The Logic of Conditional Negation

Notre Dame Journal of Formal Logic 49 (3):245-260 (2008)
It is argued that the "inner" negation $\mathord{\sim}$ familiar from 3-valued logic can be interpreted as a form of "conditional" negation: $\mathord{\sim}$ is read '$A$ 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 $A \rightarrow \nega B$ to $\nega(A\rightarrow B)$ to
Keywords three-valued logic   inner negation   outer negation   conditionals
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DOI 10.1215/00294527-2008-010
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Vít Punčochář (2015). Weak Negation in Inquisitive Semantics. Journal of Logic, Language and Information 24 (3):323-355.
Andreas Kapsner (2012). Strong Connexivity. Thought: A Journal of Philosophy 1 (2):141-145.

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Stephen Read (2000). Harmony and Autonomy in Classical Logic. Journal of Philosophical Logic 29 (2):123-154.
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