We investigate the role of coalgebraic predicate logic , a logic for neighborhood frames first proposed by Chang, in the study of monotonic modal logics. We prove analogues of the Goldblatt–Thomason theorem and Fine’s canonicity theorem for classes of monotonic neighborhood frames closed under elementary equivalence in coalgebraic predicate logic. The elementary equivalence here can be relativized to the classes of monotonic, quasi-filter, augmented quasi-filter, filter, or augmented filter neighborhood frames, respectively. The original, Kripke-semantic versions of the theorems follow as a special case concerning the classes of augmented filter neighborhood frames.

中文翻译：

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单调模态逻辑的对应、规范和模型理论

我们研究了代数谓词逻辑（Chang 首次提出的邻域框架逻辑）在单调模态逻辑研究中的作用。我们证明了 Goldblatt-Thomason 定理和 Fine's canonicity theorem 的类似物，用于在代数谓词逻辑中的基本等价下封闭的单调邻域框架类。这里的基本等价可以分别与单调、准滤波器、增广准滤波器、滤波器或增广滤波器邻域帧的类相对化。这些定理的原始 Kripke 语义版本是关于增强滤波器邻域框架类的特殊情况。