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.
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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)
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)
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)
Harel, D., Rumpe, B.: Modeling languages: Syntax, semantics and all that stuff. Technical Report MCS00-16, The Weizmann Institute of Science, Rehovot, Israel (2000)
Berardi, D., Calvanese, D., De Giacomo, G.: Reasoning on UML class diagrams. Artificial Intelligence 168(1-2), 70–118 (2005)
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)
Artale, A., Calvanese, D., Kontchakov, R., Zakharyaschev, M.: The DL-Lite family and relations. J. of Artificial Intelligence Research 36, 1–69 (2009)
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)
Kaneiwa, K., Satoh, K.: On the complexities of consistency checking for restricted UML class diagrams. Theoretical Computer Science 411(2), 301–323 (2010)
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)
Bergamaschi, S., Sartori, C.: On taxonomic reasoning in conceptual design. ACM Trans. on Database Systems 17(3), 385–422 (1992)
Borgida, A.: Description logics in data management. IEEE Trans. on Knowledge and Data Engineering 7(5), 671–682 (1995)
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)
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)
Calvanese, D., Lenzerini, M., Nardi, D.: Unifying class-based representation formalisms. J. of Artificial Intelligence Research 11, 199–240 (1999)
Borgida, A., Brachman, R.J.: Conceptual modeling with description logics. In: [10], ch. 10, pp. 349–372
Möller, R., Haarslev, V.: Description logic systems. In: [10], ch. 8, pp. 282–305
Buchheit, M., Donini, F.M., Schaerf, A.: Decidable reasoning in terminological knowledge representation systems. J. of Artificial Intelligence Research 1, 109–138 (1993)
Lenzerini, M., Nobili, P.: On the satisfiability of dependency constraints in entity-relationship schemata. Information Systems 15(4), 453–461 (1990)
Jarrar, M., Heymans, S.: Towards pattern-based reasoning for friendly ontology debugging. Int. J. on Artificial Intelligence Tools 17(4), 607–634 (2008)
Papadimitriou, C.H.: Computational Complexity. Addison Wesley Publ. Co., Reading (1994)
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Artale, A., Calvanese, D., Ibáñez-García, A. (2010). Full Satisfiability of UML Class Diagrams. In: Parsons, J., Saeki, M., Shoval, P., Woo, C., Wand, Y. (eds) Conceptual Modeling – ER 2010. ER 2010. Lecture Notes in Computer Science, vol 6412. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16373-9_23
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DOI: https://doi.org/10.1007/978-3-642-16373-9_23
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