Lecomte, Alain, and Christian Retoré, ‘Words as modules: a lexicalised grammar in the framework of linear logic proof nets’, in Carlos Martin-Vide (ed.), Mathematical and Computational Analysis of Natural Language — selected papers from ICML‘96, volume 45 of Studies in Functional and Structural Linguistics, John Benjamins publishing company, 1998, pp. 129–144.

  14. Morrill, Glyn V., ‘Memoisation of categorial proof nets: parallelism in categorial processing’, in Third Roma Workshop: Proofs and Linguistics Categories — Applications of Logic to the analysis and implementation of Natural Language, Bologna:CLUEB, 1996.

  15. Pentus, Mati, ‘Lambek grammars are context-free’, in Logic in Computer Science, IEEE Computer Society Press, 1993.

  16. Pentus Mati, (1997). ‘Product-free Lambek calculus and context-free grammars’. Journal of Symbolic Logic 62 (2):648–660

    Google Scholar 

  17. Roorda, Dirk, Resource logics: Proof-theoretical investigations, Phd thesis, University of Amsterdam, 1991.

  18. Yetter David N., (1990). ‘Quantales and (non-commutative) linear logic’. Journal of Symbolic Logic 55:41–64

    Article  Google Scholar 

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Béchet, D. Parsing Pregroup Grammars and Lambek Calculus Using Partial Composition. Stud Logica 87, 199–224 (2007). https://doi.org/10.1007/s11225-007-9084-3

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