Bi-intuitionistic logics through the abstract algebraic logic lens
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866917964627836928 |
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| author | Deakin, Jonte Shillito, Ian |
| author_facet | Deakin, Jonte Shillito, Ian |
| contents | Since the discovery of critical mistakes in Rauszer's work on bi-intuitionistic logics, solid foundations for these have progressively been rebuilt. However, the algebraic treatment of these logics has not yet been tended to. We fill this gap by algebraically analysing the bi-intuitionistic logics wBIL and sBIL. Given that these logics are only distinguished as consequence relations, and not as sets of theorems (hence the conflation in Rauszer's work), the algebraic tools we use are tailored to the treatment of such relations. We mainly inspect these logics through the lens of abstract algebraic logic, but we also provide an alternative algebraic analysis of wBIL and sBIL as logic preserving degrees of truth and truth, respectively. Our results pertaining to wBIL and sBIL are formalised in the interactive theorem prover Rocq. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17159 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bi-intuitionistic logics through the abstract algebraic logic lens Deakin, Jonte Shillito, Ian Logic Since the discovery of critical mistakes in Rauszer's work on bi-intuitionistic logics, solid foundations for these have progressively been rebuilt. However, the algebraic treatment of these logics has not yet been tended to. We fill this gap by algebraically analysing the bi-intuitionistic logics wBIL and sBIL. Given that these logics are only distinguished as consequence relations, and not as sets of theorems (hence the conflation in Rauszer's work), the algebraic tools we use are tailored to the treatment of such relations. We mainly inspect these logics through the lens of abstract algebraic logic, but we also provide an alternative algebraic analysis of wBIL and sBIL as logic preserving degrees of truth and truth, respectively. Our results pertaining to wBIL and sBIL are formalised in the interactive theorem prover Rocq. |
| title | Bi-intuitionistic logics through the abstract algebraic logic lens |
| topic | Logic |
| url | https://arxiv.org/abs/2503.17159 |