Advertisement

Logica Universalis

, Volume 8, Issue 1, pp 61–81 | Cite as

Towards a More General Concept of Inference

  • Ivo PezlarEmail author
Article
  • 156 Downloads

Abstract

The main objective of this paper is to sketch unifying conceptual and formal framework for inference that is able to explain various proof techniques without implicitly changing the underlying notion of inference rules. We base this framework upon the so-called two-dimensional, i.e., deduction to deduction, account of inference introduced by Tichý in his seminal work The Foundation’s of Frege’s Logic (1988). Consequently, it will be argued that sequent calculus provides suitable basis for such general concept of inference and therefore should not be seen just as technical tool, but philosophically well-founded system that can rival natural deduction in terms of its “naturalness”.

Mathematics Subject Classification (2010)

Primary 03F03 03A05 Secondary 03B99 01A60 01-01 03-01 03-03 

Keywords

Proof theory inference two-dimensional inference 2D inference inference rule natural deduction sequent calculus Tichý Frege 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Dummett M.: The Logical Basis of Metaphysics. Duckworth, London (1991)Google Scholar
  2. 2.
    Euclid: Euclid’s Elements. Richard Fitzpatrick (2007)Google Scholar
  3. 3.
    Jaśkowski, S.: On the Rules of Suppositions in Formal Logic. Studia Logica. Nakładem Seminarjum Filozoficznego Wydziału Matematyczno-Przyrodniczego Uniwersytetu Warszawskiego (1934)Google Scholar
  4. 4.
    Girard, J., Taylor, P., Lafont, Y.: Proofs and Types. Cambridge Tracts in Theoretical Computer Science 7. Cambridge University Press, Cambridge (1989)Google Scholar
  5. 5.
    Prawitz, D.: Natural Deduction: A Proof-theoretical Study. Dover Books on Mathematics Series. Dover Publications, Incorporated (2006)Google Scholar
  6. 6.
    Tichý, P.: The Foundations of Frege’s Logic. Foundations of Communication. de Gruyter (1988)Google Scholar
  7. 7.
    Frege, G.: The Foundations of Arithmetic: A Logico-Mathematical Enquiry Into the Concept of Number, 2nd edn. Oxford University Press, Oxford (1953) (Originally published in 1884. Translated by J.L. Austin.).Google Scholar
  8. 8.
    Frege G.: Collected Papers on Mathematics, Logic, and Philosophy. Wiley, New York (1991)Google Scholar
  9. 9.
    Frege G., Hermes H., Kambartel F., Long P., White R.: Posthumous Writings. Wiley, New York (1979)Google Scholar
  10. 10.
    Frege, G., Carnap, R., Reck, E., Awodey, S., Gabriel, G.: Frege’s Lectures on Logic: Carnap’s Jena Notes, 1910–1914. Full Circle. Open Court Publishing, USA (2004)Google Scholar
  11. 11.
    Gentzen G., Szabo E.: The collected papers of Gerhard Gentzen. Studies in logic and the foundations of mathematics. North-Holland Publishing Company, USA (1969)zbMATHGoogle Scholar

Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Department of Philosophy, Faculty of ArtsMasaryk UniversityBrnoCzech Republic

Personalised recommendations