On the Role of the Complementation Rule for Data Dependencies over Incomplete Relations

Recently, an axiomatization for functional dependencies (FDs) and multivalued dependencies (MVDs) has been established where arbitrary attributes can be specified as NOT NULL. That is, the information stored over such attributes must not be incomplete. The axiomatization subsumes previous axiomatizations of FDs and MVDs where every attribute is declared to be NOT NULL, and where no attribute is declared to be NOT NULL. We establish axiomatizations which underpin formally the intuition that the complementation rule is a mere means of database normalization. The results unburden the existing theory of the strong assumption that all attributes are known at the time when the dependencies are specified. The findings extend and unify previous results for the special cases above.