Double negation as minimal negation

  • N. Kamide introduced a pair of classical and constructive logics, each with a peculiar type of negation: its double negation behaves as classical and intuitionistic negation, respectively. A consequence of this is that the systems prove contradictions but are non-trivial. The present paper aims at giving insights into this phenomenon by investigating subsystems of Kamide’s logics, with a focus on a system in which the double negation behaves as the negation of minimal logic. We establish the negation inconsistency of the system and embeddability of contradictions from other systems. In addition, we attempt at an informational interpretation of the negation using the dimathematical framework of H. Wansing.

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Author:Satoru NikiORCiDGND
Parent Title (English):Journal of logic, language and information
Publisher:Springer Nature
Place of publication:Berlin
Document Type:Article
Date of Publication (online):2024/04/10
Date of first Publication:2023/11/11
Publishing Institution:Ruhr-Universität Bochum, Universitätsbibliothek
Tag:ConLog, Projekt ID: 101018280
Contradiction; Dimathematism; Double negation; Minimal logic; Negation inconsistency; Strong negation
First Page:861
Last Page:886
ConLog, Projekt ID: 101018280
Relation (DC):info:eu-repo/grantAgreement/EC/H2020/101018280
Institutes/Facilities:Institut für Philosophie I
Dewey Decimal Classification:Philosophie und Psychologie / Philosophie
faculties:Fakultät für Philosophie und Erziehungswissenschaft
Licence (German):License LogoCreative Commons - CC BY 4.0 - Namensnennung 4.0 International