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IMPROVING STRONG NEGATION

Part of: General logic

Published online by Cambridge University Press:  02 July 2021

SATORU NIKI
SATORU NIKI*
Affiliation:
DEPARTMENT OF PHILOSOPHY I RUHR UNIVERSITY BOCHUM, UNIVERSITÄTSSTRASSE BOCHUM 150 D-44780, GERMANY
*
E-mail: Satoru.Niki@rub.de
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Abstract

Strong negation is a well-known alternative to the standard negation in intuitionistic logic. It is defined virtually by giving falsity conditions to each of the connectives. Among these, the falsity condition for implication appears to unnecessarily deviate from the standard negation. In this paper, we introduce a slight modification to strong negation, and observe its comparative advantages over the original notion. In addition, we consider the paraconsistent variants of our modification, and study their relationship with non-constructive principles and connexivity.

Keywords

connexive logicdouble negationintuitionistic logicstrong negationquasi-truth

MSC classification

Primary: 03B20: Subsystems of classical logic (including intuitionistic logic)
Type
Research Article
Information
The Review of Symbolic Logic , Volume 16 , Issue 3 , September 2023 , pp. 951 - 977
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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