论文标题
通过稳定的规范规则，blok-esakia定理
Blok-Esakia Theorems via Stable Canonical Rules
论文作者
论文摘要
我们提出了一种基于稳定规范规则的机制，提出了一种研究新的统一方法，用于研究超持续规则系统和相关概念的模态伴侣。使用此方法，我们获得了Blok-esakia定理和规则系统的Dummett-Lemmon猜想的替代证明。由于可以针对任何规则系统制定稳定的规则规则，因此我们的方法可以顺利地将其概括为更丰富的签名。使用本质上相同的论点，我们获得了Blok-Esakia定理的证明，用于双性观念和紧张的规则系统，以及在扩展模态直觉逻辑$ \\逻辑$ \\ logic {kmm} $ logical logity logitigation progigity prog的规则系统之间的kuznetsov-muravitsky同构$ c $ c $ c $ c $ \ y c.此外，我们对Dummet-Lemmon猜想的证明也概括为双性观念和紧张的案例。
We present a new uniform method for studying modal companions of superintuitionistic rule systems and related notions, based on the machinery of stable canonical rules. Using this method, we obtain alternative proofs of the Blok-Esakia theorem and of the Dummett-Lemmon conjecture for rule systems. Since stable canonical rules may be developed for any rule system admitting filtration, our method generalizes smoothly to richer signatures. Using essentially the same argument, we obtain a proof of an analogue of the Blok-Esakia theorem for bi-superintuitionistic and tense rule systems, and of the Kuznetsov-Muravitsky isomorphism between rule systems extending the modal intuitionistic logic $\logic{KM}$ and modal rule systems extending the provability logic $\logic{GL}$. In addition, our proof of the Dummett-Lemmon conjecture also generalizes to the bi-superintuitionistic and tense cases.
