The logic of conditional negation
type: Item
instance of: scholarly article
title: The logic of conditional negation
zbMATH Open document ID: 1161.03012
DOI: 10.1215/00294527-2008-010
author: John Cantwell
published in: Notre Dame Journal of Formal Logic
publication date: 2008-10-20T00:00:00Z
review text: This paper presents a form of conditional negation in the context of familiar 3-valued logic, whereby \(\sim\! A\) is read `\(A\) is false if it has a truth-value'. This is supposed to coordinate well with a 3-valued conditional that captures many aspects of the ordinary-language indicative if-then. The logic of this negation is similar to classical negation, but different from that and from intuitionistic negation in that the inference from \(A\to\,\sim\! B\) to \(\sim\!(A\to B)\) is valid. This logic is presented both semantically, by standard matrices, and proof-theoretically, and the latter shown to be sound and complete with respect to the former. Key to these results is to take validity not in the sense of preserving truth, but as not introducing falsity, so that an inference is valid just in case the conclusion is false only if at least one premise is false. The paper includes valuable informal discussion to motivate the various concepts.
reviewed by: Louis F. Goble
Mathematics Subject Classification ID: 03B50
zbMATH DE Number: 5353772
zbMATH Keywords: negation
zbMATH Keywords: conditionals
zbMATH Keywords: 3-valued logic
zbMATH Keywords: validity
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/00294527-2008-010
OpenAlex ID: W1963891102
description: scientific article; zbMATH DE number 5353772