The Monadic Grzegorczyk Logic
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912786194366464 |
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| author | Bezhanishvili, Guram Khan, Mashiath |
| author_facet | Bezhanishvili, Guram Khan, Mashiath |
| contents | We develop a semantic criterion for determining whether a given monadic modal logic axiomatizes the one-variable fragment of a predicate modal logic. We show that the criterion applies to the monadic Grzegorczyk logic $\textbf{MGrz}$, thus establishing that $\textbf{MGrz}$ axiomatizes the one-variable fragment of the predicate Grzegorczyk logic $\textbf{QGrz}$. This we do by proving the finite model property of $\textbf{MGrz}$, which is achieved by strengthening the notion of a maximal point of a descriptive $\textbf{MGrz}$-frame and by refining the existing selective filtration methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10854 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Monadic Grzegorczyk Logic Bezhanishvili, Guram Khan, Mashiath Logic 03B45, 03C90, 06E25 We develop a semantic criterion for determining whether a given monadic modal logic axiomatizes the one-variable fragment of a predicate modal logic. We show that the criterion applies to the monadic Grzegorczyk logic $\textbf{MGrz}$, thus establishing that $\textbf{MGrz}$ axiomatizes the one-variable fragment of the predicate Grzegorczyk logic $\textbf{QGrz}$. This we do by proving the finite model property of $\textbf{MGrz}$, which is achieved by strengthening the notion of a maximal point of a descriptive $\textbf{MGrz}$-frame and by refining the existing selective filtration methods. |
| title | The Monadic Grzegorczyk Logic |
| topic | Logic 03B45, 03C90, 06E25 |
| url | https://arxiv.org/abs/2412.10854 |