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Dual intuitionistic logic and a variety of negations: the logic of scientific research. (English) Zbl 1085.03022
Summary: We consider a logic which is semantically dual (in some precise sense of the term) to intuitionistic logic. 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.

MSC:
03B60 Other nonclassical logic
Software:
KRIPKE
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