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Finite nest structures and propositional logic

Published online by Cambridge University Press:  12 March 2014

Raymond M. Smullyan
Raymond M. Smullyan*
Affiliation:
Belfer Graduate School of Science, New York, New York
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Extract

Our terminology and notation is the same as that of [1], of which this note is a sequel.

We wish to show that if we take the natural deduction system (N) described in [1], and delete the rules for the quantifiers, we obtain a complete system for propositional logic. [Of course we now construe “X”, “Y”, “Z” as syntactic variables ranging over formulas of propositional logic, rather than sentences of quantification theory.] Moreover the system serves as a neat decision procedure.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 31 , Issue 3 , 02 September 1966 , pp. 322 - 324
Copyright
Copyright © Association for Symbolic Logic 1996

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References

[1]Smullyan, R. M., Analytic natural deduction, this Journal, vol. 30 (1965), pp. 123–139.Google Scholar
[2]Hintikka, K. J. J., Form and content in quantification theory, Acta Philoso-phica Fennica no. 8, Helsinki 1955, pp. 7–55.Google Scholar
[3]Hintikka, K. J. J., A new approach to sentential logic, Societas Scientiarutn Fennica, Commentationes physica-mathematicae, vol. 17, no. 2 (1953).Google Scholar
[4]Smullyan, R. M., Trees and nest structures, this Journal, vol. 31 (1966), pp. 303–321.Google Scholar