Non-contingecy in a paraconsistent setting
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916129805434880 |
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| author | Kozhemiachenko, Daniil Vashentseva, Liubov |
| author_facet | Kozhemiachenko, Daniil Vashentseva, Liubov |
| contents | We study an extension of First Degree Entailment (FDE) by Dunn and Belnap with a non-contingency operator $\blacktriangleϕ$ which is construed as "$ϕ$ has the same value in all accessible states" or "all sources give the same information on the truth value of $ϕ$". We equip this logic dubbed $\mathbf{K}^\blacktriangle_\mathbf{FDE}$ with frame semantics and show how the bi-valued models can be interpreted as interconnected networks of Belnapian databases with the $\blacktriangle$ operator modelling search for inconsistencies in the provided information. We construct an analytic cut system for the logic and show its soundness and completeness. We prove that $\blacktriangle$ is not definable via the necessity modality $\Box$ of $\mathbf{K_{FDE}}$. Furthermore, we prove that in contrast to the classical non-contingency logic, reflexive, $\mathbf{S4}$, and $\mathbf{S5}$ (among others) frames \emph{are definable}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11249 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-contingecy in a paraconsistent setting Kozhemiachenko, Daniil Vashentseva, Liubov Logic We study an extension of First Degree Entailment (FDE) by Dunn and Belnap with a non-contingency operator $\blacktriangleϕ$ which is construed as "$ϕ$ has the same value in all accessible states" or "all sources give the same information on the truth value of $ϕ$". We equip this logic dubbed $\mathbf{K}^\blacktriangle_\mathbf{FDE}$ with frame semantics and show how the bi-valued models can be interpreted as interconnected networks of Belnapian databases with the $\blacktriangle$ operator modelling search for inconsistencies in the provided information. We construct an analytic cut system for the logic and show its soundness and completeness. We prove that $\blacktriangle$ is not definable via the necessity modality $\Box$ of $\mathbf{K_{FDE}}$. Furthermore, we prove that in contrast to the classical non-contingency logic, reflexive, $\mathbf{S4}$, and $\mathbf{S5}$ (among others) frames \emph{are definable}. |
| title | Non-contingecy in a paraconsistent setting |
| topic | Logic |
| url | https://arxiv.org/abs/2402.11249 |