A correspondence between variable relations and three-valued propositional logic

Herein, relations are generalised to variable length tuple relations (variabe relations) wherein tuples are allowed to be of variable length. We define the concept of a functional dependency (FD) holding in variable relations and present a sound and complete axiom system for them. Our main result shows an equivalence between FDs holding in variable relations and propositional implications holding in (a subset of) a three-valued propositional logic. We extend this result to object relations, which are a subclass of variable relations enabling us to view tuples as objects