Document Open Access Logo

The Montagovian Generative Lexicon Lambda Ty_n: a Type Theoretical Framework for Natural Language Semantics

Author Christian Retoré

PDF
Thumbnail PDF

File

LIPIcs.TYPES.2013.202.pdf
  • Filesize: 2.38 MB
  • 28 pages

Document Identifiers

Author Details

Christian Retoré

Cite As Get BibTex

Christian Retoré. The Montagovian Generative Lexicon Lambda Ty_n: a Type Theoretical Framework for Natural Language Semantics. In 19th International Conference on Types for Proofs and Programs (TYPES 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 26, pp. 202-229, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014) https://doi.org/10.4230/LIPIcs.TYPES.2013.202

Abstract

We present a framework, named the Montagovian generative lexicon, for computing the semantics of natural language sentences, expressed in many sorted higher order logic. Word meaning is depicted by several lambda terms of second order lambda calculus (Girard's system F): the principal lambda term encodes the argument structure, while the other lambda terms implement meaning transfers. The base types include a type for propositions and many types for sorts of a many sorted logic for expressing restriction of selection. This framework is able to integrate a proper treatment of lexical phenomena into a Montagovian compositional semantics, like the (im)possible arguments of a predicate, and the adaptation of a word meaning to some contexts. Among these adaptations of a word's sense to the context, ontological inclusions are handled by coercive subtyping, an extension of system F introduced in the present paper. The benefits of this framework for lexical semantics and pragmatics are illustrated on meaning transfers and coercions, on possible and impossible copredication over different senses, on deverbal ambiguities, and on "fictive motion". Next we show that the compositional treatment of determiners, quantifiers, plurals,... are finer grained in our framework. We then conclude with the linguistic, logical and computational perspectives opened by the Montagovian generative lexicon.

