一个旧的模态不完备性定理的新版本
A new version of an old modal incompleteness theorem
摘要：
Kripson \cite{Thomason74}证明了一个特定的模态逻辑$\mathbf{L}\subset \mathbf{S4}$相对于Kripke语义是不完全的。后来Gerson \cite{Gerson75}证明了$\mathbf{L}$在邻域语义方面也是不完整的。本文证明了$\mathbf{L}$对于任何一类带算子的完备布尔代数都是不完备的，即它是完全不完备的.
英文摘要：
Thomason \cite{Thomason74} showed that a certain modal logic $\mathbf{L}\subset \mathbf{S4}$ is incomplete with respect to Kripke semantics. Later Gerson \cite{Gerson75} showed that $\mathbf{L}$ is also incomplete with respect to neighborhood semantics. In this paper we show that $\mathbf{L}$ is in fact incomplete with respect to any class of complete Boolean algebras with operators, i.e. that it is completely incomplete.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
