Kamide is in America, Moisil and Leitgeb are in Australia
- It is not uncommon for a logic to be invented multiple times, hinting at its robustness. This trend is followed also by the expansion BD+ of Belnap-Dunn logic by Boolean negation. Ending up in the same logic, however, does not mean that the semantic interpretations are always the same as well. In particular, different interpretations can bring us to different logics, once the basic setting is moved from a classical one to an intuitionistic one. For BD+, two such paths seem to have been taken; one (BDi) by N. Kamide along the so-called American plan, and another (HYPE) by G. Moisil and H. Leitgeb along the so-called Australian plan. The aim of this paper is to better understand this divergence. This task is approached mainly by (i) formulating a semantics for first-order BD+ that provides an Australian view of the system; (ii) showing connections of the less explored (first-order) BDi with neighbouring systems, including an intermediate logic and variants of Nelson's logics.
| Author: | Satoru NikiORCiDGND, Hitoshi OmoriGND |
|---|---|
| URN: | urn:nbn:de:hbz:294-128113 |
| DOI: | https://doi.org/10.4204/EPTCS.415.17 |
| Parent Title (English): | Electronic proceedings in theoretical computer science |
| Subtitle (English): | Proceedings Eleventh International Conference on-Classical Logics. Theory and Applications, Electronic Proceedings in Theoretical Computer Science |
| Publisher: | NICTA |
| Place of publication: | Sydney, Australien |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2025/01/17 |
| Date of first Publication: | 2024/12/31 |
| Publishing Institution: | Ruhr-Universität Bochum, Universitätsbibliothek |
| Tag: | ConLog, Projekt ID: 101018280 |
| Volume: | 415 |
| First Page: | 180 |
| Last Page: | 194 |
| 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 (English): |  Creative Commons - CC BY 4.0 - Attribution 4.0 International |
