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Postulates for implicational calculi

Published online by Cambridge University Press:  12 March 2014

C. A. Meredith
C. A. Meredith*
Affiliation:
Trinity College, DublinIreland
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Extract

I. (Bull's system OIC, defined in [1] as positive implication plus ССССpqqrСССpqrr, can be axiomatised by adding this to a weaker base.)

1. СpСqp

2. ССpqССqrСpr

3. ССССpqqrСССpqrr

4. ССССqrСprsССpqs = D22

5. ССrСpqСССpqСrqСrq = D43

6. СССССpqССrqСrqsССrСpqs = D25

7. ССpСqrССpqСpr = D64

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 31 , Issue 1 , March 1966 , pp. 7 - 9
Copyright
Copyright © Association for Symbolic Logic 1996

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References

[1]Bull, R. A., Some results for implicational calculi, this Journal, vol. 29 (1964), pp. 33–39.Google Scholar
[2]Łukasiewicz, J., On variable functors of propositional arguments, Proceedings of the Royal Irish Academy, 52 A 3 (1948).Google Scholar
[3]Meredith, C. A. and Prior, A. N., Notes on the axiomatics of the propositional calculus, Notre Dame Journal of Formal Logic, vol. 4, No. 3 (1963), pp. 171–187.CrossRefGoogle Scholar