Hostname: page-component-745bb68f8f-lrblm Total loading time: 0 Render date: 2025-01-26T01:50:00.473Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

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

[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