A Mathematical Framework to Analyze the Concept of Constraining Relationships in Entity Relationship Modeling

摘要

This paper expands previous work in the areas of constraining relationships. It provides a mathematical framework for unary, binary, and constraining unary relationships in the entity-relationship modeling paradigm. Relationships are mathematically defined in terms of their instance mappings, and further definitions of operations on relationships lead to mathematical definitions of maximum and minimum cardinality. The paper also mathematically investigates the ability of unary relationships to constrain binary relationships. The importance of this paper is it provides a mathematical framework for analyzing constraining relationships in data and object modeling and other research areas, such as embedded relationships, relationship decomposition, and n-ary generalization.