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Mashu Noguchi

Publications and source records attributed to Mashu Noguchi.

2 recordsLinked to original sources
arXiv2026

Embeddings of Propositional Logics into the Provability Logics $\mathbf{S}$ and $\mathbf{D}$

Just as Visser showed that the formal propositional logic $\mathbf{FPL}$ can be embedded into G\"odel-L\"ob provability logic $\mathbf{GL}$, Petrukhin proposed a propositional logic $\mathbf{SPL}$ that can be embedded into Solovay's non-normal provability logic $\mathbf{S}$. In this paper, we fix Petrukhin's proof and extend the result to Japaridze's provability logic $\mathbf{D}$, and propose a propositional logic $\mathbf{DPL}$ that can be embedded into $\mathbf{D}$.

math.LO↗
arXiv2026

Very weak subintuitionistic logics

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.

math.LO↗