Axiomatisations of functional dependencies in the presence of records, lists, sets and multisets

We investigate functional dependencies in databases that support complex values such as records, lists, sets and multisets. Therefore, an abstract algebraic framework is proposed that classifies data models according to the underlying types they support. This allows to emphasise the impact of the data types rather than the specifics of a particular data model.The main results are finite, minimal, sound and complete sets of inference rules for the implication of functional dependencies in the presence of records and all combinations of lists, sets and multisets. The inference rules are similar to Armstrong's original axioms for the relational data model, thanks to the algebraic framework. The completeness result, however, requires a deep analysis in the case of sets and, in particular, multisets.