On Inferences of Full First-Order Hierarchical Decompositions

Database design aims to find a database schema that permits the efficient processing of common types of queries and updates on future database instances. Full first-order hierarchical decompositions constitute a large class of database constraints that can provide assistance to the database designer in identifying a suitable database schema. We establish finite axiomatisations of full first-order hierarchical decompositions that mimic best database design practice. That is, an inference engine derives all the independent collections of the universal schema during database normalization, and the designer determines during database denormalization which re-combinations of these independent collections manifest the final database schema. We also show that well-known correspondences between multivalued dependencies, degenerated multivalued dependencies, and a fragment of Boolean propositional logic do not extend beyond binary full first-order hierarchical decompositions.