Reasoning about functional and full hierarchical dependencies over partial relations

We study the implication problem for the combined class of functional and full hierarchical dependencies in the presence of SQL’s NOT NULL constraints. Two different notions of implication are addressed: one where a dependency is implied by the given set of dependencies plus the underlying schema, and one where a dependency is implied by the given set of dependencies alone. We establish axiomatizations for both notions of implication, and reveal deep relationships between them.