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arXiv · 2412.10854

The Monadic Grzegorczyk Logic

Guram Bezhanishvili·Mashiath Khan
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Abstract

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.

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BibTeXRIS

Guram Bezhanishvili, Mashiath Khan. 2024-12-14. The Monadic Grzegorczyk Logic. https://doi.org/10.1016/j.apal.2026.103793

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