The basic constructive logic for negation-consistency
type: Item
instance of: scholarly article
title: The basic constructive logic for negation-consistency
zbMATH Open document ID: 1173.03026
author: Gemma Robles
published in: Journal of Logic, Language and Information
publication date: 2009-03-24T00:00:00Z
review text: In a previous paper [ibid. 17, No.~1, 89--107 (2008; Zbl 1173.03027)], reviewed below, \textit{G. Robles} and \textit{J. M. Méndez} extended the Routley-Meyer basic positive logic \(\text{B}_+\) to \(\text{B}_{\text{K}+}\), by adding the rule K: \({\vdash A} \Rightarrow {\vdash B} \rightarrow A\), and then to \(\text{B}_{\text{Kc}1}\), \(\text{B}_{\text{Kc}2}\) and \(\text{B}_{\text{Kc}3}\) by also adding various negation axioms. They provided sound and complete Routley-Meyer-type semantics for these systems there. In this paper, the authors introduce negation extensions \(\text{B}_{\text{Kc}4}\) of \(\text{B}_{\text{Kc}1}\) and \(\text{B}_{\text{Kc}5}\) of \(\text{B}_{\text{Kc}2}\). These are shown to be independent of each other and also sound and complete under variants of the semantics for \(\text{B}_{\text{Kc}1}\). How \(\text{B}_{\text{Kc}2}\) and \(\text{B}_{\text{Kc}3}\) are related to \(\text{B}_{\text{Kc}4}\) and \(\text{B}_{\text{Kc}5}\) to \(\text{B}_{\text{Kc}3}\) is not discussed.
reviewed by: Martin W. Bunder
Mathematics Subject Classification ID: 03B53
Mathematics Subject Classification ID: 03B47
zbMATH DE Number: 5532543
zbMATH Keywords: constructive negation
zbMATH Keywords: substructural logics
zbMATH Keywords: Routley-Meyer semantics
zbMATH Keywords: paraconsistent logic
describes a project that uses: MaGIC
MaRDI profile type: Publication
full work available at URL: s10849-007-9056-z
OpenAlex ID: W2148798252
cites work: Q3781068
cites work: Q4826043
cites work: The basic constructive logic for a weak sense of consistency
cites work: Strong paraconsistency and the basic constructive logic for an even weaker sense of consistency
cites work: Q5488259
cites work: Q3701398
DOI: 10.1007/S10849-007-9056-Z
description: scientific article; zbMATH DE number 5532543