Recently, Baltag and van Benthem introduced a decidable logic of functional dependence (LFD) that extends the logic of Cylindrical Relativized Set Algebras (CRS) with atomic local dependence statements. Its semantics can be given in terms of generalised assignment models or their modal counterparts, hence the logic is both a first-order and a modal logic. We show that LFD has the finite model property (FMP) using Herwig's theorem on extending partial isomorphisms, and prove a bisimulation invariance theorem characterizing LFD as a fragment of first-order logic.

中文翻译：

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LFD 的有限模型性质和互模拟

最近，Baltag 和 van Benthem 引入了函数依赖（LFD）的可判定逻辑，它用原子局部依赖语句扩展了圆柱相对化集合代数（CRS）的逻辑。它的语义可以根据广义赋值模型或其模态对应物给出，因此该逻辑既是一阶逻辑又是模态逻辑。我们使用关于扩展部分同构的 Herwig 定理证明了 LFD 具有有限模型属性 (FMP)，并证明了将 LFD 表征为一阶逻辑片段的互模拟不变性定理。