Skip to main content
SpringerLink
Log in
Book cover

International Workshop on Computer Science Logic

CSL 2009: Computer Science Logic pp 470–484Cite as

Non-Commutative First-Order Sequent Calculus

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5771))

Abstract

This paper investigates a non-commutative first-order sequent calculus NCLK. For that, this paper extends a non-commutative positive fragment to a full first-order sequent calculus LK− having antecedent-grouping and no right exchange rule. This paper shows (1) NCLK is equivalent to LJ, (2) NCLK with the exchange rule is equivalent to LK, (3) LK− is equivalent to LJ, and (4) translations between LK− and NCLK.

This is a preview of subscription content, 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   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Berardi, S., Yamagata, Y.: A sequent calculus for Limit Computable Mathematics. Annals of Pure and Applied Logic 153(1-3), 111–126 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  2. Berardi, S., Tatsuta, M.: Positive arithmetic without exchange is a subclassical logic. In: Shao, Z. (ed.) APLAS 2007. LNCS, vol. 4807, pp. 271–285. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  3. Girard, J.Y.: Linear logic. Theoretical Computer Science 50(1), 1–102 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  4. Maehara, S.: Eine Darstellung der intuitionistischen Logik in der Klassischen. Nagoya Mathematical Journal 7, 45–64 (1954)

    Article  MathSciNet  MATH  Google Scholar 

  5. Nakano, H.: A Constructive Formalization of the Catch and Throw Mechanism. In: Proceedings of Seventh Annual IEEE Symposium on Logic in Computer Science, pp. 82–89 (1992)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Institute of Informatics, 2-1-2 Hitotsubashi, Tokyo, 101-8430, Japan

    Makoto Tatsuta

Authors
  1. Makoto Tatsuta
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Mathematische Grundlagen der Informatik, RWTH Aachen, 52056, Aachen, Germany

    Erich Grädel

  2. CENTRIA and Departamento de Matemática, Universidade Nova de Lisboa, 2829-516, Caparica, Portugal

    Reinhard Kahle

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Tatsuta, M. (2009). Non-Commutative First-Order Sequent Calculus. In: Grädel, E., Kahle, R. (eds) Computer Science Logic. CSL 2009. Lecture Notes in Computer Science, vol 5771. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04027-6_34

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-04027-6_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04026-9

  • Online ISBN: 978-3-642-04027-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation