Skip to main content

Mappings, Maps and Tables: Towards Formal Semantics for Associations in UML2

  • Conference paper
Model Driven Engineering Languages and Systems (MODELS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 4199))

Abstract

In fact, UML2 offers two related yet different definitions of associations. One is implicit in several Description and Semantics sections of the specification and belongs to the UML folklore. It simply says that an association is a set of links. The other – official and formal – definition is explicitly fixed by the UML metamodel and shows that there is much more to associations than just being sets of links. Particularly, association ends can be owned by either participating classes or by the very association (with a striking difference between binary and multiary associations), be navigable or not, and have some constraints on combining ownership and navigability.

The paper presents a formal framework, based on sets and mappings, where all notions involved in the both definitions can be accurately explained and formally explicated. Our formal definitions allow us to reconcile the two views of associations, unify ownership for binary and multiary associations and, finally, detect a few flaws in the association part of the UML2 metamodel.

Research supported by OCE Centre for Communications and Information Technology and IBM CAS Ottawa.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Diskin, Z.: Visualization vs. specification in diagrammatic notations: A case study with the UML. In: Hegarty, M., Meyer, B., Narayanan, N.H. (eds.) Diagrams 2002. LNCS (LNAI), vol. 2317, pp. 112–115. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  2. Diskin, Z., Kadish, B.: Variable set semantics for keyed generalized sketches: Formal semantics for object identity and abstract syntax for conceptual modeling. Data & Knowledge Engineering 47, 1–59 (2003)

    Article  Google Scholar 

  3. Génova, G., Llorens, J., Martínez, P.: Semantics of the minimum multiplicity in ternary associations in UML. In: Gogolla, M., Kobryn, C. (eds.) UML 2001. LNCS, vol. 2185, pp. 329–341. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  4. Gunter, C.: Semantics of programming languages. MIT Press, Cambridge (1992)

    MATH  Google Scholar 

  5. Hull, R., King, R.: Semantic database modeling: Survey, applications and research issues. ACM Computing Surveys 19(3), 201–260 (1987)

    Article  Google Scholar 

  6. Milicev, D.: On the semantics of associations and association ends in UML (submitted for publication)

    Google Scholar 

  7. Milicev, D., Selic, B., et al.: Joint E-mail Discussion, Fall (2005)

    Google Scholar 

  8. Object Management Group, Unified Modeling Language: Superstructure. version 2.0. Formal/05-07-04 (2005), http://www.uml.org

  9. Rumbaugh, J., Jacobson, I., Booch, G.: The Unified Modeling Language Reference Manual, 2nd edn. Addison-Wesley, Reading (2004)

    Google Scholar 

  10. Selic, B.: Personal Communication, Fall (2005)

    Google Scholar 

  11. Stevens, P.: On the interpretation of binary associations in the unified modeling language. Software and Systems Modeling (1) (2002)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Diskin, Z., Dingel, J. (2006). Mappings, Maps and Tables: Towards Formal Semantics for Associations in UML2. In: Nierstrasz, O., Whittle, J., Harel, D., Reggio, G. (eds) Model Driven Engineering Languages and Systems. MODELS 2006. Lecture Notes in Computer Science, vol 4199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11880240_17

Download citation

  • DOI: https://doi.org/10.1007/11880240_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-45772-5

  • Online ISBN: 978-3-540-45773-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics