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Some calculi with strong negation primitive1

Published online by Cambridge University Press:  12 March 2014

J. Jay Zeman
J. Jay Zeman*
Affiliation:
University of Florida
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Extract

We shall take “strong negation” to be a unary operator with some of the properties usually associated with negation, and such that the strong negation of a statement implies the “ordinary” negation ofthat statement, but not vice-versa. This paper will consider two varieties of strong negation: first, strong negation set in the context of the propositional calculus, specifically, the intuitionist PC, and secondly, strong negation in modal systems, that is, strong negation as impossibility. In the latter part of the paper, we shall present axiomatizations of several classical Lewis-modal systems having only material implication and impossibility primitive.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 33 , Issue 1 , 26 April 1968 , pp. 97 - 100
Copyright
Copyright © Association for Symbolic Logic 1968

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Footnotes

1

The author wishes to thank Ivo Thomas for his comments and suggestions regarding the organization and content of this paper. The effects of these suggestions are felt through the entire work.

References

[1]Curry, H. B., Foundations of mathematical logic, McGraw-Hill, New York, 1963.Google Scholar
[2]Sobocinski, B., Modal system S4.4, Notre Dame journal of formal logic, v. 5 (1964), p. 155.CrossRefGoogle Scholar
[3]Thomas, Ivo, Modal systems in the neighbourhood of T, Notre Dame journal of formal logic, v. 5 (1964), p. 59.CrossRefGoogle Scholar