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Non-null implication1

Published online by Cambridge University Press:  12 March 2014

David Nelson
David Nelson*
Affiliation:
The George Washington University, Washington, D.C.
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Extract

An implication A ⊃ B is said to be null in case A is false in all instances. This note describes several formal systems for first-order predicate logic and arithmetic in which null implications do not occur. In fact, the most restrictive systems avoid the occurrences of any formulas which represent null predicates. The precise sense of this avoidance is explained below.

An intuitionistic negation is a statement of the form A ⊃ F where F is a contradiction. The absence of null implications among true statements entails the absence of intuitionistic negations, and hence systems described here might be called negationless intuitionistic systems.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 31 , Issue 4 , December 1966 , pp. 562 - 572
Copyright
Copyright © Association for Symbolic Logic 1997

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Footnotes

1

Acknowledgment is given for support by The Office of Naval Research, Grant Nonr (G)-00065–64.

References

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