Functional dependencies add semantics to a database schema, and are useful for studying various problems, such as database design, query optimization and how dependencies are carried into a view. In the context of a nested relational model, these dependencies can be extended by using path expressions instead of attribute names, resulting in a class of dependencies that we call nested functional dependencies (NFDs). NFDs define a natural class of dependencies in complex data structures; in particular they allow the specification of many useful intra- and inter-set dependencies (i.e., dependencies that are local to a set and dependencies that require consistency between sets). Such constraints cannot be captured by existing notions of functional, multi-valued, or join dependencies. This paper presents the definition of NFDs and gives their meaning by translation to logic. It then presents a sound and complete set of eight inference rules for NFDs, and discusses approaches to handling the existence of empty sets in instances. Empty sets add complexity in reasoning since formulas such as ∀x ∈ R.P (x) are trivially true when R is empty. This axiomatization represents a first step in reasoning about constraints on data warehouse applications, where both the source and target databases support complex types.