Abstract
Automatic debugging of UML class diagrams helps in the visual specification of software systems because users cannot detect errors in logical inconsistency easily. This paper focuses on tractable consistency checking of UML class diagrams. We accurately identify inconsistencies in these diagrams by translating them into first-order predicate logic generalized by counting quantifiers and classify their expressivities by eliminating some components. For class diagrams of different expressive powers, we introduce optimized algorithms that compute their respective consistencies in P, NP, PSPACE, or EXPTIME with respect to the size of a class diagram. In particular, for two cases in which class diagrams contain (i) disjointness constraints and overwriting/multiple inheritances and (ii) these components along with completeness constraints, the restriction of attribute value types decreases the complexities from EXPTIME to P and PSPACE. Additionally, we confirm the existence of a meaningful restriction of class diagrams that prevents any logical inconsistency.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Beckert, B., Keller, U., Schmitt, P.H.: Translating the object constraint language into first-order predicate logic. In: Proceedings of VERIFY, Workshop at Federated Logic Conferences, FLoC (2002)
Berardi, D., Cali, A., Calvanese, D., De Giacomo, G.: Reasoning on UML class diagrams. Artificial Intelligence 168(1-2), 70–118 (2005)
Donini, F.M.: Complexity of reasoning. In: Description Logic Handbook, pp. 96–136 (2003)
Donini, F.M., Massacci, F.: EXPTIME tableaux for ALC. Artificial Intelligence 124(1), 87–138 (2000)
Evans, A.S.: Reasoning with UML class diagrams. In: Second IEEE Workshop on Industrial Strength Formal Specification Techniques, WIFT 1998, USA (1998)
Fowler, M.: UML Distilled: A Brief Guide to the Standard Modeling Object Language, 3rd edn. Object Technology Series. Addison-Wesley, Reading (2003)
Franconi, E., Ng, G.: The i.com tool for intelligent conceptual modeling. In: KRDB, pp. 45–53 (2000)
Kaneiwa, K., Satoh, K.: Consistency checking algorithms for restricted UML class diagrams. NII Technical Report, NII-2005-013E, National Institute of Informatics (2005), http://research.nii.ac.jp/TechReports/05-013E.html
Kolaitis, P.G., Väänänen, J.A.: Generalized quantifiers and pebble games on finite structures. Annals of Pure and Applied Logic 74(1), 23–75 (1995)
Mannila, H., Räihä, K.-J.: On the complexity of inferring functional dependencies. Discrete Applied Mathematics 40(2), 237–243 (1992)
Rumbaugh, J., Jacobson, I., Booch, G.: The Unified Modeling Language Reference Manual, 1st edn. Addison-Wesley, Reading (1999)
Schewe, K.-D., Thalheim, B.: Fundamental concepts of object oriented databases. Acta Cybern. 11(1-2), 49–84 (1993)
Tsiolakis, A., Ehrig, H.: Consistency analysis between UML class and sequence diagrams using attributed graph gammars. In: Proceedings of joint APPLIGRAPH/ GETGRATS Workshop on Graph Transformation Systems, pp. 77–86 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kaneiwa, K., Satoh, K. (2006). Consistency Checking Algorithms for Restricted UML Class Diagrams. In: Dix, J., Hegner, S.J. (eds) Foundations of Information and Knowledge Systems. FoIKS 2006. Lecture Notes in Computer Science, vol 3861. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11663881_13
Download citation
DOI: https://doi.org/10.1007/11663881_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31782-1
Online ISBN: 978-3-540-31784-5
eBook Packages: Computer ScienceComputer Science (R0)