Studia Logica

, Volume 71, Issue 3, pp 443–451 | Cite as

A Rule-Extension of the Non-Associative Lambek Calculus

  • Heinrich Wansing


An extension L+ of the non-associative Lambek calculus Lis defined. In L+ the restriction to formula-conclusion sequents is given up, and additional left introduction rules for the directional implications are introduced. The system L+ is sound and complete with respect to a modification of the ternary frame semantics for L.

Categorial Grammar Lambek Calculus coimplication 


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  1. [1]
    Ajdukiewicz, K., ‘Die syntaktische Konnexität’, Studia Philosophica 1 (1935), 1-27.Google Scholar
  2. [2]
    Bar-Hillel, Y., ‘A quasiarithmetical notation for syntactic description’, Language 29 (1953), 47-58.Google Scholar
  3. [3]
    Bar-Hillel, Y., ‘The present status of automatic translation of languages’, in: F. L. Alt (ed.), Advances in computers, Vol. 1, Academic Press, New York, 1960, 91-163.Google Scholar
  4. [4]
    Buszkowski, W., ‘Mathematical linguistics and proof theory’, in: J. van Benthem and A. ter Meulen (eds.), Handbook of Logic and Language, North-Holland, Amsterdam, 1997, 683-736.Google Scholar
  5. [5]
    Došen, K., ‘A brief survey of frames for the Lambek calculus’, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 38 (1992), 179-187.Google Scholar
  6. [6]
    Goré, R., ‘Dual intuitionistic logic revisited’, in: R. Dyckhoff (ed.), Proceedings Tableaux 2000, LNAI 1847, Springer-Verlag, Berlin, 2000, 252-267.Google Scholar
  7. [7]
    Lambek, J., ‘The mathematics of sentence structure’, American Mathematical Monthly 65 (1958), 154-170.Google Scholar
  8. [8]
    Lambek, J., ‘On the calculus of syntactic types’, in: R. Jakobson (ed.), Structure of Language and Its Mathematical Aspects, American Mathematical Society, Providence R.I., 1961, 166-178.Google Scholar
  9. [9]
    G. Morrill, Type Logical Grammar, Kluwer Academic Publishers, Dordrecht, 1994.Google Scholar
  10. [10]
    Moortgat, M., ‘Categorial type logics’, in: J. van Benthem and A. ter Meulen (eds.), Habdbook of Logic and Language, North-Holland, Amsterdam, 1997, 93-177.Google Scholar
  11. [11]
    Rauszer, C., ‘An algebraic and Kripke-style approach to a certain extension of intuitionistic logic’, Dissertationes Mathematicae, vol. CLXVII, Warsaw, 1980.Google Scholar
  12. [12]
    Restall, G., ‘A useful substructural logic’, Bulletin of the IGPL 2 (1994), 137-148.Google Scholar
  13. [13]
    Wansing, H., ‘On the expressiveness of categorial grammar’, in: V. Sinsini and J. Woleński (eds.), The Heritage of Kazimierz Ajdukiewicz, Rodopi, Amsterdam, 1995, 337-351.Google Scholar
  14. [14]
    Wolter, F., ‘On logics with coimplication’, Journal of Philosophical Logic 27 (1998), 353-387.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Heinrich Wansing
    • 1
  1. 1.Institute of PhilosophyDresden University of TechnologyDresdenGermany

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