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Proof Nets for the Multimodal Lambek Calculus: From Theory to a Wide-Coverage Categorial Parser

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The Logic of Categorial Grammars

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6850))

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Summary

In this chapter, we will extend the proof nets of the previous chapter to the multimodal Lambek calculus discussed in Chapter 5. This means incorporating non-associativity, mode information, unary connectives and structural rules in the proof nets. Fortunately, we will see that there is a single proof net calculus which can handle all these extensions together. The resulting proof nets will be two sided and have a more procedural correctness condition in the form of graph contractions. This correctness condition will also have a modular nature, due to the fact that different grammars may allow different classes of structural rules. These multimodal proof nets form the basis of an implementation and we will discuss the Grail theorem prover in Section 7.2.

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References

  • AbeillĂ©, A., ClĂ©ment, L., Toussenel, F.: Building a treebank for French. In: AbeillĂ©, A. (ed.) Treebanks: Building and Using Parsed Corpora, ch. 10, pp. 165–187. Kluwer, Dordrecht (2003)

    Chapter  Google Scholar 

  • Asher, N., Lascarides, A.: Logics of Conversation. Cambridge University Press (1993)

    Google Scholar 

  • Asher, N., Muller, P., Gaio, M.: Spatial entities are temporal entities too: The case of motion verbs. In: LREC 2008 Workshop on Methodologies and Resources for Processing Spatial Language, Marrakech (2008)

    Google Scholar 

  • Bangalore, S., Joshi, A.K. (eds.): Supertagging: Using Complex Lexical Descriptions in Natural Language Processing. MIT Press (2010)

    Google Scholar 

  • Bittar, A.: Building a Timebank for French: A reference corpus annotated according to the ISO-TimeML standard. PhD thesis, Ecole Doctoral de Sciences du Language Laboratoire Alpage (2010)

    Google Scholar 

  • Bos, J., Clark, S., Steedman, M., Curran, J.R., Hockenmaier, J.: Wide-coverage semantic representation from a CCG parser. In: Proceedings of the 20th International Conference on Computational Linguistics (COLING 2004), Geneva, Switzerland, pp. 1240–1246 (2004)

    Google Scholar 

  • Clark, S., Curran, J.R.: Parsing the WSJ using CCG and log-linear models. In: Proceedings of the 42nd Annual Meeting of the Association for Computational Linguistics (ACL 2004), Barcelona, Spain, pp. 104–111 (2004)

    Google Scholar 

  • Danos, V.: La logique linĂ©aire appliquĂ©e Ă  l’étude de divers processus de normalisation et principalement du λ-calcul. Thèse de Doctorat, spĂ©cialitĂ© MathĂ©matiques, UniversitĂ© Paris 7 (1990)

    Google Scholar 

  • Girard, J.Y., Lafont, Y., Taylor, P.: Proofs and Types. Cambridge Tracts in Theoretical Computer Science, vol. 7. Cambridge University Press (1988)

    Google Scholar 

  • Guerrini, S.: Correctness of multiplicative proof nets is linear. In: 14th Symposium on Logic in Computer Science (LICS 1999), pp. 454–463. IEEE (1999)

    Google Scholar 

  • Hockenmaier, J., Steedman, M.: CCGbank, a corpus of CCG derivations and dependency structures extracted from the Penn Treebank. Computational Linguistics 33(3), 355–396 (2007)

    Article  MATH  Google Scholar 

  • Joshi, A., Srinivas, B.: Disambiguation of super parts of speech (or supertags): Almost parsing. In: Proceedings of the 17th International Conference on Computational Linguistics, Kyoto (1994)

    Google Scholar 

  • Kamp, H., Reyle, U.: From Discourse to Logic. D. Reidel, Dordrecht (1993)

    MATH  Google Scholar 

  • Loustau, P.: InterprĂ©tation automatique d’itinĂ©raires dans des rĂ©cits de voyages d’une information gĂ©ographique du syntagme une information gĂ©ographique du discours. PhD thesis, UniversitĂ© de Pau (2008)

    Google Scholar 

  • Manning, C., SchĂ¼tze, H.: Foundations of statistical natural language processing. MIT Press (1999)

    Google Scholar 

  • Moortgat, M., Moot, R.: CGN to Grail: Extracting a type-logical lexicon from the CGN annotation. In: Daelemans, W. (ed.) Proceedings of CLIN 2000 (2001)

    Google Scholar 

  • Moot, R.: Proof nets for linguistic analysis. PhD thesis, Utrecht Institute of Linguistics OTS, Utrecht University (2002)

    Google Scholar 

  • Moot, R.: Graph algorithms for improving type-logical proof search. In: Proceedings Categorial Grammars 2004: an Efficient Tool for Natural Language Processing (2004)

