Skip to main content
SpringerLink
Log in

The Conjoinability Relation in Discontinuous Lambek Calculus

  • Conference paper
Formal Grammar (FG 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8612))

Included in the following conference series:

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Béchet, D.: Parsing pregroup grammars and Lambek grammars using partial composition. Studia Logica 87(2-3), 199–224 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  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. Lambek, J.: The mathematics of sentence structure. American Mathematical Monthly 65(3), 154–170 (1958)

    Article  MATH  MathSciNet  Google Scholar 

  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. 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. Morrill, G., Valentín, O., Fadda, M.: The displacement calculus. Journal of Logic, Language and Information 20(1), 1–48 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  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. Pentus, M.: Lambek grammars are context-free. In: Logic in Computer Science, Proceedings of the LICS 1993, pp. 429–433 (1993)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  10. Valentín, O.: Theory of discontinuous Lambek calculus: PhD Thesis. Universitat Autònoma de Barcelona, Barcelona (2012)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mathematics and Mechanics Moscow Institute of Physics and Technology, Faculty of Innovations and High Technologies, Moscow State University, Russia

    Alexey Sorokin

Authors
  1. Alexey Sorokin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Departament de Llenguatges i Sistemes,Informàtics, Universitat Politècnica de Catalunya, Jordi Girona Salgado,1-3, 08034, Barcelona, Spain

    Glyn Morrill

  2. Department of Philosophy, Tilburg University, P.O. Box 90153, NL 5000, LE Tilburg, The Netherlands

    Reinhard Muskens

  3. Department of Linguistics and Information Science, Heinrich-Heine-University Düsseldorf, Universitätsstrasse 1, 40225, Düsseldorf, Germany

    Rainer Osswald

  4. Institute for English and American Studies, Department of Linguistic, Goethe University Frankfurt am Main, Grüneburgplatz 1, 60323, Frankfurt, Germany

    Frank Richter

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Sorokin, A. (2014). The Conjoinability Relation in Discontinuous Lambek Calculus. In: Morrill, G., Muskens, R., Osswald, R., Richter, F. (eds) Formal Grammar. FG 2014. Lecture Notes in Computer Science, vol 8612. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44121-3_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-44121-3_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44120-6

  • Online ISBN: 978-3-662-44121-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation