Abstract
The concept of multiplicity in UML derives from that of cardinality in entity-relationship modeling techniques. The UML documentation defines this concept but at the same time acknowledges some lack of obviousness in the specification of multiplicities for n-ary associations. This paper shows an ambiguity in the definition given by UML documentation and proposes a clarification to this definition, as well as a simple extension to the current notation to represent other multiplicity constraints, such as participation constraints, that are equally valuable in understanding n-ary associations.
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References
Batini, C., Ceri, S., Navathe, S. B.: Conceptual Database Design: an Entity-Relationship Approach. Benjamin-Cummings (1992)
Castellani, X., Habrias, H., Perrin, Ph.: “A Synthesis on the Definitions and Notations of Cardinalities of Relationships”, Journal of Object Oriented Programming, 13(6):32–35 (2000)
Ceri, S., Fraternali, P.: Designing Database Applications with Objects and Rules: the IDEA Methodology. Addison-Wesley (1997)
Chen, P. P.: “The Entity-Relationship Model”, ACM Transactions on Database Systems, 1(1):9–36 (1976)
Coad, P., Yourdon, E.: Object-Oriented Analysis, 2nd ed. Prentice-Hall (1991)
Codd, E. F.: The Relational Model for Database Managament: Version 2. Addison-Wesley (1990)
Date, C. J.: An Introduction to Database Systems, 6th ed. Addison-Wesley (1995)
De Miguel, A., Piattini, M., Marcos, E.: Diseño de bases de datos relacionales. Ra-Ma, Madrid (1999)
Dullea, J., Song, I.-Y.: “An Analysis of Structural Validity of Ternary Relationships in Entity-Relationship Modeling”, Proceedings of the 7th International Conference on Information and Knowledge Management, 331–339, Washington, D.C., Nov. 3–7 (1998)
Elmasri, R., Navathe, S. B.: Fundamentals of Database Systems, 2nd ed. Benjamin-Cummings (1994)
Embley, D. W.: Object Database Development: Concepts and Principles. Addison-Wesley (1998)
Genilloud, G.: “Common Domain Objects in the RM-ODP Viewpoints”, Computer Standards and Interfaces, 19(7):361–374 (1998)
Hitchman, S.: “Ternary Relationships—To Three or not to Three, Is there a Question?” European Journal of Information Systems, 8:224–231 (1999)
Jones, T. H., Song, I.-Y.: “Binary Representations of Ternary Relationships in ER Conceptual Modeling”, 14th International Conference on Object-oriented and Entity-Relationship Approach, pp. 216–225, Gold Coast, Australia, Dec. 12-15 (1995)
Jones, T. H., Song, I.-Y.: “Analysis of Binary/Ternary Cardinality Combinations in Entity-Relationship Modeling”, Data & Knowledge Engineering, 19(1):39–64 (1996)
Jones, T. H., Song, I.-Y.: “Binary Equivalents of Ternary Relationships in Entity-Relationship Modeling: a Logical Decomposition Approach”, Journal of Database Management, April-June:12–19 (2000)
Kilov, H., Ross, J.: Information Modeling: An Object-Oriented Approach. Prentice Hall (1994)
Martin, J., Odell, J.: Object-Oriented Methods: A Foundation. Prentice Hall (1995)
Martínez, P., Nieto, C., Cuadra, D., De Miguel, A.: “Profundizando en la semántica de las cardinalidades en el modelo E/R extendido”, IV Jornadas de Ingeniería del Software y Bases de Datos, pp. 53–54, Cáceres, Spain, Nov. 24–26 (1999)
McAllister, A.: “Modeling N-ary Data Relationships in CASE Environments”, Proceedings of the 7th International Workshop on Computer Aided Software Engineering, pp. 132–140, Toronto, Canada (1995)
Metodología de planificación y desarrollo de sistemas de información, METRICA versión Tomo 3: Guía de técnicas. Instituto Nacional de Administración Pública, España. Madrid (1993)
Rumbaugh, J., Jacobson, I., Booch, G.: The Unified Modeling Language Reference Manual. Addison-Wesley (1998)
Rumbaugh, J.: “Relations as Semantic Constructs in an Object-Oriented Language”, Proceedings of the ACM Conference on Object-Oriented Programming: Systems, Languages and Applications, pp. 466–481, Orlando, Florida (1987)
Rumbaugh, J., Blaha, M., Premerlani, W., Eddy, F., Lorensen, W.: Object-Oriented Modeling and Design. Prentice-Hall International (1991)
Song, I.-Y., Jones, T. H.: “Analysis of binary relationships within ternary relationships in ER Modeling”, Proceedings of the 12th International Conference on Entity-Relationship Approach, pp. 265–276, Dallas, Texas, Dec. 15-17 (1993)
Song, I.-Y., Evans, M., Park, E. K.: “A Comparative Analysis of Entity-Relationship Diagrams”, Journal of Computer and Software Engineering, 3(4):427–459 (1995)
Tardieu, H., Rochfeld, A., Coletti, R.: La méthode MERISE. Tome 1: Principles et outils. Les Editions d’Organisation, Paris (1983, 1985)
Teorey, T. J.: Database Modeling and Design, 3rd ed, Morgan Kaufmann Publishers (1999)
Object Management Group: Unified Modeling Language Specification, Version 1–3, (June 1999)
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Génova, G., Llorens, J., Martínez, P. (2001). Semantics of the Minimum Multiplicity in Ternary Associations in UML. In: Gogolla, M., Kobryn, C. (eds) ≪UML≫ 2001 — The Unified Modeling Language. Modeling Languages, Concepts, and Tools. UML 2001. Lecture Notes in Computer Science, vol 2185. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45441-1_25
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DOI: https://doi.org/10.1007/3-540-45441-1_25
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