Embeddings of Propositional Logics into the Provability Logics $\mathbf{S}$ and $\mathbf{D}$
Year: 2026
Type: preprint
Abstract: Just as Visser showed that the formal propositional logic $\mathbf{FPL}$ can be embedded into Gödel-Löb 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 $\mathbf{D}$.
Source: arXiv (Cornell University)
Author: Noguchi, Mashu
Institution: Kobe University
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7196993910
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