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2008 The Logic of Conditional Negation
John Cantwell
Notre Dame J. Formal Logic 49(3): 245-260 (2008). DOI: 10.1215/00294527-2008-010

Abstract

It is argued that the "inner" negation familiar from 3-valued logic can be interpreted as a form of "conditional" negation: A 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 B to A B .

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John Cantwell. "The Logic of Conditional Negation." Notre Dame J. Formal Logic 49 (3) 245 - 260, 2008. https://doi.org/10.1215/00294527-2008-010

Information

Published: 2008
First available in Project Euclid: 15 July 2008

zbMATH: 1161.03012
MathSciNet: MR2428553
Digital Object Identifier: 10.1215/00294527-2008-010

Subjects:
Primary: 03B50

Rights: Copyright © 2008 University of Notre Dame

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Vol.49 • No. 3 • 2008
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