Subject Classification

Keywords
  • type theory
  • computational linguistics

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. Vito Michele Abrusci and Christian Retoré. Quantification in ordinary language: from a critic of set-theoretic approaches to a proof-theoretic proposal. In Peter Schröder-Heister, editor, 14th Congress of Logic, Methodology and Philosophy of Sciences, 2011. Google Scholar
  2. W. Ackermann. Begründung des "tertium non datur" mittels der Hilbertschen Theorie der Widerspruchsfreiheit. Mathematische Annalen, 93:1-36, 1924. Google Scholar
  3. Nicholas Asher. Lexical Meaning in context - a web of words. Cambridge University press, 2011. Google Scholar
  4. Nicholas Asher and Zhaohui Luo. Formalization of coercions in lexical semantics. In Emmanuel Chemla, Vincent Homer, and Grégoire Winterstein, editors, Sinn und Bedeutung 17, pages 63-80, 2012. URL: http://semanticsarchive.net/sub2012/.
  5. Nicholas Asher and James Pustejovsky. The metaphysics of words in contexts, 2000. Google Scholar
  6. Nicolas Asher. A type driven theory of predication with complex types. Fundamenta Informaticae, 84(2):151-183, 2008. Google Scholar
  7. Gunter Asser. Theorie der logischen auswahlfunktionen. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 1957. Google Scholar
  8. Christian Bassac, Bruno Mery, and Christian Retoré. Towards a Type-Theoretical Account of Lexical Semantics. Journal of Logic Language and Information, 19(2):229-245, April 2010. Google Scholar
  9. Denis Béchet and Alexander Ja. Dikovsky, editors. Logical Aspects of Computational Linguistics - 7th International Conference, LACL 2012, Nantes, France, July 2-4, 2012. Proceedings, volume 7351 of Lecture Notes in Computer Science. Springer, 2012. Google Scholar
  10. Gilad Ben-Avi and Nissim Francez. Categorial grammars with ontology-refined types. In Categorial grammars - an efficient tool for natural language processing, pages 99-113, Montpellier, June 2004. C.N.R.S. Google Scholar
  11. Manfred Bierwisch. Wörtliche bedeutung - eine pragmatische gretchenfrage. In G. Grewendorf, editor, Sprechakttheorie und Semantik, pages 119-148. Surkamp, Frankfurt, 1979. Google Scholar
  12. Manfred Bierwisch. Semantische und konzeptuelle repräsentation lexikalischer einheiten. In R. R\.u\uzic̆ka and W. Motsch, editors, Untersuchungen zur Semantik, pages 61-99. Akademie-Verlag, Berlin, 1983. Google Scholar
  13. Reinhard Blutner. Lexical semantics and pragmatics. In Fritz Hamm and Thomas Ede Zimmermann, editors, Semantics, volume 10 (Sonderheft), pages 27-58, Hamburg, 2002. Buske. Google Scholar
  14. J. T. Canty. Zbl0327.02013 : review of "on an extension of Hilbert’s second ε-theorem" by T. B. Flanagan (journal of symbolic logic, 1975). Zentralblatt Math. Google Scholar
  15. Luca Cardelli, Simone Martini, John C. Mitchell, and Andre Scedrov. An extension of system F with subtyping. Information and Computation, 109(1/2):4-56, 1994. Google Scholar
  16. Stergios Chatzikyriakidis and Zhaohui Luo. An account of natural language coordination in type theory with coercive subtyping. In Denys Duchier and Yannick Parmentier, editors, 7th International Workshop on Constraint Solving and Language Processing (CSLP'12). Selected and Revised Papers, number 8114 in Lecture Notes in Computer Science. Springer, 2013. Google Scholar
  17. Stergios Chatzikyriakidis and Zhaohui Luo. Adjectives in a modern type-theoretical setting. In Glyn Morrill and Mark-Jan Nederhof, editors, FG, volume 8036 of Lecture Notes in Computer Science, pages 159-174. Springer, 2013. Google Scholar
  18. Philipp Cimiano and Johanna Wenderoth. Automatic acquisition of ranked qualia structures from the web. In John A. Carroll, Antal van den Bosch, and Annie Zaenen, editors, ACL. The Association for Computational Linguistics, 2007. Google Scholar
  19. Robin Cooper. Copredication, dynamic generalized quantification and lexical innovation by coercion. In Fourth International Workshop on Generative Approaches to the Lexicon. Université de Genève, 2007. Google Scholar
  20. Robin Cooper. Copredication, quantification and frames. In Pogodalla and Prost [60], pages 64-79. Google Scholar
  21. D.A. Cruse. Lexical semantics. Cambridge textbooks in linguistics. Cambridge University Press, 1986. Google Scholar
  22. Urs Egli and Klaus von Heusinger. The epsilon operator and E-type pronouns. In Urs Egli, Peter E. Pause, Christoph Schwarze, Arnim von Stechow, and Götz Wienold, editors, Lexical Knowledge in the Organization of Language, pages 121-141. Benjamins, 1995. Google Scholar
  23. Peter Flach. Machine Learning: The Art and Science of Algorithms That Make Sense of Data. Cambridge University Press, New York, NY, USA, 2012. Google Scholar
  24. Jean-Yves Girard. Une extension de l'interprétation de Gödel à l'analyse et son application: l'élimination des coupures dans l'analyse et la théorie des types. In Jens Erik Fenstad, editor, Proceedings of the Second Scandinavian Logic Symposium, volume 63 of Studies in Logic and the Foundations of Mathematics, pages 63-92, Amsterdam, 1971. North Holland. Google Scholar
