Software & Systems Modeling

, Volume 13, Issue 3, pp 1167–1187 | Cite as

Numeric semantics of class diagrams with multiplicity and uniqueness constraints

Regular Paper

Abstract

We translate class diagrams with multiplicity constraints and uniqueness attributes to inequalities over non-negative integers. Based on this numeric semantics we check the satisfiability and consistency of class diagrams and compute minimal models. We show that this approach is efficient and provides succinct user feedback in the case of errors. In an experimental section we demonstrate that general off-the-shelf solvers for integer linear programming perform as well on real-world and synthetic benchmarks as specialised algorithms do, facilitating the extension of the formal model by further numeric constraints like cost functions. Our results are embedded in a research programme on reasoning about class diagrams and are motivated by applications in configuration management. Compared to other (for instance logic-based) approaches our aim is to hide the complexity of formal methods behind familiar user interfaces like class diagrams and to concentrate on problems that can be solved efficiently in order to be able to provide immediate feedback to users.

Keywords

Model engineering Formal methods  Reasoning about class diagrams Integer linear programming Configuration management 

References

  1. 1.
    Anastasakis, K., Bordbar, B., Georg, G., Ray, I.: On challenges of model transformation from UML to Alloy. Softw. Syst. Model. 9(1), 69–86 (2010)CrossRefGoogle Scholar
  2. 2.
    André, P., Romanczukand, A., Royer, J.: Checking the consistency of UML class diagrams using Larch prover. In: Proceedings of Rigorous Object-Oriented Methods 2000, pp. 1–16 (2000)Google Scholar
  3. 3.
    Artale, A., Calvanese, D., Kontchakov, R., Ryzhikov, V., Zakharyaschev, M.: Reasoning over extended ER models. In: Proceedings of the 26th International Conference on Conceptual Modeling (ER 2007). Lecture Notes in Computer Science, vol. 4801, pp. 277–292. Springer, Berlin (2007)Google Scholar
  4. 4.
    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
  5. 5.
    Aschinger, M., Drescher, C., Gottlob, G.: Introducing LoCo, a logic for configuration problems. In: Proceedings of the 2nd Workshop on Logics for Component Configuration, LoCoCo 2011, Perugia, Italy (2011)Google Scholar
  6. 6.
    Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P. (eds.): The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press, London (2003)Google Scholar
  7. 7.
    Balaban, M., Maraee, A.: Consistency of UML class diagrams with hierarchy constraints. In: Next Generation Information Technologies and Systems. Lecture Notes in Computer Science, vol. 4032, pp. 71–82. Springer, Berlin (2006)Google Scholar
  8. 8.
    Beckert, B., Keller, U., Schmitt, P.: Translating the Object Constraint Language into first-order predicate logic. In: Proceedings, VERIFY, Workshop at Federated Logic Conferences (FLoC), Copenhagen, Denmark (2002)Google Scholar
  9. 9.
    Ali, A. B. H., Boufares, F., Abdellatif, A.: Checking constraints consistency in UML class diagrams. In: 2nd International Conference on Information and Communication Technologies, 2006. ICTTA ’06, vol. 2, pp. 3599–3604 (2006)Google Scholar
  10. 10.
    Berardi, D., Calvanese, D., De Giacomo, G.: Reasoning on UML class diagrams. Artif. Intell. 168(1–2), 70–118 (2005). http://www.inf.unibz.it/~calvanese/papers-html/AIJ-2005.html
  11. 11.
