Skip to main content
SpringerLink
Log in

Representation theorems for residuated groupoids

  • Conference paper
  • First Online:
Logical Aspects of Computational Linguistics (LACL 1996)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1328))

Abstract

In this paper we will prove two representation theorems for residuated groupoids with respect to two kinds of powerset frames: powerset residuated groupoids [4] and relativized relational frames [1]. They yield the strong completeness of the Non Associative Lambek Calculus with respect to these frames.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andréka, H., Mikulás, Sz., “Lambek Calculus and its Relational Semantics: Completeness and Incompleteness”, Journal of Logic, Language and Information, 3(1), 1994.

    Google Scholar 

  2. van Benthem, J., Language in action, North-Holland, Amsterdam, 1991.

    Google Scholar 

  3. Buszkowski, W., “Completeness results for Lambek Syntactic Calculus”, Zeitschr. f. math. Logik und Grundlagen d. Math., 32, 13–28, 1986

    MATH  MathSciNet  Google Scholar 

  4. Buszkowski, W., “Mathematical Linguistics and Proof Theory”, in J. van Benthem and A. ter Menlen (eds.), Handbook of Logic and Language, North Holland, Amsterdam, to appear.

    Google Scholar 

  5. Kolowska-Gawiejnowicz, M., “Powerset Residuated Algebras and Generalized Lambek Calculus”, Mathematical Logic Quarterly, to appear.

    Google Scholar 

  6. Kurtonina, N., Frames and Labels. A Model Analysis of Categorial Inference, Ph.D. Thesis, University of Utrecht, 1995.

    Google Scholar 

  7. Lambek, J., “The mathematics of sentence structure”, American Mathematical Monthly, 65, 154–170, 1958.

    Article  MathSciNet  Google Scholar 

  8. Lambek, J. “On the calculus of syntactic types”, in R. Jacobson (ed.), Structure of Language and Its Mathematical Aspects, AMS, Providence, 1961.

    Google Scholar 

  9. Moortgat, “Categorial Gramar”, in: J. van Benthem and A. ter Menlen (eds.), Handbook of Logic and Language, North Holland, Amsterdam, to appear.

    Google Scholar 

  10. Rasiowa, H., An algebraic approach to non-classical logics, Polish Scientific Publishers and North Holland, Amsterdam, 1974.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Matejki 48/49, 60-769, Poznań, Poland

    Maxek Szczerba

Authors
  1. Maxek Szczerba
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Christian Retoré

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Szczerba, M. (1997). Representation theorems for residuated groupoids. In: Retoré, C. (eds) Logical Aspects of Computational Linguistics. LACL 1996. Lecture Notes in Computer Science, vol 1328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0052170

Download citation

  • DOI: https://doi.org/10.1007/BFb0052170

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63700-4

  • Online ISBN: 978-3-540-69631-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation