Are Types Needed for Natural Language?

  • Fairouz Kamareddine
Part of the Synthese Library book series (SYLI, volume 247)


Mixing type freeness and logic leads to contradictions. This can be seen by taking the following simple example.


Natural Language Variable Type Propositional Logic Type Theory Semantic Type 
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. Aczel, P.: 1980, “Frege structures and the notions of truth and proposition”, Kleene SymposiumGoogle Scholar
  2. Kleene Symposium Aczel, P.: 1984, Non well founded sets, CSLI lecture notes, No 14Google Scholar
  3. Barendregt, H. and Hemerik, C: 1990, “Types in Lambda calcului and programming languages”, in: N. Jones (ed.), European Symposium on pro-gramming, Lecture notes in Computer Science 423, Berlin, Springer Verlag, pp. 1–36Google Scholar
  4. Boolos, G.: 1971, “The iterative conception of sets”, Journal of PhilosophyLXVIII, pp. 215–231CrossRefGoogle Scholar
  5. Chierchia, and Turner, R.: 1988, “Semantics and property theory”, Linguistics and Philosophy 11, pp. 261–302CrossRefGoogle Scholar
  6. Cocchiarella, N.: 1984, “Frege’s Double Correlation Thesis and Quine’s set theories NF and ML”, Journal of Philosophical Logic 14, pp. 1–39CrossRefGoogle Scholar
  7. Feferman, S.: 1979, “Constructive theories of functions and classes”, in: M. Boffa et al. (eds), Logic Colloquium’78, North Holland, pp. 159–224Google Scholar
  8. Feferman, S.: 1984, “Towards useful type free theories I”, Journal of Symbolic Logic 49, pp 75–111CrossRefGoogle Scholar
  9. Girard, J.Y.: “The system F of variable types, fifteen years later”, Theoretical Computer Science 45, North-Holland, pp. 159–192Google Scholar
  10. Kamareddine, F.: 1989, Semantics in a Frege structure, PhD thesis, University of EdinburghGoogle Scholar
  11. Kamareddine, F.: 1992a, “A system at the cross roads of logic and functional programming”, Science of Computer Programming19, pp. 239–279CrossRefGoogle Scholar
  12. Kamareddine, F.: 1992b, “A-terms, logic, determiners and quantifiers”, Journal of Logic, Language and Information, Vol. 1, no 1, pp. 79–103CrossRefGoogle Scholar
  13. Kamareddine, F.: 1992c, “Set Theory and Nominalisation, Part I”, Journal of Logic and Computation, Vol. 2, no 5, pp. 579–604CrossRefGoogle Scholar
  14. Kamareddine, F.: 1992d, “Set Theory and Nominalisation, Part IF, Journal of Logic and Computation, Vol. 2, no 6, pp. 687–707CrossRefGoogle Scholar
  15. Kamareddine, F. and Klein, E.: 1993, “Polymorphism, Type containment and Nominalisation”, Journal of Logic, Language and Information 2, pp. 171–215CrossRefGoogle Scholar
  16. Kamareddine, F. and Nederpelt, R.P.: 1993, “On Stepwise explicit substitution”, International Journal of Foundations of Computer Science Vol.4, no.3, pp. 197–240CrossRefGoogle Scholar
  17. Kamareddine, F.: 1994a, “A Unified Framework of Logic and Polymorphism”, to appear in Journal of Semantics Google Scholar
  18. Kamareddine, F.: 1994b, “Non well-typedness and Type-freeness can unify the interpretation of functional application”, Journal of Logic, Language and Information, to appearGoogle Scholar
  19. Nederpelt, R.P., and Kamareddine, F.: 1994, “A unified approach to Type Theory through a refined A-calculus”, in: Michael Mislove et al. (ed.), Proceedings of the 1992 conference on Mathematical Foundations of Pro¬gramming Langauge Semantics Google Scholar
  20. Kamareddine, F. and Nederpelt, R.P.: 1995, The beauty of the X-Calculus, to appearGoogle Scholar
  21. Martin-Löf, P.: 1973, “An intuitionistic theory of types: predicative part”, in: Rose and Shepherdson (eds), logic colloquium ‘73, North HollandGoogle Scholar
  22. Milner, R.: 1978, “A theory of type polymorphism in programming”, Journalof Computer and System Sciences, Vol. 17, no 3 Google Scholar
  23. Parsons, T.: 1979, “Type Theory and Natural Language”, in: S. Davis and M. Mithum (eds), Linguistics, Philosophy and Montague grammar, University of Texas Press, pp. 127–151Google Scholar
  24. Poincare, H.: 1900, “Du role de Pintuition et de la logique en mathematiques”, CR. du II Congr. Intern, des Math., pp. 200–202Google Scholar
  25. Russell, B.: 1908, “Mathematical logic as based on the theory of types”, American Journal of Math. 30, pp. 222–262CrossRefGoogle Scholar
  26. Scott, D.: 1975, “Combinators and classes”, in: Böhm (ed.), Lambda Calculus and Computer Science, Lecture Notes in Computer Science 37, Berlin, Springer Verlag, pp. 1–26CrossRefGoogle Scholar
  27. Turner, R.: 1984, “Three Theories of Nominalized Predicates”, Studia Logica XLIV2, pp. 165–186Google Scholar
  28. Turner, R.: 1987, “A Theory of properties”, Journal of Symbolic Logic 52, pp. 63–89CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • Fairouz Kamareddine
    • 1
  1. 1.Department of Computing ScienceUniversity of GlasgowGlasgowScotland

Personalised recommendations