This paper introduces a temporal class diagram language useful to model temporal varying data. The atemporal portion of the language contains the core constructors available in both EER diagrams and UML class diagrams. The temporal part of the language is able to distinguish between temporal and atemporal constructs, and it has the ability to represent dynamic constraints between classes. The language is characterized by a model-theoretic (temporal) semantics. Reasoning services as logical implication and satisfiability are also defined. We show that reasoning on finite models is different from reasoning on unrestricted ones. Then, we prove that reasoning on temporal class diagrams is an undecidable problem on both unrestricted models and on finite ones.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
A. Artale and E. Franconi, Temporal ER modeling with description logics, in: Proc. of the International Conference on Conceptual Modeling (ER'99), Lecture Notes in Computer Science (Springer, 1999).
A. Artale and E. Franconi, A survey of temporal extensions of description logics, Annals of Mathematics and Artificial Intelligence 30(1–4) (2001).
A. Artale, Reasoning on temporal conceptual schemas with dynamic constraints, in: 11th International Symposium on Temporal Representation and Reasoning (TIME04) (IEEE Computer Society, 2004). Also in Proc. of the 2004 International Workshop on Description Logics (DL'04).
A. Artale, E. Franconi and F. Mandreoli, Description logics for modelling dynamic information, in: Logics for Emerging Applications of Databases, eds. J. Chomicki, R. van der Meyden and G. Saake, Lecture Notes in Computer Science (Springer, 2003).
A. Artale, E. Franconi, F. Wolter and M. Zakharyaschev, A temporal description logic for reasoning about conceptual schemas and queries, in: Proceedings of the 8th Joint European Conference on Logics in Artificial Intelligence (JELIA-02), volume 2424 of LNAI, eds. S. Flesca, S. Greco, N. Leone and G. Ianni (Springer, 2002) pp. 98–110.
F. Baader, D. Calvanese, D. McGuinness, D. Nardi and P.F. Patel-Schneider, eds., in: Description Logic Handbook: Theory, Implementation and Applications (Cambridge University Press, 2002).
D. Berardi, D. Calvanese and G. De Giacomo, Reasoning on UML class diagrams, Artificial Intelligence 168(1–2) (2005) 70–118.
D. Calvanese, G. De Giacomo and M. Lenzerini, On the decidability of query containment under constraints, in: Proc. of the 17th ACM SIGACT SIGMOD SIGART Sym. on Principles of Database Systems (PODS'98) (1998) pp. 149–158.
D. Calvanese, M. Lenzerini and D. Nardi, Unifying class-based representation formalisms, Journal of Artificial Intelligence Research 11 (1999) 199–240.
J. Chomicki and D. Toman, Temporal logic in information systems, in: Logics for Databases and Information Systems, chapter 1, eds. J. Chomicki and G. Saake (Kluwer, 1998).
R. Elmasri and S.B. Navathe, Fundamentals of Database Systems, 2nd edition (Benjamin/Cummings, 1994).
D. Gabbay, A. Kurucz, F. Wolter and M. Zakharyaschev, Many-Dimensional Modal Logics: Theory and Applications, Studies in Logic (Elsevier, 2003).
H. Gregersen and J.S. Jensen, Conceptual modeling of time-varying information, Technical Report TimeCenter TR-35 (Aalborg University, Denmark, 1998).
H. Gregersen and J.S. Jensen, Temporal entity-relationship models – A survey, IEEE Transactions on Knowledge and Data Engineering 11(3) (1999) 464–497.
R. Gupta and G. Hall, Modeling transition, in: Proc. of ICDE'91 (1991) pp. 540–549.
C.S. Jensen, J. Clifford, S.K. Gadia, P. Hayes and S. Jajodia et al., The consensus glossary of temporal database concepts, Temporal Databases – Research and Practice, eds. O. Etzion, S. Jajodia and S. Sripada (Springer, 1998) pp. 367–405.
C.S. Jensen and R.T. Snodgrass, Temporal data management, IEEE Transactions on Knowledge and Data Engineering 111(1) (1999) 36–44.
C.S. Jensen, M. Soo and R.T. Snodgrass, Unifying temporal data models via a conceptual model, Information Systems 9(7) (1994) 513–547.
S. Spaccapietra, C. Parent and E. Zimanyi, Modeling time from a conceptual perspective, in: Int. Conf. on Information and Knowledge Management (CIKM98) (1998).
C. Theodoulidis, P. Loucopoulos and B. Wangler, A conceptual modelling formalism for temporal database applications, Information Systems 16(3) (1991) 401–416.
F. Wolter and M. Zakharyaschev, Satisfiability problem in description logics with modal operators, in: Proc. of the 6 \(^{th}\) International Conference on Principles of Knowledge Representation and Reasoning (KR'98) (Trento, Italy, June 1998) pp. 512–523.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Artale, A. Reasoning on temporal class diagrams: Undecidability results. Ann Math Artif Intell 46, 265–288 (2006). https://doi.org/10.1007/s10472-006-9019-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10472-006-9019-0