Skip to main content

Reducing Multiplicities in Class Diagrams

  • Conference paper
Model Driven Engineering Languages and Systems (MODELS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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)

    Article  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. Baader, F., et al. (eds.): The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press, Cambridge (2003)

    MATH  Google Scholar 

  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. Berardi, D., Calvanese, D., De Giacomo, G.: Reasoning on UML class diagrams. Artificial Intelligence 168(1–2), 70–118 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  7. Calvanese, D., Lenzerini, M., Nardi, D.: Unifying class-based representation formalisms. Journal of Artificial Intelligence Research 11, 199–240 (1999)

    MATH  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  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. 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. 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. 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. 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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  19. Krishnan, P.: Consistency checks for UML. In: Proceedings of APSEC 2000, p. 162. IEEE Computer Society, Washington, DC (2000)

    Google Scholar 

  20. Lenzerini, M., Nobili, P.: On the satisfiability of dependency constraints in entity-relationship schemata. Information Systems 15(4), 453–461 (1990)

    Article  Google Scholar 

  21. Niederbrucker, G., Sisel, T.: Clews Website (2011), http://www.logic.at/clews

  22. Object Management Group: Object Constraint Language 2.3 (2011), www.omg.org

  23. Object Management Group: Unified Modeling Language 2.4 (2011), www.omg.org

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Article  Google Scholar 

  27. The Alliance for Telecommunications Industry Solutions: ATIS telecom glossary 2000 (2000), www.atis.org (approved February 28, 2001 by ANSI)

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints 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)

Publish with us

Policies and ethics