  25. Jean-Yves Girard. The blind spot - lectures on logic. European Mathematical Society, 2011. Google Scholar
  26. David Hilbert. Die logischen grundlagen der mathematik. Mathematische Annalen, 88:151-165, 1922. Google Scholar
  27. David Hilbert and Paul Bernays. Grundlagen der Mathematik. Bd. 2. Springer, 1939. Traduction française de F. Gaillard, E. Guillaume et M. Guillaume, L'Harmattan, 2001. Google Scholar
  28. Gérard P. Huet. Résolution d'équations dans des langages d'ordre 1,2,...,ω. Thèse de doctorat d'état, Université Paris VII, 1976. Google Scholar
  29. Hans Kamp and Uwe Reyle. From Discourse to Logic. D. Reidel, Dordrecht, 1993. Google Scholar
  30. Yves Lafont. Soft linear logic and polynomial time. Theoretical Computer Science, 318(1-2):163 - 180, 2004. Google Scholar
  31. Mathieu Lafourcade and Alain Joubert. Computing trees of named word usages from a crowdsourced lexical network. In IMCSIT, volume Computational Linguistics - Applications (CLA'10), pages 439-446, 2010. Google Scholar
  32. Sven Lauer. A comparative study of current theories of polysemy in formal semantics. Master’s thesis, Cognitive science Osnabrück - Computational Linguistics, 2004. Google Scholar
  33. Alain Lecomte and Myriam Quatrini. Figures of dialogue: a view from ludics. Synthese, 183:59-85, 2011. Google Scholar
  34. Anaïs Lefeuvre, Richard Moot, and Christian Retoré. Traitement automatique d'un corpus de récits de voyages pyrénéens : analyse syntaxique, sémantique et pragmatique dans le cadre de la théorie des types. In SHS Web of Conferences, editor, Congrès mondial de linguistique française, pages 2485-2497, 2012. Google Scholar
  35. Anaïs Lefeuvre, Richard Moot, Christian Retoré, and Noémie-Fleur Sandillon-Rezer. Traitement automatique sur corpus de récits de voyages pyrénéens : Une analyse syntaxique, sémantique et temporelle. In Traitement Automatique du Langage Naturel, TALN'2012, volume 2, pages 43-56, 2012. Google Scholar
  36. Albert C. Leisenring. Mathematical logic and Hilbert’s ε symbol. University Mathematical Series. Mac Donald & Co., 1967. Google Scholar
  37. Giuseppe Longo, Kathleen Milsted, and Sergei Soloviev. Coherence and transitivity of subtyping as entailment. Journal of Logic and Computation, 10(4):493-526, 2000. Google Scholar
  38. Zhaohui Luo. Contextual analysis of word meanings in type-theoretical semantics. In Pogodalla and Prost [60], pages 159-174. Google Scholar
  39. Zhaohui Luo. Common nouns as types. In Béchet and Dikovsky [9], pages 173-185. Google Scholar
  40. Zhaohui Luo, Sergei Soloviev, and Tao Xue. Coercive subtyping: Theory and implementation. Inf. Comput., 223:18-42, 2013. Google Scholar
  41. Bruno Mery, Richard Moot, and Christian Retoré. Plurals: individuals and sets in a richly typed semantics. In Shunsuke Yatabe, editor, Logic and Engineering of Natural Language Semantics 10 (LENLS 10), pages 143-156. Keio University, 2013. ISBN 978-4-915905-57-5. Google Scholar
  42. Bruno Mery and Christian Retoré. Advances in the logical representation of lexical semantics. In Valeria de Paiva and Larry Moss, editors, Natural Language and Computer Science (LICS 2013 satellite workshop), New-Orleans, 2013. Google Scholar
  43. Bruno Mery and Christian Retoré. Semantic types, lexical sorts and classifiers. In B. Sharp and M. Zock, editors, 10th International Workshop on Natural Language Processing and Cognitive Science, Marseilles, September 2013. Google Scholar
  44. G. Mints. Zbl0381.03042: review of "cut elimination in a Gentzen-style ε-calculus without identity" by Linda Wessels (Z. math Logik Grundl. Math., 1977). Zentralblatt Math. Google Scholar
  45. Grigori Mints. Cut elimination for a simple formulation of epsilon calculus. Ann. Pure Appl. Logic, 152(1-3):148-160, 2008. Google Scholar
  46. Richard Montague. English as a formal language. In Bruno Visentini, editor, Linguaggi nella Societa e nella Tecnica, pages 189-224. Edizioni di Communità, Milan, Italy, 1970. (Reprinted in R. Thomason (ed) The collected papers of Richard Montague Yale University Press, 1974.). Google Scholar
  47. Richard Moot. Automated extraction of type-logical supertags from the spoken dutch corpus. In Srinivas Bangalore and Aravind Joshi, editors, The Complexity of Lexical Descriptions and its Relevance to Natural Language Processing: A Supertagging Approach. MIT Press, 2007. Google Scholar
  48. Richard Moot. Semi-automated extraction of a wide-coverage type-logical grammar for French. In Proceedings of Traitement Automatique des Langues Naturelles (TALN), Montreal, 2010. Google Scholar
  49. Richard Moot. Wide-coverage French syntax and semantics using Grail. In Proceedings of Traitement Automatique des Langues Naturelles (TALN), Montreal, 2010. Google Scholar
  50. Richard Moot, Laurent Prévot, and Christian Retoré. A discursive analysis of itineraries in an historical and regional corpus of travels. In Constraints in discourse, Ayay-roches-rouges, France, September 2011. URL: http://passage.inria.fr/cid2011/doku.php.
