Advertisement

Reducing Multiplicities in Class Diagrams

  • Ingo Feinerer
  • Gernot Salzer
  • Tanja Sisel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6981)

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    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)CrossRefGoogle Scholar
  2. 2.
    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)CrossRefGoogle Scholar
  3. 3.
    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)Google Scholar
  4. 4.
    Baader, F., et al. (eds.): The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press, Cambridge (2003)zbMATHGoogle Scholar
  5. 5.
    Beckert, B., Keller, U., Schmitt, P.: Translating the Object Constraint Language into first-order predicate logic. In: VERIFY, FLoC Workshop (2002)Google Scholar
  6. 6.
    Berardi, D., Calvanese, D., De Giacomo, G.: Reasoning on UML class diagrams. Artificial Intelligence 168(1–2), 70–118 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Calvanese, D., Lenzerini, M., Nardi, D.: Unifying class-based representation formalisms. Journal of Artificial Intelligence Research 11, 199–240 (1999)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Chen, P.P.S.: The entity-relationship model: toward a unified view of data. ACM Transactions on Database Systems 1(1), 9–36 (1976)CrossRefGoogle Scholar
  9. 9.
    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)Google Scholar
  10. 10.
    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)CrossRefGoogle Scholar
  11. 11.
    Falkner, A., Feinerer, I., Salzer, G., Schenner, G.: Computing product configurations via UML and integer linear programming. Int. J. Mass Cust. 3(4) (2010)Google Scholar
  12. 12.
    Feinerer, I.: A Formal Treatment of UML Class Diagrams as an Efficient Method for Configuration Management. Dissertation, Vienna University of Technology (2007)Google Scholar
  13. 13.
    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)Google Scholar
  14. 14.
    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)Google Scholar
  15. 15.
    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)CrossRefGoogle Scholar
  16. 16.
    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)CrossRefGoogle Scholar
  17. 17.
    Jones, T.H., Song, I.Y.: Analysis of binary/ternary cardinality combinations in entity-relationship modeling. Data & Knowledge Engineering 19(1), 39–64 (1996)CrossRefzbMATHGoogle Scholar
  18. 18.
    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)CrossRefGoogle Scholar
  19. 19.
    Krishnan, P.: Consistency checks for UML. In: Proceedings of APSEC 2000, p. 162. IEEE Computer Society, Washington, DC (2000)Google Scholar
  20. 20.
    Lenzerini, M., Nobili, P.: On the satisfiability of dependency constraints in entity-relationship schemata. Information Systems 15(4), 453–461 (1990)CrossRefGoogle Scholar
  21. 21.
    Niederbrucker, G., Sisel, T.: Clews Website (2011), http://www.logic.at/clews
  22. 22.
    Object Management Group: Object Constraint Language 2.3 (2011), www.omg.org
  23. 23.
    Object Management Group: Unified Modeling Language 2.4 (2011), www.omg.org
  24. 24.
    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)CrossRefGoogle Scholar
  25. 25.
    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)CrossRefGoogle Scholar
  26. 26.
    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)CrossRefGoogle Scholar
  27. 27.
    The Alliance for Telecommunications Industry Solutions: ATIS telecom glossary 2000 (2000), www.atis.org (approved February 28, 2001 by ANSI)

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Ingo Feinerer
    • 1
  • Gernot Salzer
    • 2
  • Tanja Sisel
    • 2
  1. 1.Institut für InformationssystemeTechnische Universität WienViennaAustria
  2. 2.Institut für ComputersprachenTechnische Universität WienViennaAustria

Personalised recommendations