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Full Satisfiability of UML Class Diagrams

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

Abstract

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.

Keywords

Reasoning over Conceptual Models Description Logics Complexity Analysis 

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References

  1. 1.
    Artale, A., Calvanese, D., Ibanez-Garcia, A.: Full satisfiability of UML class diagrams (extended abstract). Technical Report 127, Roskilde University Computer Science Research Reports. In: Proc. of the 2009 Int. Workshop on Logic in Databases (LID 2009) (2009)Google Scholar
  2. 2.
    Clark, T., Evans, A.S.: Foundations of the Unified Modeling Language. In: Duke, D., Evans, A. (eds.) Proc. of the 2nd Northern Formal Methods Workshop, Springer, Heidelberg (1997)Google Scholar
  3. 3.
    Evans, A., France, R., Lano, K., Rumpe, B.: Meta-modelling semantics of UML. In: Kilov, H. (ed.) Behavioural Specifications for Businesses and Systems. Kluwer Academic Publishers, Dordrecht (1999)Google Scholar
  4. 4.
    Harel, D., Rumpe, B.: Modeling languages: Syntax, semantics and all that stuff. Technical Report MCS00-16, The Weizmann Institute of Science, Rehovot, Israel (2000)Google Scholar
  5. 5.
    Berardi, D., Calvanese, D., De Giacomo, G.: Reasoning on UML class diagrams. Artificial Intelligence 168(1-2), 70–118 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    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
  7. 7.
    Artale, A., Calvanese, D., Kontchakov, R., Zakharyaschev, M.: The DL-Lite family and relations. J. of Artificial Intelligence Research 36, 1–69 (2009)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Kaneiwa, K., Satoh, K.: Consistency checking algorithms for restricted UML class diagrams. In: Dix, J., Hegner, S.J. (eds.) FoIKS 2006. LNCS, vol. 3861, pp. 219–239. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  9. 9.
    Kaneiwa, K., Satoh, K.: On the complexities of consistency checking for restricted UML class diagrams. Theoretical Computer Science 411(2), 301–323 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P.F. (eds.): The Description Logic Handbook: Theory, Implementation and Applications. Cambridge University Press, Cambridge (2003)zbMATHGoogle Scholar
  11. 11.
    Bergamaschi, S., Sartori, C.: On taxonomic reasoning in conceptual design. ACM Trans. on Database Systems 17(3), 385–422 (1992)CrossRefGoogle Scholar
  12. 12.
    Borgida, A.: Description logics in data management. IEEE Trans. on Knowledge and Data Engineering 7(5), 671–682 (1995)CrossRefGoogle Scholar
  13. 13.
    Artale, A., Cesarini, F., Soda, G.: Describing database objects in a concept language environment. IEEE Trans. on Knowledge and Data Engineering 8(2), 345–351 (1996)CrossRefGoogle Scholar
  14. 14.
    Calvanese, D., Lenzerini, M., Nardi, D.: Description logics for conceptual data modeling. In: Chomicki, J., Saake, G. (eds.) Logics for Databases and Information Systems, pp. 229–264. Kluwer Academic Publishers, Dordrecht (1998)CrossRefGoogle Scholar
  15. 15.
    Calvanese, D., Lenzerini, M., Nardi, D.: Unifying class-based representation formalisms. J. of Artificial Intelligence Research 11, 199–240 (1999)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Borgida, A., Brachman, R.J.: Conceptual modeling with description logics. In: [10], ch. 10, pp. 349–372Google Scholar
  17. 17.
    Möller, R., Haarslev, V.: Description logic systems. In: [10], ch. 8, pp. 282–305Google Scholar
  18. 18.
    Buchheit, M., Donini, F.M., Schaerf, A.: Decidable reasoning in terminological knowledge representation systems. J. of Artificial Intelligence Research 1, 109–138 (1993)MathSciNetzbMATHGoogle Scholar
  19. 19.
    Lenzerini, M., Nobili, P.: On the satisfiability of dependency constraints in entity-relationship schemata. Information Systems 15(4), 453–461 (1990)CrossRefGoogle Scholar
  20. 20.
    Jarrar, M., Heymans, S.: Towards pattern-based reasoning for friendly ontology debugging. Int. J. on Artificial Intelligence Tools 17(4), 607–634 (2008)CrossRefGoogle Scholar
  21. 21.
    Papadimitriou, C.H.: Computational Complexity. Addison Wesley Publ. Co., Reading (1994)zbMATHGoogle Scholar

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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