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arXiv · 2605.20769

Very weak subintuitionistic logics

Taishi Kurahashi·Mashu Noguchi
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Abstract

We introduce a new propositional logic, called very weak subintuitionistic logic $\mathbf{VF}$, by adapting the relational semantics of Fitting, Marek, and Truszczy\'nski for the pure logic of necessitation $\mathbf{N}$ to the propositional setting. We prove that $\mathbf{VF}$ and its closed negative extensions are sound and complete with respect to this semantics, and that they have the disjunction property and the finite frame property. We also prove that $\mathbf{VF}$ is strictly weaker than the weak subintuitionistic logic $\mathbf{WF}$ of Maleki and de Jongh. Finally, we study modal companions of $\mathbf{VF}$ and its closed negative extensions via Corsi's modified G\"odel translation.

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Taishi Kurahashi, Mashu Noguchi. 2026-05-20. Very weak subintuitionistic logics. https://arxiv.org/abs/2605.20769

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