Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 49, Number 3 (2008), 245-260.
The Logic of Conditional Negation
It is argued that the "inner" negation familiar from 3-valued logic can be interpreted as a form of "conditional" negation: is read ' is false if it has a truth value'. It is argued that this reading squares well with a particular 3-valued interpretation of a conditional that in the literature has been seen as a serious candidate for capturing the truth conditions of the natural language indicative conditional (e.g., "If Jim went to the party he had a good time"). It is shown that the logic induced by the semantics shares many familiar properties with classical negation, but is orthogonal to both intuitionistic and classical negation: it differs from both in validating the inference from to .
Notre Dame J. Formal Logic, Volume 49, Number 3 (2008), 245-260.
First available in Project Euclid: 15 July 2008
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Primary: 03B50: Many-valued logic
Cantwell, John. The Logic of Conditional Negation. Notre Dame J. Formal Logic 49 (2008), no. 3, 245--260. doi:10.1215/00294527-2008-010. https://projecteuclid.org/euclid.ndjfl/1216152549