Full Satisfiability of UML Class Diagrams

  • Alessandro Artale
  • Diego Calvanese
  • Angélica Ibáñez-García
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6412)


UML class diagrams (UCDs) are the de-facto standard formalism for the analysis and design of information systems. By adopting formal language techniques to capture constraints expressed by UCDs one can exploit automated reasoning tools to detect relevant properties, such as schema and class satisfiability and subsumption between classes. Among the reasoning tasks of interest, the basic one is detecting full satisfiability of a diagram, i.e., whether there exists an instantiation of the diagram where all classes and associations of the diagram are non-empty and all the constraints of the diagram are respected. In this paper we establish tight complexity results for full satisfiability for various fragments of UML class diagrams. This investigation shows that the full satisfiability problem is ExpTime-complete in the full scenario, NP-complete if we drop isa between relationships, and NLogSpace-complete if we further drop covering over classes.


Reasoning over Conceptual Models Description Logics Complexity Analysis 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Alessandro Artale
    • 1
  • Diego Calvanese
    • 1
  • Angélica Ibáñez-García
    • 1
  1. 1.KRDB Research CentreFree University of Bozen-BolzanoItaly

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