Unified characterization of symmetric dependencies with lattices

Abstract

Symmetric dependencies, or MultiValued Dependencies-like, are those dependencies that follow the deduction rules of MultiValued Dependencies (MVD’s). These are MVD-clauses, Degenerate MultiValued Dependencies (DMVD’s), and MVD’s, being the latter ones relevant to the 4th normal form in the relational database model. Previous results have explained how to characterize these dependencies with lattices. However, these characterizations were ad-hoc, and no unified characterization has been provided yet. The purpose of this paper is to present such a common characterization for all these kind of dependencies providing the same framework for all of them, and to extend this generalization to the construction of Armstrong relations.