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Complexity of Reasoning over Temporal Data Models

  • Alessandro Artale
  • Roman Kontchakov
  • Vladislav Ryzhikov
  • Michael Zakharyaschev
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6412)

Abstract

We investigate the computational complexity of reasoning over temporal extensions of conceptual data models. The temporal conceptual models we analyse include the standard UML/EER constructs, such as isa between entities and relationships, disjointness and covering, cardinality constraints and their refinements, multiplicity and key constraints; in the temporal dimension, we have timestamping, evolution, transition and lifespan cardinality constraints. We give a nearly comprehensive picture of the impact of these constructs on the complexity of reasoning, which can range from NLogSpace to undecidability.

Keywords

Description Logic Temporal Constraint Evolution Constraint Cardinality Constraint Temporal Extension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Artale, A.: Reasoning on temporal class diagrams: Undecidability results. Annals on Mathematics and Artificial Intelligence (AMAI) 46, 265–288 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    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)CrossRefGoogle Scholar
  3. 3.
    Artale, A., Calvanese, D., Kontchakov, R., Zakharyaschev, M.: The DL-Lite family and relations. J. of Artificial Intelligence Research 36, 1–69 (2009)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Artale, A., Franconi, E., Mandreoli, F.: Description logics for modelling dynamic information. In: Chomicki, J., van der Meyden, R., Saake, G. (eds.) Logics for Emerging Applications of Databases, pp. 239–275. Springer, Heidelberg (2003)Google Scholar
  5. 5.
    Artale, A., Franconi, E., Wolter, F., Zakharyaschev, M.: A temporal description logic for reasoning about conceptual schemas and queries. In: Flesca, S., Greco, S., Leone, N., Ianni, G. (eds.) JELIA 2002. LNCS (LNAI), vol. 2424, pp. 98–110. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  6. 6.
    Artale, A., Kontchakov, R., Ryzhikov, V., Zakharyaschev, M.: Past and future of DL-Lite. In: Proc. of the 24th AAAI Conf. on Artificial Intelligence, AAAI 2010 (2010)Google Scholar
  7. 7.
    Artale, A., Parent, C., Spaccapietra, S.: Evolving objects in temporal information systems. Annals of Mathematics and Artificial Intelligence 50(1-2), 5–38 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Artale, A., Toman, D.: Decidable reasoning over timestamped conceptual models. In: Proc. of the 21th Int. Workshop on Description Logics (DL 2008), Dresden, Germany (May 2008)Google Scholar
  9. 9.
    Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P.F. (eds.): Description Logic Handbook: Theory, Implementation and Applications. Cambridge University Press, Cambridge (2002)Google Scholar
  10. 10.
    Berardi, D., Calvanese, D., De Giacomo, G.: Reasoning on UML class diagrams. Artificial Intelligence 168(1-2), 70–118 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Calvanese, D., Lenzerini, M., Nardi, D.: Unifying class-based representation formalisms. J. of Artificial Intelligence Research 11, 199–240 (1999)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Combi, C., Degani, S., Jensen, C.S.: Capturing temporal constraints in temporal ER models. In: Li, Q., Spaccapietra, S., Yu, E., Olivé, A. (eds.) ER 2008. LNCS, vol. 5231, pp. 397–411. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  13. 13.
    Etzion, O., Gal, A., Segev, A.: Extended update functionality in temporal databases. In: Temporal Databases — Research and Practice. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  14. 14.
    Gregersen, H., Jensen, J.S.: Conceptual modeling of time-varying information. Technical Report TimeCenter TR-35, Aalborg University, Denmark (1998)Google Scholar
  15. 15.
    Gregersen, H., Jensen, J.S.: Temporal Entity-Relationship models — a survey. IEEE Transactions on Knowledge and Data Engineering 11(3), 464–497 (1999)CrossRefGoogle Scholar
  16. 16.
    Gupta, R., Hall, G.: An abstraction mechanism for modeling generation. In: Proc. of the 8th Int. Conf. on Data Engineering (ICDE 1992), pp. 650–658. IEEE Computer Society, Los Alamitos (1992)Google Scholar
  17. 17.
    Hall, G., Gupta, R.: Modeling transition. In: Proc. of the 7th Int. Conf. on Data Engineering (ICDE 1991), pp. 540–549. IEEE Computer Society, Los Alamitos (1991)Google Scholar
  18. 18.
    Jensen, C.S., Clifford, J., Gadia, S.K., Hayes, P., Jajodia, S., et al.: The Consensus Glossary of Temporal Database Concepts. In: Temporal Databases — Research and Practice, Springer, Heidelberg (1998)Google Scholar
  19. 19.
    Jensen, C.S., Snodgrass, R.T.: Temporal data management. IEEE Transactions on Knowledge and Data Engineering 111(1), 36–44 (1999)CrossRefGoogle Scholar
  20. 20.
    Jensen, C.S., Soo, M., Snodgrass, R.T.: Unifying temporal data models via a conceptual model. Information Systems 9(7), 513–547 (1994)CrossRefGoogle Scholar
  21. 21.
    Lutz, C., Wolter, F., Zakharyaschev, M.: Temporal description logics: A survey. In: Proc. of the 15th Int. Symposium on Temporal Representation and Reasoning (TIME 2008), pp. 3–14. IEEE Computer Society, Los Alamitos (2008)CrossRefGoogle Scholar
  22. 22.
    Sistla, A., Clarke, E.: The complexity of propositional linear temporal logics. In: Proc. of the 14th Annual ACM Symposium on Theory of Computing, pp. 159–168. ACM, New York (1982)Google Scholar
  23. 23.
    Spaccapietra, S., Parent, C., Zimanyi, E.: Conceptual Modeling for Traditional and Spatio-Temporal Applications—The MADS Approach. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  24. 24.
    Tauzovich, B.: Towards temporal extensions to the entity-relationship model. In: Proc. of the 10th Int. Conf. on Conceptual Modeling (ER 1991), pp. 163–179. ER Institute (1991)Google Scholar
  25. 25.
    Theodoulidis, C., Loucopoulos, P., Wangler, B.: A conceptual modelling formalism for temporal database applications. Information Systems 16(3), 401–416 (1991)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Alessandro Artale
    • 1
  • Roman Kontchakov
    • 2
  • Vladislav Ryzhikov
    • 1
  • Michael Zakharyaschev
    • 2
  1. 1.Faculty of Computer ScienceFree University of Bozen-BolzanoBolzanoItaly
  2. 2.Department of Computer ScienceBirkbeck CollegeLondonUK

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