Binary Equivalents of Ternary Relationships in Entity-Relationship Modeling

Abstract

Little work has been completed which addresses the logical composition and use of ternary relationships in entity-relationship modeling. Many modeling notations and most CASE tools do not allow for ternary relationships. Alternative methods and substitutes for ternary relationship structures do not necessarily reflect the original logic, semantics or constraints of a given situation. Furthermore, it has been shown that ternary relationships can be constrained by additional implicit binary constraints which do not occur in the logic of binary relationships. This paper develops an analytical perspective of ternary relationships. We investigate the logical relationships implicit to the ternary structure and then identify potential simplification through decomposition into binary equivalents. These alternative binary equivalents allow retention of the implicit logical structure, and consequently also retain the semantics of the original structure. The analysis investigates equivalency of lossless decompositions, preservation of functional dependencies and finally the ability to preserve update constraints (insertions and deletions). We identify which ternary relationships have true, fully equivalent, binary equivalents and those which do not. We provide an exhaustive analysis of cardinality combinations found in ternary relationships which practitioners can use to guide the way in which they deal with ternary relationships in conceptual modeling.