Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.00495 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929653930786816 |
|---|---|
| author | Niki, Satoru Omori, Hitoshi |
| author_facet | Niki, Satoru Omori, Hitoshi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00495 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kamide is in America, Moisil and Leitgeb are in Australia Niki, Satoru Omori, Hitoshi Logic in Computer Science 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. |
| title | Kamide is in America, Moisil and Leitgeb are in Australia |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2501.00495 |