Armstrong Databases and Reasoning for Functional Dependencies and Cardinality Constraints over Partial Bags

Data dependencies capture meaningful information about an application domain within the target database. The theory of data dependencies is largely a theory over relations. To make data processing more efficient in practice, partial bags are permitted as database instances to accommodate partial and duplicate information. However, data dependencies interact differently over partial bags than over the idealized special case of relations. In this paper, we study the implication problem of the combined class of functional dependencies and cardinality constraints over partial bags. We establish an axiomatic and an algorithmic characterization of the implication problem. These findings have important applications in database design and data processing. Finally, we investigate structural and computational properties of Armstrong databases for the class of data dependencies under consideration. These results can be utilized to consolidate and communicate the understanding of the application domain between different stake-holders of a database.