Sub-sub-intuitionistic logic
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911999155240960 |
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| author | Deakin, Jonte de Groot, Jim |
| author_facet | Deakin, Jonte de Groot, Jim |
| contents | Sub-sub-intuitionistic logic is obtained from intuitionistic logic by weakening the implication and removing distributivity. It can alternatively be viewed as conditional weak positive logic. We provide semantics for sub-sub-intuitionistic logic by means of semilattices with a selection function, prove a categorical duality for the algebraic semantics of the logic, and use this to derive completeness. We then consider the extension of sub-sub-intuitionistic logic with a variety of axioms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12030 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sub-sub-intuitionistic logic Deakin, Jonte de Groot, Jim Logic 03F55 (Primary) 03B45, 03G10 (Secondary) Sub-sub-intuitionistic logic is obtained from intuitionistic logic by weakening the implication and removing distributivity. It can alternatively be viewed as conditional weak positive logic. We provide semantics for sub-sub-intuitionistic logic by means of semilattices with a selection function, prove a categorical duality for the algebraic semantics of the logic, and use this to derive completeness. We then consider the extension of sub-sub-intuitionistic logic with a variety of axioms. |
| title | Sub-sub-intuitionistic logic |
| topic | Logic 03F55 (Primary) 03B45, 03G10 (Secondary) |
| url | https://arxiv.org/abs/2408.12030 |