    Boufares, F., Bennaceur, H.: Consistency problems in ER-schemas for database systems. Inf. Sci. 163(4), 263–274 (2004). doi:10.1016/j.ins.2003.06.015 CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Cadoli, M., Calvanese, D., Giacomo, G.D., Mancini, T.: Finite model reasoning on UML class diagrams via constraint programming. In: AI*IA 2007: Artificial Intelligence and Human-Oriented Computing. Lecture Notes in Computer Science, vol. 4733, pp. 36–47. Springer, Berlin (2007)Google Scholar
  13. 13.
    Calì, A., Calvanese, D., Giacomo, G.D., Lenzerini, M.: A formal framework for reasoning on UML class diagrams. In: ISMIS ’02: Proceedings of the 13th International Symposium on Foundations of Intelligent Systems, pp. 503–513. Springer, London (2002)Google Scholar
  14. 14.
    Calvanese, D., Lenzerini, M., Nardi, D.: Unifying class-based representation formalisms. J. Artif. Intell. Res. 11, 199–240 (1999)MATHMathSciNetGoogle Scholar
  15. 15.
    Chen, P.P.S.: The entity-relationship model: toward a unified view of data. ACM Trans. Database Syst. 1(1), 9–36 (1976). doi:10.1145/320434.320440 CrossRefGoogle Scholar
  16. 16.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms. The MIT Press and McGraw-Hill Book Company, London (1989)Google Scholar
  17. 17.
    Dupuy, S., Ledru, Y., Chabre-Peccoud, M.: An overview of RoZ: a tool for integrating UML and Z specifications. In: Wangler, B., Bergman, L. (eds.) Proceedings of CAiSE 2000. LNCS, vol. 1789, pp. 417–430. Springer, Berlin (2000)Google Scholar
  18. 18.
    Egyed, A.: Instant consistency checking for the UML. In: ICSE ’06: Proceeding of the 28th International Conference on Software Engineering, pp. 381–390. ACM Press, New York (2006). doi:10.1145/1134285.1134339
  19. 19.
    Falkner, A., Feinerer, I., Salzer, G., Schenner, G.: Computing product configurations via UML and integer linear programming. Int. J. Mass Cust. 3(4) (2010). doi:10.1504/IJMASSC.2010.037650
  20. 20.
    Feinerer, I.: A formal treatment of UML class diagrams as an efficient method for configuration management. Dissertation, Theory and Logic Group, Institute of Computer Languages, Vienna University of Technology, Austria (2007)Google Scholar
  21. 21.
    Feinerer, I., Salzer, G.: Consistency and minimality of UML class specifications with multiplicities and uniqueness constraints. In: Proceedings of the 1st IEEE/IFIP International Symposium on Theoretical Aspects of Software Engineering, Shanghai, China, 6–8 June 2007, pp. 411–420. IEEE Computer Society Press, New York (2007). doi:10.1109/TASE.2007.17
  22. 22.
    Feinerer, I., Salzer, G., Sisel, T.: Reducing multiplicities in class diagrams. In: Whittle, J., Clark, T., Kühne, T. (eds.) Proceedings of the 14th International Conference on Model Driven Engineering Languages and Systems, MODELS 2011, Wellington, New Zealand, 16–21 October 2011, Lecture Notes in Computer Science, vol. 6981, pp. 379–393. Springer, Berlin (2011). doi:10.1007/978-3-642-24485-8
  23. 23.
    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
  24. 24.
    Génova, G., Llorens, J., Martínez, P.: Semantics of the minimum multiplicity in ternary associations in UML. In: Proceedings of the 4th International Conference on the Unified Modeling Language, Modeling Languages, Concepts, and Tools, pp. 329–341. Springer, London (2001)Google Scholar
  25. 25.
    Génova, G., Llorens, J., Martínez, P.: The meaning of multiplicity of n-ary associations in UML. Softw. Syst. Model. 1(2), 86–97 (2002) Google Scholar
  26. 26.
    Hartmann, S.: On interactions of cardinality constraints, key, and functional dependencies. In: FoIKS ’00: Proceedings of the First International Symposium on Foundations of Information and Knowledge Systems, pp. 136–155. Springer, London (2000)Google Scholar
  27. 27.