  51. Richard Moot, Laurent Prévot, and Christian Retoré. Un calcul de termes typés pour la pragmatique lexicale - chemins et voyageurs fictifs dans un corpus de récits de voyages. In Traitement Automatique du Langage Naturel, TALN 2011, pages 161-166, Montpellier, France, June 2011. Google Scholar
  52. Richard Moot and Christian Retoré. Second order lambda calculus for meaning assembly: on the logical syntax of plurals. In Reinhard Muskens, editor, Coconat: Conference on Computing Natural Reasoning. University of Tilburg, December 2011. URL: http://hal.inria.fr/hal-00650644.
  53. Richard Moot and Christian Retoré. The logic of categorial grammars: a deductive account of natural language syntax and semantics, volume 6850 of LNCS. Springer, 2012. Google Scholar
  54. Georg Moser and Richard Zach. The epsilon calculus and herbrand complexity. Studia Logica, 82(1):133-155, 2006. Google Scholar
  55. Reinhard Muskens. Anaphora and the logic of change. In Jan van Eijck, editor, JELIA, volume 478 of Lecture Notes in Computer Science, pages 412-427. Springer, 1990. Google Scholar
  56. Reinhard Muskens. Combining Montague Semantics and Discourse Representation. Linguistics and Philosophy, 19:143-186, 1996. Google Scholar
  57. Geoffrey Nunberg. Transfers of meaning. Journal of semantics, 12(2):109-132, 1995. Google Scholar
  58. Barbara Partee. Noun phrase interpretation and type shifting principles. In B.H. Partee and P.H. Portner, editors, Formal Semantics: The Essential Readings, pages 357-381. Wiley, 2008. Google Scholar
  59. Stanley Peters and Dag Westerståhl. Quantifiers in Language and Logic. Clarendon Press, 2006. Google Scholar
  60. Sylvain Pogodalla and Jean-Philippe Prost, editors. Logical Aspects of Computational Linguistics - 6th International Conference, LACL 2011, Montpellier, France, June 29 to July 1, 2011. Proceedings, volume 6736 of LNCS. Springer, 2011. Google Scholar
  61. James Pustejovsky. The generative lexicon. Computational Linguistics, 17(4):409-441, 1991. Google Scholar
  62. James Pustejovsky. The generative lexicon. M.I.T. Press, 1995. Google Scholar
  63. Livy Real and Christian Retoré. Deverbal semantics and the Montagovian generative lexicon Λ Ty_n. Journal of Logic Language and Information, 2014. 10.1007/s10849-014-9187-y. Google Scholar
  64. Christian Retoré. Variable types for meaning assembly: a logical syntax for generic noun phrases introduced by "most". Recherches Linguistiques de Vincennes, 41:83-102, 2012. Google Scholar
  65. Christian Retoré. A natural framework for natural language semantics: many sorted logic and Hilbert operators in type theory. In Mário Edmundo and Boban Velickovic, editors, Logic colloquium, Evora, 2013. Google Scholar
  66. Christian Retoré. Sémantique des déterminants dans un cadre richement typé. In Emmanuel Morin and Yannick Estève, editors, Traitement Automatique du Langage Naturel, TALN RECITAL 2013, volume 1, pages 367-380. ACL Anthology, 2013. Google Scholar
  67. Christian Retoré. Typed hilbert epsilon operators and the semantics of determiner phrases (invited lecture). In Glyn Morrill, Reinhard Muskens, Rainer Osswald, and Frank Richter, editors, Proceedings of Formal Grammar 2014, number 8612 in LNCS/FoLLI, pages 15-33. Springer, 2014. Invited lecture. Google Scholar
  68. Bertrand Russell. On denoting. Mind, 56(14):479-493, 1905. Google Scholar
  69. Sergei Soloviev and David Chemouil. Some Algebraic Structures in Lambda-Calculus with Inductive Types. In Stefano Berardi, Mario Coppo, and Ferruccio Damiani, editors, TYPES, volume 3085 of Lecture Notes in Computer Science, pages 338-354. Springer, 2003. Google Scholar
  70. Sergei Soloviev and Zhaohui Luo. Coercion completion and conservativity in coercive subtyping. Annals of Pure and Applied Logic, 1-3(113):297-322, 2000. Google Scholar
  71. Mark Steedman. Taking Scope: The Natural Semantics of Quantifiers. MIT Press, 2012. Google Scholar
  72. Leonard Talmy. Fictive motion in language and "ception". In Paul Bloom, Mary A. Peterson, Lynn Nadel, and Merrill F. Garrett, editors, Language and Space, pages 211-276. MIT Press, 1999. Google Scholar
  73. Jan van Eijck and Christina Unger. Computational Semantics with Functional Programming. Cambridge University Press, 2010. Google Scholar
  74. Luis von Ahn. Games with a purpose. Computer, 39(6):92-94, 2006. Google Scholar
  75. Klaus von Heusinger. Definite descriptions and choice functions. In S. Akama, editor, Logic, Language and Computation, pages 61-91. Kluwer, 1997. Google Scholar
  76. Klaus von Heusinger. Choice functions and the anaphoric semantics of definite nps. Research on Language and Computation, 2:309-329, 2004. Google Scholar
  77. Tao Xue and Zhaohui Luo. Dot-types and their implementation. In Béchet and Dikovsky [9], pages 234-249. Google Scholar
  78. Luke S. Zettlemoyer and Michael Collins. Learning context-dependent mappings from sentences to logical form. In Keh-Yih Su, Jian Su, and Janyce Wiebe, editors, ACL/IJCNLP, pages 976-984. The Association for Computer Linguistics, 2009. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact