Strong keys and functional dependencies in partial database relations

We study keys and functional dependencies in the context of partial relations that permit null values with the interpretation no information. Based on Codd’s principle of entity integrity we propose the class of strong keys over partial database relations. These keys enforce both uniqueness and totality of tuples. We study the interaction of strong keys with Lien, Atzeni and Morfuni’s classes of functional dependencies and null-free subschemata. For various subclasses we establish axiomatisations, linear-time algorithms to decide implication, and characterisations and computations of Armstrong relations. Interestingly, the class of general functional dependencies does not enjoy Armstrong relations over partial relations, but even the combined class of strong keys and standard functional dependencies does. We also settle various questions related to the maximal size of a family of non-redundant strong keys over partial relations.