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 |
|---|---|
| URN: | urn:nbn:de:hbz:294-125526 |
| DOI: | https://doi.org/10.1007/s10849-023-09413-1 |
| Parent Title (English): | Journal of logic, language and information |
| Publisher: | Springer Nature |
| Place of publication: | Berlin |
| Document Type: | Article |
| Language: | English |
| 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 |
| Volume: | 32 |
| First Page: | 861 |
| Last Page: | 886 |
| Note: | 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 |
| OpenAIRE: | OpenAIRE |
| faculties: | Fakultät für Philosophie und Erziehungswissenschaft |
| Licence (German): |  Creative Commons - CC BY 4.0 - Namensnennung 4.0 International |
