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An extended procedure in quantificational logic1

Published online by Cambridge University Press:  12 March 2014

Robert Stanley
Robert Stanley*
Affiliation:
University of British Columbia
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Extract

The aim of this paper is to present a decision procedure which seems to be as easy to use as other available procedures in quantification theory, but which is considerably stronger than the others, providing a mechanical test for a sub-species of polyadic validity which is very much broader than monadic validity. Of course, a test for polyadic validity in general is out of the question, but the present test's limits, short of polyadic validity, are not known. That is, of all the polyadically valid schemata which have been tested, ncne has failed to yield decisions under this method. The material thus examined includes schemata corresponding to the cases of all absolute metatheorems in ML's Chapters II and III, and five polyadic samples from MeL. The handiness of this test is illustrated by sample applications in § 3 below.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 18 , Issue 2 , June 1953 , pp. 97 - 104
Copyright
Copyright © Association for Symbolic Logic 1953

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Footnotes

1

This procedure copies, essentially, a slightly weaker one which was presented in A basis for logic in natural deduction, a thesis submitted toward the doctoral degree at Harvard University. I am indebted to Professor Quine for many helpful suggestions.

References

BIBLIOGRAPHY

MLQuine, W. V., Mathematical logic, New York, 1940.Google Scholar
LQQuine, W. V., On the logic of quantification, this Journal, vol. 10 (1945), pp. 1–12.Google Scholar
MeLQuine, W. V., Methods of logic, New York, 1950.Google Scholar