    Google Scholar 

  • Moot, R.: Filtering axiom links for proof nets. In: Kallmeyer, L., Monachesi, P., Penn, G., Satta, G. (eds.) Proceedings of the 12th Conference on Formal Grammar (FG 2007). CSLI Publications, Dublin (2007) (to appear) ISSN 1935-1569

    Google Scholar 

  • Moot, R.: Lambek grammars and hyperedge replacement grammars. Tech. rep., LaBRI, CNRS (2008a)

    Google Scholar 

  • Moot, R.: Lambek grammars, tree adjoining grammars and hyperedge replacement grammars. In: Gardent, C., Sarkar, A. (eds.) Proceedings of TAG+9, The Ninth International Workshop on Tree Adjoining Grammars and Related Formalisms, pp. 65–72 (2008b)

    Google Scholar 

  • Moot, R.: Automated extraction of type-logical supertags from the Spoken Dutch Corpus. In: Bangalore, S., Joshi, A. (eds.) Supertagging: Using Complex Lexical Descriptions in Natural Language Processing. MIT Press (2010a)

    Google Scholar 

  • Moot, R.: Semi-automated extraction of a wide-coverage type-logical grammar for french. In: Proceedings of Traitement Automatique des Langues Naturelles (TALN 2010), Montreal (2010b)

    Google Scholar 

  • Moot, R.: Wide-coverage french syntax and semantics using Grail. In: Proceedings of Traitement Automatique des Langues Naturelles (TALN 2010), Montreal, System Demo (2010c)

    Google Scholar 

  • Moot, R.: Main Grail website (2012a), http://www.labri.fr/perso/moot/grail3.html

  • Moot, R.: Grail tutorial (2012b), http://www.labri.fr/perso/moot/tutorial/

  • Moot, R., Piazza, M.: Linguistic applications of first order multiplicative linear logic. Journal of Logic, Language and Information 10(2), 211–232 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  • Moot, R., Puite, Q.: Proof nets for the multimodal Lambek calculus. Studia Logica 71(3), 415–442 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  • Moot, R., RetorĂ©, C., PrĂ©vot, L.: Discursive analysis of itineraries in an historical and regional corpus of travels: syntax, semantics, and pragmatics in a unied type theoretical framework. In: Constraints in Discourse, Agay-Roches Rouges (2011)

    Google Scholar 

  • Morrill, G.: Higher order linear logic programming for categorial deduction. In: Proceedings of the European Association for Computational Linguistics, EACL 1995, Dublin, pp. 133–140 (1995)

    Google Scholar 

  • Murawski, A., Ong, C.H.: Dominator trees and fast verification of proof nets. In: 15th Symposium on Logic in Computer Science (LICS 2000), pp. 181–191. IEEE (2000)

    Google Scholar 

  • Partee, B.: Nominal and temporal anaphora. Linguistics and Philosophy 7(3), 243–286 (1984)

    Article  Google Scholar 

  • Puite, Q.: Proof nets with explicit negation for multiplicative linear logic. Tech. rep., Department of Mathematics, Utrecht University (1998), preprint 1079

    Google Scholar 

  • Puite, Q.: Sequents and link graphs: Contraction criteria for refinements of multiplicative linear logic. PhD thesis, Department of Mathematics, Utrecht University (2001)

    Google Scholar 

  • Pustejovsky, J.: The generative lexicon. MIT Press (1995)

    Google Scholar 

  • RĂ©gin, J.C.: A filtering algorithm for constraints of difference in CSPs. In: Proceedings of the Twelfth National Conference on Artificial Intelligence, pp. 362–367. AAAI, Seattle (1994)

    Google Scholar 

  • Sandillon-Rezer, N.-F., Moot, R.: Using tree Using Tree Transducers for Grammatical Inference. In: Pogodalla, S., Prost, J.-P. (eds.) LACL 2011. LNCS (LNAI), vol. 6736, pp. 235–250. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  • Savateev, Y.: Product-Free Lambek Calculus Is NP-Complete. In: Artemov, S., Nerode, A. (eds.) LFCS 2009. LNCS, vol. 5407, pp. 380–394. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

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Authors
  1. Richard Moot
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  2. Christian Retoré
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Moot, R., Retoré, C. (2012). Proof Nets for the Multimodal Lambek Calculus: From Theory to a Wide-Coverage Categorial Parser. In: The Logic of Categorial Grammars. Lecture Notes in Computer Science, vol 6850. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31555-8_7

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  • DOI: https://doi.org/10.1007/978-3-642-31555-8_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31554-1

  • Online ISBN: 978-3-642-31555-8

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