Ternary relationship decomposition and higher normal form structures derived from entity relationship conceptual modeling

Abstract

Our paper looks at the potential decomposition of ternary relationships in ER modeling. We suggest that the decomposition of ternary relationships is not provided for by traditional normalization theory which does not consider the specific and implicit semantics of these structures. We provide an analysis which identifies the lossless, functional dependency preserving equivalency between ternary relationships and subsequent binary decompositions. This demonstration of equivalency is based on notation, constructs and semantic requirements which are available at the entity relationship modeling level. We provide a template showing all allowable combinations of ternary/binary cardinalities, and which of those can be losslessly decomposed while preserving functional dependencies. Because of the nature of ternary relationships and the implicit involvement of composite keys, comparisons are often made to the higher normal forms. We discuss the obvious similarities between the decomposition of ternary relationships presented in this paper and the traditional theory behind 4NF and 5NF decompositions. We show that from an entity relationship modeling perspective, it is impractical and inappropriate to consider ternary relationship decomposition under the umbrella of higher normal form decomposition. We suggest that although the theory of the higher normal forms is sound, it has limited practical application when considering ternary relationships. We also discuss the relevancy of this work with regard to their representation in CASE tools, and the inability of binary modeling to logically represent certain ternary relationship cardinalities.