### The Logic of Conditional Negation

John Cantwell
Source: Notre Dame J. Formal Logic Volume 49, Number 3 (2008), 245-260.

#### Abstract

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 .

First Page:
Primary Subjects: 03B50
Full-text: Open access

Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1216152549
Digital Object Identifier: doi:10.1215/00294527-2008-010
Mathematical Reviews number (MathSciNet): MR2428553
Zentralblatt MATH identifier: 1161.03012

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