Skip to main content
SpringerLink
Log in

Intuitionistic Logic and Computability Theory

  • Conference paper
Logic, Language, Information and Computation (WoLLIC 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6188))

Abstract

In this first tutorial we review the basics of intuitionistic logic. We start with L. E. J. Brouwer’s philosophy of mathematics, intuitionism, and the subsequent formalization by Heyting [1] of its underlying logic. The Brouwer-Heyting-Kolmogorov interpretation is an informal manner (in fact consisting of various ideas lumped together) of motivating the formal rules of deduction in this logic.

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

References

  1. Heyting, A.: Die formalen Regeln der intuitionistischen Logik. Sitzungsberichte der Preussisischen Akademie von Wissenschaften, Physikalisch-mathematische Klasse, 42–56 (1930)

    Google Scholar 

  2. Iemhoff, R.: On the rules of intermediate logics. Archive for Mathematical Logic 45(5), 581–599 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  3. Kleene, S.C.: On the interpretation of intuitionistic number theory. Journal of Symbolic Logic 10, 109–124 (1945)

    Article  MATH  MathSciNet  Google Scholar 

  4. Kolmogorov, A.: Zur Deutung der intuitionistischen Logik. Mathematische Zeitschrift 35(1), 58–65 (1932)

    Article  MATH  MathSciNet  Google Scholar 

  5. Medvedev, Y.T.: Degrees of difficulty of the mass problems. Dokl. Akad. Nauk. SSSR 104(4), 501–504 (1955)

    MATH  MathSciNet  Google Scholar 

  6. van Oosten, J.: Realizability: An introduction to its categorical side. Studies in logic and the foundations of mathematics, vol. 152. Elsevier, Amsterdam (2008)

    MATH  Google Scholar 

  7. Skvortsova, E.Z.: A faithful interpretation of the intuitionistic propositional calculus by means of an initial segment of the Medvedev lattice. Sibirsk. Math. Zh. 29(1), 171–178 (in Russian, 1988)

    MATH  MathSciNet  Google Scholar 

  8. Simpson, S.G.: \(\Pi^0_1\) sets and models of WKL0. In: Reverse Mathematics 2001. Lecture Notes in Logic, vol. 21. ASL (2005)

    Google Scholar 

  9. Sorbi, A.: The Medvedev lattice of degrees of difficulty. In: Cooper, S.B., Slaman, T.A., Wainer, S.S. (eds.) Computability, Enumerability, Unsolvability: Directions in Recursion Theory, London. Mathematical Society Lecture Notes, vol. 224, pp. 289–312. Cambridge University Press, Cambridge (1996)

    Chapter  Google Scholar 

  10. Sorbi, A., Terwijn, S.A.: Intermediate logics and factors of the Medvedev lattice. Annals of Pure and Applied Logic 155, 69–85 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  11. Terwijn, S.A.: Syllabus computabiliy theory, Vienna. Available at the author’s web pages (2004)

    Google Scholar 

  12. Terwijn, S.A.: The Medvedev lattice of computably closed sets. Archive for Mathematical Logic 45(2), 179–190 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  13. Terwijn, S.A.: Constructive logic and computational lattices, habilitation thesis, Technical University of Vienna (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Radboud University Nijmegen, P.O. Box 9010, 6500, GL, Nijmegen, The Netherlands

    Sebastiaan A. Terwijn

Authors
  1. Sebastiaan A. Terwijn
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Computer Laboratory, University of Cambridge, J.J. Thomson Avenue, CB3 0FD, Cambridge, UK

    Anuj Dawar

  2. Centro de Informática, Universidade Federal de Pernambuco, Avenida Prof Luis Freire s/n, Cidade Universitária, 50740-540, Recife, PE, Brazil

    Ruy de Queiroz

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Terwijn, S.A. (2010). Intuitionistic Logic and Computability Theory. In: Dawar, A., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2010. Lecture Notes in Computer Science(), vol 6188. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13824-9_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-13824-9_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13823-2

  • Online ISBN: 978-3-642-13824-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation