Hostname: page-component-745bb68f8f-lrblm Total loading time: 0 Render date: 2025-01-12T21:22:35.560Z Has data issue: false hasContentIssue false
  • English
  • Français

On the admissible rules of intuitionistic propositional logic

Published online by Cambridge University Press:  12 March 2014

Rosalie Iemhoff
Rosalie Iemhoff*
Affiliation:
ILLC/Department of Mathematics and Computer Science, Universiteit Van Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands, E-mail: iemhoff@wins.uva.nl
Get access Rights & Permissions [Opens in a new window]

Abstract

We present a basis for the admissible rules of intuitionistic propositional logic. Thereby a conjecture by de Jongh and Visser is proved. We also present a proof system for the admissible rules, and give semantic criteria for admissibility.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 1 , March 2001 , pp. 281 - 294
Copyright
Copyright © Association for Symbolic Logic 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1977] Citkin, A. I., On admissible rules of intuitionistic propositional logic, Mathematics of the USSR, Sbornik, vol. 31 (1977), pp. 314–323.CrossRefGoogle Scholar
[1974] Fine, K., Logics containing KA, part I, this Journal, vol. 34 (1974), pp. 31–42.Google Scholar
[1985] Fine, K., Logics containing KA, part II, this Journal, vol. 50 (1985), pp. 619–651.Google Scholar
[to appear] Ghilhardi, S., Unification in intuitionistic and De Morgan Logic, this Journal, (to appear).Google Scholar
[1960] Harrop, R., Concerning formulas of the types A → B ⋁ C, A → (Ex)B(x) in intuitionistic formal systems, this Journal, vol. 25 (1960), pp. 27–32.Google Scholar
[1976] Mints, G. E., Derimbility of admissible rules, Journal of Soviet Mathematics, vol. 6 (1976).CrossRefGoogle Scholar
[1997] Rybakov, V. V., Admissibility of Logical Inference Rules, Elsevier, Amsterdam, 1997.Google Scholar
[1988] Troelstra, A. S. and van Dalen, D., Constructivism in Mathmatics I, Elsevier, Amsterdam, 1988.Google Scholar
[to appear] Visser, A., Rules and arithmetics, Notre Dame Journal of Formal Logic, (to appear).Google Scholar