The Monadic Grzegorczyk Logic

2024/12/14 by Bezhanishvili, Guram, Khan, Mashiath · 2 citations
#03B45 #03C90 #06E25 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2412.10854

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 MGrz, thus establishing that MGrz axiomatizes the one-variable fragment of the predicate Grzegorczyk logic QGrz. This we do by proving the finite model property of MGrz, which is achieved by strengthening the notion of a maximal point of a descriptive MGrz-frame and by refining the existing selective filtration methods.

Cited by

• Esakia's theorem for the amended monadic intuitionistic calculus
• Finite axiomatization of GL×S5 and Grz×S5

Related

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• Failure of Esakia's theorem in the monadic setting
• Esakia's theorem for the amended monadic intuitionistic calculus
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