论文标题
模态Fairtlough-Mendler语义的对应理论直觉模态逻辑
Correspondence Theory for Modal Fairtlough-Mendler Semantics of Intuitionistic Modal Logic
论文作者
论文摘要
我们研究了模态Fairtlough-Mendler语义（模态FM语义）中直觉模态逻辑的对应理论\ cite {fame97}，这是可能语义的直觉模态版本\ cite \ cite {ho16}。我们用这种语言确定归纳公式\ cite {gorankov06}的片段，并在这种语义环境中给出算法$ \ mathsf {alba} $ \ cite {copa12}。本文中有两个主要特征：一个是，在扩展的模态语言中，名义变量被解释为完美布尔代数的原子，完整的连接元素中的完整连接元素元素在完美的分布式晶格中，完整的结合元素中的完整粘合元素在完美的lattices中被解释为在当前的类似于现状的典型性，类似于现有的典范，类似于现有的典型性，类似于现有的单元，类似于类似的单元格式，类似\ cite {zh21d};另一个特征是我们不使用共同体或钻石，这严重限制了电感公式的碎片。我们证明了$ \ mathsf {alba} $相对于模态FM帧的合理性，并证明$ \ m athsf {alba} $在电感公式下成功，类似于\ cite {copa12，zh21d，zh21d，zh22a}的现有设置。
We study the correspondence theory of intuitionistic modal logic in modal Fairtlough-Mendler semantics (modal FM semantics) \cite{FaMe97}, which is the intuitionistic modal version of possibility semantics \cite{Ho16}. We identify the fragment of inductive formulas \cite{GorankoV06} in this language and give the algorithm $\mathsf{ALBA}$ \cite{CoPa12} in this semantic setting. There are two major features in the paper: one is that in the expanded modal language, the nominal variables, which are interpreted as atoms in perfect Boolean algebras, complete join-prime elements in perfect distributive lattices and complete join-irreducible elements in perfect lattices, are interpreted as the refined regular open closures of singletons in the present setting, similar to the possibility semantics for classical normal modal logic \cite{Zh21d}; the other feature is that we do not use conominals or diamond, which restricts the fragment of inductive formulas significantly. We prove the soundness of the $\mathsf{ALBA}$ with respect to modal FM frames and show that the $\mathsf{ALBA}$ succeeds on inductive formulas, similar to existing settings like \cite{CoPa12,Zh21d,Zh22a}.
