This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized assignment semantics for first order logic. The expressive strength, complete proof calculus and meta-properties of LFD are explored. Various language extensions are presented as well, up to undecidable modal-style logics for independence and dynamic logics of changing dependence models. Finally, more concrete settings for dependence are discussed: continuous dependence in topological models, linear dependence in vector spaces, and temporal dependence in dynamical systems and games.

本文基于一阶逻辑的广义赋值语义设置中，在经典命题逻辑的扩展基础上，将依赖原子和依赖量词视为模态，提出了一种功能依赖LFD的简单可判定逻辑。探讨了LFD的表达强度，完全证明演算和元属性。还介绍了各种语言扩展，包括不确定性的模态样式逻辑（用于独立性和变化的依赖模型的动态逻辑）。最后，讨论了更具体的依赖性设置：拓扑模型中的连续依赖性，向量空间中的线性依赖性以及动力学系统和游戏中的时间依赖性。