The Conjoinability Relation in Discontinuous Lambek Calculus

  • Alexey Sorokin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8612)


In 2013 Sorokin proved that the criterion of type conjoinability in 1-discontinuous Lambek calculus is the equality of interpretations in the free abelian group generated by primitive types. We extend the method to obtain the analogous result in full discontinuous Lambek calculus. It holds that the criterion is exactly the same as in 1-discontinuous Lambek calculus.


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  1. 1.
    Béchet, D.: Parsing pregroup grammars and Lambek grammars using partial composition. Studia Logica 87(2-3), 199–224 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Buszkowski, W., Moroz, K.: Pregroup grammars and context-free grammars. In: Computational Algebraic Approaches to Natural Language, pp. 1–21. Polimetrica (2008)Google Scholar
  3. 3.
    Lambek, J.: The mathematics of sentence structure. American Mathematical Monthly 65(3), 154–170 (1958)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Moortgat, M., Pentus, M.: Type similarity for the Lambek-Grishin calculus. In: Proceedings of the 12th Conference on Formal Grammar, Dublin (2007)Google Scholar
  5. 5.
    Morrill, G., Valentín, O.: On calculus of displacement. In: Proceedings of the 10th International Workshop on Tree Adjoining Grammars and Related Formalisms, pp. 45–52 (2010)Google Scholar
  6. 6.
    Morrill, G., Valentín, O., Fadda, M.: The displacement calculus. Journal of Logic, Language and Information 20(1), 1–48 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Pentus, M.: The conjoinability relation in Lambek calculus and linear logic. ILLC Prepublication Series ML–93–03, Institute for Logic, Language and Computation, University of Amsterdam (1993)Google Scholar
  8. 8.
    Pentus, M.: Lambek grammars are context-free. In: Logic in Computer Science, Proceedings of the LICS 1993, pp. 429–433 (1993)Google Scholar
  9. 9.
    Sorokin, A.: Conjoinability in 1-discontinuous Lambek calculus. In: Casadio, C., Coecke, B., Moortgat, M., Scott, P. (eds.) Lambek Festschrift. LNCS, vol. 8222, pp. 393–401. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  10. 10.
    Valentín, O.: Theory of discontinuous Lambek calculus: PhD Thesis. Universitat Autònoma de Barcelona, Barcelona (2012)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Alexey Sorokin
    • 1
  1. 1.Faculty of Mathematics and Mechanics Moscow Institute of Physics and Technology, Faculty of Innovations and High TechnologiesMoscow State UniversityRussia

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