By Lotfi Asker Zadeh
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But are the two storage structures equivalent from the perspective of FD preservation? Consider the same decompositional scenario from a functional dependency perspective. We have previously defined the set of functional dependencies that were present in the original ternary structure. In the decomposed structure, we identify the following functional dependency set: X → Y, X → Z, XY → Z (augmentation), XZ → Y (augmentation) We note that in this decomposition strategy, we lose the functional dependency of YZ → X, and there is no way to recover it through reconstruction based on Armstrong’s Axioms (Armstrong, 1974).
This is done from two perspectives: 1. The theoretical approach to understanding this type of conceptual construct and the subsequent analysis of logical and relational models founded on these theories. 2. The practical aspects of using these constructs in entity-relationship modeling and how the various construct combinations can be mapped to the logical/physical model. The second aspect is partly founded on the first, because the potential decomposition of N-ary constructs and their final representations can be derived from theoretical analysis of the implicit relationships.
Complete rules for n-ary relationship cardinality constraints. Data and Knowledge Engineering, 27, 255-288. McKee, R. L. and Rodgers, J. (1992). N-ary versus binary data modeling: A matter of perspective. Data Resource Management, 3(4), Fall, 22-32. Song, I. , Jones, T. H. and Park, E. K. (1993). Binary relationship imposition rules on ternary relationships in ER modeling. C. Song, I. , Evans, M. and Park, E. K. (1995). A comparative analysis of entity-relationship diagrams. Journal of Computer & Software Engineering, 3(4), 427-459.