Logical Data Expiration for Fixpoint Extensions of Temporal Logics

  • David Toman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2750)


We study the differences between the future and the past fragments of fixpoint extensions of first-order temporal logics in their relationship to expiration of database histories. We show that while the past fragment admits a bounded expiration operator, the future one requires retaining data of size bounded from below by a function linear in the length of the history. We also discuss fragments of future fixpoint temporal logic for which bounded expiration operators can exist.


Temporal Logic Query Language Integrity Constraint Data Expiration Predicate Symbol 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley, Reading (1995)zbMATHGoogle Scholar
  2. 2.
    Chomicki, J.: Efficient Checking of Temporal Integrity Constraints Using Bounded History Encoding. ACM Transactions on Database Systems 20(2), 149–186 (1995)CrossRefGoogle Scholar
  3. 3.
    Chomick, J., Niwinski, D.: On the Feasibility of Checking Temporal Integrity Constraints. Journal of Computer and System Sciences 51(3), 523–535 (1995)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Chomicki, J., Toman, D.: Implementing Temporal Integrity Constraints Using an Active DBMS. IEEE Transactions on Data and Knowledge Engineering 7(4), 566–582 (1995)CrossRefGoogle Scholar
  5. 5.
    Chomicki, J., Toman, D.: Temporal Logic in Information Systems. In: Chomicki, J., Saake, G. (eds.) Logics for Databases and Information Systems, pp. 31–70. Kluwer, Dordrecht (1998)Google Scholar
  6. 6.
    Chomicki, J., Toman, D., Böhlen, M.H.: Querying ATSQL databases with temporal logic. ACM Transactions on Database Systems (TODS) 26(2), 145–178 (2001)zbMATHCrossRefGoogle Scholar
  7. 7.
    Gabbay, D.M., Hodkinson, I.M., Reynolds, M.: Temporal Logic: Mathematical Foundations and Computational Aspects. Oxford University Press, Oxford (1994)zbMATHGoogle Scholar
  8. 8.
    Hodkinson, I.M., Wolter, F., Zakharyaschev, M.: Decidable fragment of first-order temporal logics. Annals of Pure and Applied Logic 106(1-3), 85–134 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Hülsmann, K., Saake, G.: Theoretical Foundations of Handling Large Substitution Sets in Temporal Integrity Monitoring. Acta Informatica 28(4) (1991)Google Scholar
  10. 10.
    Jensen, C.S.: Vacuuming. In: Snodgrass, R.T. (ed.) The TSQL2 Temporal Query Language, pp. 447–460. Kluwer Academic Publishers, Dordrecht (1995)Google Scholar
  11. 11.
    Lipeck, U.W.: Transformation of Dynamic Integrity Constraints into Transaction Specifications. Theoretical Computer Science 76(1) (1990)Google Scholar
  12. 12.
    Lipeck, U.W., Feng, D.: Construction of Deterministic Transition Graphs from Dynamic Integrity Constraints. In: van Leeuwen, J. (ed.) WG 1988. LNCS, vol. 344, pp. 166–179. Springer, Heidelberg (1989)Google Scholar
  13. 13.
    Lipeck, U.W., Gertz, M., Saake, G.: Transitional Monitoring of Dynamic Integrity Constraints. IEEE Data Engineering Bulletin (June 1994)Google Scholar
  14. 14.
    Lipeck, U.W., Saake, G.: Monitoring Dynamic Integrity Constraints Based on Temporal Logic. Information Systems 12(3), 255–269 (1987)zbMATHCrossRefGoogle Scholar
  15. 15.
    Lipeck, U.W., Zhou, H.: Monitoring Dynamic Integrity Constraints on Finite State Sequences and Existence Intervals. In: Workshop on Foundations of Models and Languages for Data and Objects. FMLDO 1991, pp. 115–130 (1991)Google Scholar
  16. 16.
    Skyt, J., Jensen, C.S., Mark, L.: A foundation for Vacuuming Temporal Databases. Data and Knowledge Engineering 44(1), 1–29 (2003)zbMATHCrossRefGoogle Scholar
  17. 17.
    Snodgrass, R.T. (ed.): The TSQL2 Temporal Query Language. