Abstract
In class diagrams, so-called multiplicities are integer ranges attached to association ends. They constrain the number of instances of the associated class that an instance may be linked to, or in an alternative reading, the number of links to instances of the associated class. In complex diagrams with several chains of associations between two classes (arising e.g. in configuration management) it may happen that the lower or upper bound of a range can never be attained because of restrictions imposed by a parallel chain.
In this paper we investigate how multiplicities behave when chaining associations together, and we characterise situations where intervals can be tightened due to information from other chains. Detecting and eliminating such redundancies provides valuable feedback to the user, as redundancies may hint at some underlying misconception.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Anastasakis, K., Bordbar, B., Georg, G., Ray, I.: On challenges of model transformation from UML to Alloy. Software and System Modeling 9(1), 69–86 (2010)
Artale, A., Calvanese, D., Kontchakov, R., Ryzhikov, V., Zakharyaschev, M.: Reasoning over extended ER models. In: Parent, C., Schewe, K.-D., Storey, V.C., Thalheim, B. (eds.) ER 2007. LNCS, vol. 4801, pp. 277–292. Springer, Heidelberg (2007)
Artale, A., Calvanese, D., Kontchakov, R., Zakharyaschev, M.: Adding weight to DL-Lite. In: Grau, B.C., et al. (eds.) DL 2009. CEUR Workshop, vol. 477 (2008)
Baader, F., et al. (eds.): The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press, Cambridge (2003)
Beckert, B., Keller, U., Schmitt, P.: Translating the Object Constraint Language into first-order predicate logic. In: VERIFY, FLoC Workshop (2002)
Berardi, D., Calvanese, D., De Giacomo, G.: Reasoning on UML class diagrams. Artificial Intelligence 168(1–2), 70–118 (2005)
Calvanese, D., Lenzerini, M., Nardi, D.: Unifying class-based representation formalisms. Journal of Artificial Intelligence Research 11, 199–240 (1999)
Chen, P.P.S.: The entity-relationship model: toward a unified view of data. ACM Transactions on Database Systems 1(1), 9–36 (1976)
Dullea, J., Song, I.Y.: An analysis of cardinality constraints in redundant relationships. In: Proceedings of CIKM 1997, pp. 270–277. ACM, New York (1997)
Dupuy, S., Ledru, Y., Chabre-Peccoud, M.: An overview of roZ: A tool for integrating UML and Z specifications. In: Wangler, B., Bergman, L.D. (eds.) CAiSE 2000. LNCS, vol. 1789, pp. 417–430. Springer, Heidelberg (2000)
Falkner, A., Feinerer, I., Salzer, G., Schenner, G.: Computing product configurations via UML and integer linear programming. Int. J. Mass Cust. 3(4) (2010)
Feinerer, I.: A Formal Treatment of UML Class Diagrams as an Efficient Method for Configuration Management. Dissertation, Vienna University of Technology (2007)
Feinerer, I., Salzer, G.: Consistency and minimality of UML class specifications with multiplicities and uniqueness constraints. In: Proceedings of TASE 2007, pp. 411–420. IEEE Computer Society Press, Los Alamitos (2007)
Felfernig, A., Friedrich, G., Jannach, D., Stumptner, M., Zanker, M.: UML as knowledge acquisition frontend for semantic web configuration knowledge bases. In: Proceedings of RuleML 2002. CEUR Workshop Proceedings, vol. 60 (2002)
Hartmann, S.: On the consistency of int-cardinality constraints. In: Ling, T.-W., Ram, S., Li Lee, M. (eds.) ER 1998. LNCS, vol. 1507, pp. 150–163. Springer, Heidelberg (1998)
Hartmann, S.: On interactions of cardinality constraints,key, and functional dependencies. In: Schewe, K.-D., Thalheim, B. (eds.) FoIKS 2000. LNCS, vol. 1762, pp. 136–155. Springer, Heidelberg (2000)
Jones, T.H., Song, I.Y.: Analysis of binary/ternary cardinality combinations in entity-relationship modeling. Data & Knowledge Engineering 19(1), 39–64 (1996)
Kim, S.-K., Carrington, D.: Formalizing the UML class diagram using object-Z. In: France, R.B. (ed.) UML 1999. LNCS, vol. 1723, pp. 83–98. Springer, Heidelberg (1999)
Krishnan, P.: Consistency checks for UML. In: Proceedings of APSEC 2000, p. 162. IEEE Computer Society, Washington, DC (2000)
Lenzerini, M., Nobili, P.: On the satisfiability of dependency constraints in entity-relationship schemata. Information Systems 15(4), 453–461 (1990)
Niederbrucker, G., Sisel, T.: Clews Website (2011), http://www.logic.at/clews
Object Management Group: Object Constraint Language 2.3 (2011), www.omg.org
Object Management Group: Unified Modeling Language 2.4 (2011), www.omg.org
Queralt, A., Teniente, E.: Reasoning on UML class diagrams with OCL constraints. In: Embley, D.W., Olivé, A., Ram, S. (eds.) ER 2006. LNCS, vol. 4215, pp. 497–512. Springer, Heidelberg (2006)
Rosati, R.: Finite model reasoning in DL-lite. In: Bechhofer, S., Hauswirth, M., Hoffmann, J., Koubarakis, M. (eds.) ESWC 2008. LNCS, vol. 5021, pp. 215–229. Springer, Heidelberg (2008)
Snook, C.F., Butler, M.J.: UML-B: Formal modeling and design aided by UML. ACM Trans. Softw. Eng. Methodol. 15(1), 92–122 (2006)
The Alliance for Telecommunications Industry Solutions: ATIS telecom glossary 2000 (2000), www.atis.org (approved February 28, 2001 by ANSI)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Feinerer, I., Salzer, G., Sisel, T. (2011). Reducing Multiplicities in Class Diagrams. In: Whittle, J., Clark, T., Kühne, T. (eds) Model Driven Engineering Languages and Systems. MODELS 2011. Lecture Notes in Computer Science, vol 6981. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24485-8_27
Download citation
DOI: https://doi.org/10.1007/978-3-642-24485-8_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24484-1
Online ISBN: 978-3-642-24485-8
eBook Packages: Computer ScienceComputer Science (R0)