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Dual Intuitionistic Logic and a Variety of Negations: The Logic of Scientific Research

Yaroslav Shramko
Studia Logica: An International Journal for Symbolic Logic
Vol. 80, No. 2/3, Negation in Constructive Logic (Jul. - Aug., 2005), pp. 347-367
Published by: Springer
Stable URL: http://www.jstor.org/stable/20016721
Page Count: 21
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Dual Intuitionistic Logic and a Variety of Negations: The Logic of Scientific Research
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Abstract

We consider a logic which is semantically dual (in some precise sense of the term) to intuitionistic. This logic can be labeled as "falsification logic": it embodies the Popperian methodology of scientific discovery. Whereas intuitionistic logic deals with constructive truth and non-constructive falsity, and Nelson's logic takes both truth and falsity as constructive notions, in the falsification logic truth is essentially non-constructive as opposed to falsity that is conceived constructively. We also briefly clarify the relationships of our falsification logic to some other logical systems.

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