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.
翻译:本文介绍了功能依赖性LFD的简单可变逻辑,其依据是传统理论逻辑的延伸,其中依赖原子加上依赖性量化标准被视为模式,在为一阶逻辑设定通用分配语义的范围内,探讨了LFD的表达力、完整校正计算法和元异性,还介绍了各种语言扩展,直至不可变模式式独立逻辑和不断变化的依赖模式动态逻辑。最后,讨论了更具体的依赖性环境:地形模型的持续依赖性、矢量空间的线性依赖性、动态系统和游戏的时间依赖性。