A Simple Logic of Functional Dependence
Alexandru Baltag, Johan van Benthem

Abstract:
This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms and dependence quantifiers, modeled within the setting of generalized assignment semantics for FOL. The logic's expressive strength, complete proof calculus and meta-properties are explored. Various extensions are presented, as well as boundaries with undecidable logics for independence. 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.