论文标题
当地的依赖和守卫
Local Dependence and Guarding
论文作者
论文摘要
我们研究LFD,这是Baltag和Van Benthem(2021)引入的功能依赖性的基本逻辑,以及与一阶逻辑的守护片段GF的连接。像其他依赖逻辑一样,LFD的语义使用团队:允许变量分配的集合。 LFD与众不同的设置是其在变量之间表达局部依赖性和语句对变量的局部依赖性的能力。 LFD的已知特征包括可确定性,明确的公理化,有限模型属性和三拟合特征。其他人,包括令人满意的复杂性,到目前为止保持开放。更一般而言,缺乏的是对LFD依赖计算的方法的良好理解,以及它如何与其他可决定的逻辑相关。特别是,允许变量依赖性和保护量词将其作为逻辑设备进行比较? 我们提供了从GF到LFD的新构图翻译,相反,我们以“几乎组成”的方式将LFD转换为GF。使用这两种翻译,我们以统一的方式将有关GF的已知结果传递到LFD,例如,LFD满意度以及CRAIG插值的紧密复杂性边界。相反,例如,LFD转移到GF的有限模型属性。因此,当地的依赖和守卫是错综复杂的纠缠概念。
We study LFD, a base logic of functional dependence introduced by Baltag and van Benthem (2021) and its connections with the guarded fragment GF of first-order logic. Like other logics of dependence, the semantics of LFD uses teams: sets of permissible variable assignments. What sets LFD apart is its ability to express local dependence between variables and local dependence of statements on variables. Known features of LFD include decidability, explicit axiomatization, finite model property, and a bisimulation characterization. Others, including the complexity of satisfiability, remained open so far. More generally, what has been lacking is a good understanding of what makes the LFD approach to dependence computationally well-behaved, and how it relates to other decidable logics. In particular, how do allowing variable dependencies and guarding quantifiers compare as logical devices? We provide a new compositional translation from GF into LFD, and conversely, we translate LFD into GF in an `almost compositional' manner. Using these two translations, we transfer known results about GF to LFD in a uniform manner, yielding, e.g., tight complexity bounds for LFD satisfiability, as well as Craig interpolation. Conversely, e.g., the finite model property of LFD transfers to GF. Thus, local dependence and guarding turn out to be intricately entangled notions.