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Proof of the law of infinite conjunction using the perfect disjunctive normal form1

Published online by Cambridge University Press:  12 March 2014

James Thomson
James Thomson*
Affiliation:
Massachusetts Institute of Technology
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Extract

The law of infinite conjunction (Quine's name, see Methods of logic, rev. ed., Holt & Co., New York, p. 254) says that a set of truthfunctional formulas is satisfiable provided every finite subset is. We give a proof of the law which uses some properties of the perfect disjunctive normal form.

Any satisfiable formula can be written as a disjunction of conjunctions of literals (a literal is a statement-letter or the negation of one) in which a statement-letter which occurs in any conjunction occurs exactly once in each; a literal by itself counts as a conjunction and a conjunction by itself as a disjunction.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 32 , Issue 2 , August 1967 , pp. 196 - 197
Copyright
Copyright © Association for Symbolic Logic 1967

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Footnotes

1

I would like to thank Professor W. V. Quine for criticizing an earlier draft.

References

1 I would like to thank Professor W. V. Quine for criticizing an earlier draft.