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.

► We study functional and full hierarchical dependencies over partial relations.
► We axiomatize their implication over fixed and over undetermined schemata.
► Our axiomatization over fixed schemata enjoys desirable properties.
► The properties reveal close relationships between the two notions of implication.
► Our results apply to no information and value currently unknown nulls.