Maximal weakly-intuitionistic logics
type: Item
instance of: scholarly article
title: Maximal weakly-intuitionistic logics
zbMATH Open document ID: 0841.03009
DOI: 10.1007/BF01053037
published in: Studia Logica
publication date: 1996-07-16T00:00:00Z
review text: What happens if one adds a new truth-value \(F^*\) to the Boolean values \(\{T, F\}\) such that \(F^*\) and \(\neg F^*\) are both false (\(F\) and \(F^*\) coincide otherwise)? The setting is adequate for an axiomatic calculus \(I^1\) in a \(\{\to, \neg\}\)-language. \(I^1\) turns out to be weakly intuitionistic (or else: paracomplete, i.e. without the law of excluded middle) and not paraconsistent (unlike its companion \(P^1\) which is based on \(\{T, T^*, F\}\) with \(F^*\) and \(\neg F^*\) both being true). Furthermore, it is algebraizable in the sense of Blok and Pigozzi. Adding further truth-values one arrives at a hierarchy of calculi \(I^n\), resp. \(P^n\). The paper contains numerous misprints.
reviewed by: Max Urchs
Mathematics Subject Classification ID: 03B53
Mathematics Subject Classification ID: 03B20
Mathematics Subject Classification ID: 03A05
zbMATH DE Number: 795271
zbMATH Keywords: weakly-intuitionistic logics
zbMATH Keywords: paraconsistency
zbMATH Keywords: paracompleteness
zbMATH Keywords: algebraizable logic
zbMATH Keywords: hierarchy of calculi
author: Antonio M. A. Sette
author: Walter Carnielli
MaRDI profile type: Publication
cites work: Q3861360
cites work: Systematization of finite many-valued logics through the method of tableaux
cites work: Q4328563
cites work: Q3030797
cites work: Q5202993
cites work: An algebraic approach to non-classical logics
full work available at URL: https://doi.org/10.1007/bf01053037
OpenAlex ID: W2048502195
description: scientific article; zbMATH DE number 795271