SpringerLink
Log in

On Residuation

  • Chapter
Categories and Types in Logic, Language, and Physics

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8222))

Abstract

In this paper we explore the residuation laws that are at the basis of the Lambek calculus, and more generally of categorial grammar. We intend to show how such laws are characterized in the framework of a purely non-commutative fragment of linear logic, known as Cyclic Multiplicative Linear Logic.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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 ship** 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.

Similar content being viewed by others

References

  1. Abrusci, V.M., Ruet, P.: Non-commutative Logic I: The multiplicative fragment. Ann. Pure Appl. Logic 101(1), 29–64 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  2. Abrusci, M.: Classical Conservative Extensions of Lambek Calculus. Studia Logica 71, 277–314 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bernardi, R., Moortgat, M.: Continuation Semantics for the Lambek-Grishin Calculus. Inf. Comput. 208(5), 397–416 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Buszkowski, W.: Type Logics and Pregroups. Studia Logica 87(2/3), 145–169 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. Buszkowski, W., Farulewski, M.: Nonassociative Lambek Calculus with Additives and Context-Free Languages. In: Grumberg, O., Kaminski, M., Katz, S., Wintner, S. (eds.) Francez Festschrift. LNCS, vol. 5533, pp. 45–58. Springer, Heidelberg (2009)

    Google Scholar 

  6. Buszkowski, W.: Lambek Calculus and Substructural Logics. Linguistic Analysis 36(1-4), 15–48 (2010)

    Google Scholar 

  7. Buszkowski, W.: Interpolation and FEP for Logics of Residuated Algebras. Logic Journal of the IGPL 19(3), 437–454 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Casadio, C., Lambek, J.: A Tale of Four Grammars. Studia Logica 71, 315–329 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  9. Casadio, C., Lambek, J. (eds.): Recent Computational Algebraic Approaches to Morphology and Syntax. Polimetrica, Milan (2008)

    Google Scholar 

  10. Lambek, J.: The Mathematics of Sentence Structure. The American Mathematical Monthly 65(3), 154–170 (1958)

    Article  MathSciNet  MATH  Google Scholar 

  11. Lambek, J.: From Word to Sentence. A Computational Algebraic Approach to Grammar. Polimetrica International Publisher, Monza (2008)

    MATH  Google Scholar 

  12. Lambek, J.: Logic and Grammar. Studia Logica 100(4), 667–681 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  13. Moortgat, M.: Symmetric Categorial Grammar: Residuation and Galois Connections. Linguistic Analysis 36(1-4), 143–166 (2010)

    Google Scholar 

  14. Moortgat, M., Moot, R.: Proof-nets for the Lambek-Grishin Calculus. CoRR abs/1112.6384 (2011)

    Google Scholar 

  15. Retoré, C.: Handsome proof nets: perfect matchings and cographs. Theoretical Computer Science 294(3) (2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Philosophy, University Roma Tre, Rome, Italy

    V. Michele Abrusci

Authors
  1. V. Michele Abrusci
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Philosophy, Education and Quantitative Economics, Gabriele D’Annunzio University, Chieti-Pescara, Via dei Vestini 31, 60100, Chieti, Italy

    Claudia Casadio

  2. Department of Computer Science, Oxford University, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Bob Coecke

  3. Utrecht Institute of Linguistics OTS, Utrecht University, Trans 10,, 3512 JK, Utrecht, The Netherlands

    Michael Moortgat

  4. Department of Mathematics, University of Ottawa, 585 King Edward, K1N 6N5, Ottawa, ON, Canada

    Philip Scott

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Abrusci, V.M. (2014). On Residuation. In: Casadio, C., Coecke, B., Moortgat, M., Scott, P. (eds) Categories and Types in Logic, Language, and Physics. Lecture Notes in Computer Science, vol 8222. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54789-8_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-54789-8_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54788-1

  • Online ISBN: 978-3-642-54789-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation