Modal extension of ideal paraconsistent four-valued logic and its subsystem
type: Item
instance of: scholarly article
title: Modal extension of ideal paraconsistent four-valued logic and its subsystem
zbMATH Open document ID: 1459.03024
author: Norihiro Kamide
author: Yoni Zohar
published in: Annals of Pure and Applied Logic
publication date: 2020-10-07T00:00:00Z
review text: The paper starts from a paraconsistent four-valued logic 4CC and adds modal operators, thus defining a modal logic M4CC. This logic embeds in the modal logic S4. Moreover, for a certain subset M4CC* of M4CC, a converse embedding also exists. 4CC is both paraconsistent and paracomplete: both the principle of explosion and the law of excluded middle are rejected. Both M4CC and M4CC* are sequent calculi and enjoy Kripke completeness, cut elimination, decidability and finite model property. A further section introduces the modal diamond as a primitive operator.
reviewed by: Giacomo Lenzi
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03B50
Mathematics Subject Classification ID: 03B53
zbMATH DE Number: 7257238
zbMATH Keywords: ideal paraconsistent four-valued logic
zbMATH Keywords: Gentzen-type sequent calculus
zbMATH Keywords: Kripke-completeness theorem
zbMATH Keywords: cut-elimination theorem
zbMATH Keywords: embedding theorem
MaRDI profile type: Publication
full work available at URL: j.apal.2020.102830
OpenAlex ID: W3027391326
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DOI: 10.1016/J.APAL.2020.102830
description: scientific article; zbMATH DE number 7257238