The Logic of Conditional Negation

Cantwell, John

Notre Dame J. Formal Logic, Tome 49 (2008) no. 1, p. 245-260 / Harvested from Project Euclid

Résumé

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 $\sim \left(A\to B\right)$.

Détail

Publié le : 2008-07-15
Classification:  three-valued logic,  inner negation,  outer negation,  conditionals,  03B50