An Account of Natural Language Coordination in Type Theory with Coercive Subtyping

  • Stergios Chatzikyriakidis
  • Zhaohui Luo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8114)


We discuss the semantics of NL coordination in modern type theories (MTTs) with coercive subtyping. The issue of conjoinable types is handled by means of a type universe of linguistic types. We discuss quantifier coordination, arguing that they should be allowed in principle and that the semantic infelicity of some cases of quantifier coordination is due to the incompatible semantics of the relevant quantifiers. Non-Boolean collective readings of conjunction are also discussed and, in particular, treated as involving the vectors of type Vec(A,n), an inductive family of types in an MTT. Lastly, the interaction between coordination and copredication is briefly discussed, showing that the proposed account of coordination and that of copredication by means of dot-types combine consistently as expected.


Type Theory Proof Assistant Common Noun Vector Type Introduction Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Montague, R.: The proper treatment of quantification in ordinary English. In: Hintikka, J., Moravcsik, J., Suppes, P. (eds.) Approaches to Natural Languages (1973)Google Scholar
  2. 2.
    Martin-Löf, P.: Intuitionistic Type Theory. Bibliopolis (1984)Google Scholar
  3. 3.
    Nordström, B., Petersson, K., Smith, J.: Programming in Martin-Löf’s Type Theory: An Introduction. Oxford University Press (1990)Google Scholar
  4. 4.
    Luo, Z.: Computation and Reasoning: A Type Theory for Computer Science. Oxford Univ Press (1994)Google Scholar
  5. 5.
    The Coq Development Team: The Coq Proof Assistant Reference Manual (Version 8.3), INRIA (2010)Google Scholar
  6. 6.
    Ranta, A.: Type-Theoretical Grammar. Oxford University Press (1994)Google Scholar
  7. 7.
    Luo, Z.: Type-theoretical semantics with coercive subtyping. Semantics and Linguistic Theory 20 (SALT20), Vancouver (2010)Google Scholar
  8. 8.
    Luo, Z.: Contextual analysis of word meanings in type-theoretical semantics. In: Pogodalla, S., Prost, J.-P. (eds.) LACL 2011. LNCS, vol. 6736, pp. 159–174. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  9. 9.
    Keenan, E., Faltz, L.: Logical Types for Natural Language. In: Department of Linguistics. UCLA (1978)Google Scholar
  10. 10.
    Partee, B., Rooth, M.: Generalized conjunction and type ambiguity. In: Bauerle, R., Schwarze, C., von Stechow, A. (eds.) Meaning, use, and Interpretation of Language. Mouton De Gruyter (1983)Google Scholar
  11. 11.
    Pustejovsky, J.: The Generative Lexicon. MIT (1995)Google Scholar
  12. 12.
    Pustejovsky, J.: Meaning in Context: Mechanisms of Selection in Language. Cambridge Press (2005)Google Scholar
  13. 13.
    Asher, N.: Lexical Meaning in Context: a Web of Words. Cambridge University Press (2012)Google Scholar
  14. 14.
    Bassac, C., Mery, B., Retoré, C.: Towards a type-theoretical account of lexical semantics. Journal of Logic Language and Information 19, 229–245 (2010)CrossRefGoogle Scholar
  15. 15.
    Callaghan, P., Luo, Z.: An implementation of LF with coercive subtyping and universes. Journal of Automated Reasoning 27, 3–27 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    The Agda proof assistant (version 2), (2008)
  17. 17.
    Xue, T., Luo, Z.: Dot-types and their implementation. In: Béchet, D., Dikovsky, A. (eds.) LACL 2012. LNCS, vol. 7351, pp. 234–249. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  18. 18.
    Church, A.: A formulation of the simple theory of types. J. Symbolic Logic 5 (1940)Google Scholar
  19. 19.
    Montague, R.: Formal Philosophy. Yale University Press (1974)Google Scholar
  20. 20.
    Luo, Z.: Common nouns as types. In: Béchet, D., Dikovsky, A. (eds.) LACL 2012. LNCS, vol. 7351, pp. 173–185. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  21. 21.
    Geach, P.: Reference and Generality: An examination of some Medieval and Modern Theories. Cornell University Press (1962)Google Scholar
  22. 22.
    Curry, H., Feys, R.: Combinatory Logic, vol. 1. North-Holland (1958)Google Scholar
  23. 23.
    Howard, W.A.: The formulae-as-types notion of construction. In: Hindley, J., Seldin, J. (eds.) To H. B. Curry: Essays on Combinatory Logic. Academic Press (1980)Google Scholar
  24. 24.
    Luo, Z.: Coercive subtyping. Journal of Logic and Computation 9, 105–130 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Luo, Z., Soloviev, S., Xue, T.: Coercive subtyping: theory and implementation (2012) (submitted manuscript)Google Scholar
  26. 26.
    Winter, Y.: A unified semantic treatment of singular NP coordination. Linguistics and Philosophy 19, 337–391 (1996)CrossRefGoogle Scholar
  27. 27.
    Hoeksema, J.: The semantics of non-boolean “and”. Journal of Semantics 6, 19–40 (1998)CrossRefGoogle Scholar
  28. 28.
    Moortgat, M.: Categorial type logics. In: van Benthem, J., ter Meulen, A. (eds.) Handbook of Logic and Language. Elsevier/Mit press (1997)Google Scholar
  29. 29.
    Morril, G.: Type Logical Grammar: Categorial Logic of Signs. Kluwer Academic Publishers (1994)Google Scholar
  30. 30.
    Horn, L.: A Natural History of Negation. University of Chicago Press (1989)Google Scholar
  31. 31.
    Horn, L.: The border wars: a neo-Gricean perspective. In: von Heusinger, K., Turner, K. (eds.) Where Semantics Meets Pragmatics, pp. 21–46. Elsevier, Amsterdam (2006)Google Scholar
  32. 32.
    Geurts, B.: Quantity Implicatures. Cambridge University Press (2010)Google Scholar
  33. 33.
    Winter, Y.: Flexibility Principles in Boolean Semantics. MIT Press, New York (2002)Google Scholar
  34. 34.
    Boldini, P.: The reference of mass terms from a type-theoretical point of view. In: Paper from the 4th International Workshop on Computational Semantics (2001)Google Scholar
  35. 35.
    Sundholm, G.: Proof theory and meaning. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic III: Alternatives to Classical Logic. Reidel (1986)Google Scholar
  36. 36.
    Retoré, C.: Variable types for meaning assembly: a logical syntax for generic noun phrases introduced by ‘most’. Recherches Linguistiques de Vincennes 41, 83–102 (2012)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Stergios Chatzikyriakidis
    • 1
  • Zhaohui Luo
    • 2
  1. 1.Dept. of Computer ScienceRoyal Holloway, Univ. of London, Open University of CyprusEghamU.K.
  2. 2.Dept. of Computer ScienceRoyal Holloway, Univ. of LondonEghamU.K.

Personalised recommendations