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Independence of two nice sets of axioms for the propositional calculus

Published online by Cambridge University Press:  12 March 2014

T. Thacher Robinson
T. Thacher Robinson*
Affiliation:
University of Illinois
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Extract

Kanger [4] gives a set of twelve axioms for the classical prepositional calculus which, together with modus ponens and substitution, have the following nice properties:

(0.1) Each axiom contains =⊃, and no axiom contains more than two different connectives.

(0.2) Deletions of certain of the axioms yield the intuitionistic, minimal, and classical refutability1 subsystems of propositional calculus.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 33 , Issue 2 , 23 July 1968 , pp. 265 - 270
Copyright
Copyright © Association for Symbolic Logic 1968

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References

[1]Church, Alonzo, Introduction to mathematical logic, Princeton Univ. Press, Princeton, N.J., 1956.Google Scholar
[2]Curry, Haskell B., Foundations of mathematical logic, McGraw-Hill, New York, 1963.Google Scholar
[3]Harrop, Ronald, Some structure results for prepositional calculi, this Journal, vol. 30 (1965), pp. 271–292.Google Scholar
[4]Kanger, Stig, A note on partial postulate sets for prepositional logic, Theoria (Lund), vol. 21 (1955), pp. 99–104.CrossRefGoogle Scholar