    Hartmann, S.: Coping with inconsistent constraint specifications. In: ER ’01: Proceedings of the 20th International Conference on Conceptual Modeling, pp. 241–255. Springer, London (2001)Google Scholar
  28. 28.
    Kaneiwa, K., Satoh, K.: Consistency checking algorithms for restricted UML class diagrams. In: Dix, J., Hegner, S. (eds.) Proceedings of FoIKS. Lecture Notes of Computer Science, vol. 3861, pp. 219–239. Springer, Berlin (2006)Google Scholar
  29. 29.
    Kim, S.K., Carrington, D.A.: Formalizing the UML class diagram using Object-Z. In: France, R.B. et al. (eds.) Proceedings of UML’99. LNCS, vol. 1723, pp. 83–98 (1999)Google Scholar
  30. 30.
    Krishnan, P.: Consistency checks for UML. In: Proceedings of APSEC’00, p. 162. IEEE Computer Society, Washington, DC (2000)Google Scholar
  31. 31.
    Lagarias, J.: The computational complexity of simultaneous diophantine approximation problems. SIAM J. Comput. 14(1), 196–209 (1985). doi:10.1137/0214016 CrossRefMATHMathSciNetGoogle Scholar
  32. 32.
    Lenzerini, M., Nobili, P.: On the satisfiability of dependency constraints in entity-relationship schemata. Inf. Syst. 15(4), 453–461 (1990). doi:10.1016/0306-4379(90)90048-T CrossRefGoogle Scholar
  33. 33.
    Niederbrucker, G.: A numeric semantics for UML class diagrams: methods and tools. Master’s thesis, Technische Universität Wien (2010)Google Scholar
  34. 34.
    Niederbrucker, G., Sisel, T.: Clews Website (2011). http://www.logic.at/clews
  35. 35.
    Object Management Group: Unified Modeling Language 2.4.1 Superstructure Specification (2011)Google Scholar
  36. 36.
    Object Management Group: Unified Modeling Language 2.3.1 Object Constraint Language Specification (2012)Google Scholar
  37. 37.
    Queralt, A., Teniente, E.: Reasoning on UML class diagrams with OCL constraints. In: Embley, D.W. et al. (eds.) Proceedings of ER 2006. LNCS, vol. 4215, pp. 497–512 (2006)Google Scholar
  38. 38.
    Richters, M., Gogolla, M.: Validating UML models and OCL constraints. In: Evans, A., Kent, S., Selic, B. (eds.) Proceedings of the Third International Conference on UML 2000—the Unified Modeling Language. Advancing the Standard, York, UK, October 2000. LNCS, vol. 1939, pp. 265–277. Springer, Berlin (2000)Google Scholar
  39. 39.
    Rosati, R.: Finite model reasoning in DL-Lite. In: Bechhofer, S. et al. (eds.) Proceedings of ESWC2008. LNCS, vol. 5021, pp. 215–229. Springer, Berlin (2008)Google Scholar
  40. 40.
    Satoh, K., Kaneiwa, K., Uno, T.: Contradiction finding and minimal recovery for UML class diagrams. In: ASE ’06: Proceedings of the 21st IEEE/ACM International Conference on Automated Software Engineering, pp. 277–280. IEEE Computer Society, Washington, DC (2006). doi:10.1109/ASE.2006.30
  41. 41.
    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)CrossRefGoogle Scholar
  42. 42.
    Szlenk, M.: Formal semantics and reasoning about UML class diagram. In: DEPCOS-RELCOMEX ’06: Proceedings of the International Conference on Dependability of Computer Systems, pp. 51–59. IEEE Computer Society, Washington, DC (2006). doi:10.1109/DEPCOS-RELCOMEX.2006.27
  43. 43.
    Szlenk, M.: UML static models in formal approach. In: CEE-SET. Lecture Notes in Computer Science, vol. 5082, pp. 129–142. Springer (2007). doi:10.1007/978-3-540-85279-7\_11
  44. 44.
    The Alliance for Telecommunications Industry Solutions: ATIS telecom glossary (2000). Approved February 28, 2001 by the American National Standards Institute (ANSI). http://www.atis.org/glossary

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Technische Universität WienViennaAustria

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