A Strongly Minimal Axiomatisation of Multivalued Dependencies in Incomplete Database Relations

We study inference rules for multivalued dependencies in relational databases with null values (NMVDs). The definition of NMVDs is dependent on the underlying relation schema R and this is reflected syntactically by the R-complementation rule which is present in all previous axiomatisation of NMVDs. The main result is a sound and complete set Lfr of inference rules in which the R-axiom is the only inference rule dependent on R. This result extends work of Biskup who has provided such an axiomatisation in the absence of null values. It is proven that the set Lfr is minimal in a very strong sense. In fact, none of its rules can be omitted without losing the ability to infer all trivial NMVDs