arXiv subjects
Publications and source records attributed to Mashiath Khan.
We prove that $\mathbf{GL} \times \mathbf{S5}$ is product matching, and that $\mathbf{Grz} \times \mathbf{S5}$ is axiomatizable by adding to $[\mathbf{Grz},\mathbf{S5}]$ the G\"odel translation of the monadic Casari formula. This settles the question of the finite axiomatizability of these logics posed by Gabbay and Shehtman (1998).
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.