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The Definition of Transitive Closure with OCL – Limitations and Applications –

  • Thomas Baar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2890)

Abstract

The Object Constraint Language (OCL) is based on first-order logic and set theory. As the most well-known application, OCL is used to formulate well-formedness rules in the UML metamodel. Here, the transitive closure of a relationship is defined in terms of an OCL invariant, which seems to contradict classical results on the expressive power of first-order logic.

In this paper, we give sufficient justification for the correctness of the definition of transitive closure. Our investigation reinforces some decisions made in the semantics of UML and OCL. Currently, there is a lively debate on the same issues in the semantics of the upcoming UML 2.0.

Keywords

Class Diagram Transitive Closure Object Constraint Language Finite Model Generalization Arrow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Beckert, B., Keller, U., Schmitt, P.H.: Translating the Object Constraint Language into first-order predicate logic. In: Proceedings, VERIFY, Workshop at Federated Logic Conferences (FLoC), Copenhagen, Denmark (2002)Google Scholar
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    Ebbinghaus, H.-D., Flum, J.: Finite Model Theory. Springer, Heidelberg (1995)zbMATHGoogle Scholar
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    OMG. OMG Unified Modeling Language Specification. Technical Report OMGUML Version 1.4, Object Mangagement Group (September 2001)Google Scholar
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    Richters, M.: A precise approach to validating UML models and OCL constraints. PhD thesis, Bremer Institut für Sichere Systeme, Universität Bremen, Logos-Verlag, Berlin (2001)Google Scholar
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    Warmer, J., Kleppe, A.: The Object Constraint Language: Precise Modeling with UML. Addison-Wesley, Reading (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Thomas Baar
    • 1
  1. 1.Fakultät für Informatik, Institut für Logik, Komplexität und DeduktionssystemeUniversität KarlsruheKarlsruhe

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