Nothing Special   »   [go: up one dir, main page]

Skip to main content
Log in

Reasoning on temporal class diagrams: Undecidability results

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. 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).

  2. A. Artale and E. Franconi, A survey of temporal extensions of description logics, Annals of Mathematics and Artificial Intelligence 30(1–4) (2001).

  3. 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).

  4. 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).

  5. 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.

  6. 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).

  7. D. Berardi, D. Calvanese and G. De Giacomo, Reasoning on UML class diagrams, Artificial Intelligence 168(1–2) (2005) 70–118.

    Article  MathSciNet  MATH  Google Scholar 

  8. 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.

  9. D. Calvanese, M. Lenzerini and D. Nardi, Unifying class-based representation formalisms, Journal of Artificial Intelligence Research 11 (1999) 199–240.

    MATH  MathSciNet  Google Scholar 

  10. 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).

  11. R. Elmasri and S.B. Navathe, Fundamentals of Database Systems, 2nd edition (Benjamin/Cummings, 1994).

  12. D. Gabbay, A. Kurucz, F. Wolter and M. Zakharyaschev, Many-Dimensional Modal Logics: Theory and Applications, Studies in Logic (Elsevier, 2003).

  13. H. Gregersen and J.S. Jensen, Conceptual modeling of time-varying information, Technical Report TimeCenter TR-35 (Aalborg University, Denmark, 1998).

  14. H. Gregersen and J.S. Jensen, Temporal entity-relationship models – A survey, IEEE Transactions on Knowledge and Data Engineering 11(3) (1999) 464–497.

    Article  Google Scholar 

  15. R. Gupta and G. Hall, Modeling transition, in: Proc. of ICDE'91 (1991) pp. 540–549.

  16. 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.

  17. C.S. Jensen and R.T. Snodgrass, Temporal data management, IEEE Transactions on Knowledge and Data Engineering 111(1) (1999) 36–44.

    Article  Google Scholar 

  18. C.S. Jensen, M. Soo and R.T. Snodgrass, Unifying temporal data models via a conceptual model, Information Systems 9(7) (1994) 513–547.

    Article  Google Scholar 

  19. S. Spaccapietra, C. Parent and E. Zimanyi, Modeling time from a conceptual perspective, in: Int. Conf. on Information and Knowledge Management (CIKM98) (1998).

  20. C. Theodoulidis, P. Loucopoulos and B. Wangler, A conceptual modelling formalism for temporal database applications, Information Systems 16(3) (1991) 401–416.

    Article  Google Scholar 

  21. 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.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alessandro Artale.

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10472-006-9019-0

Keywords

AMS subject classification

Navigation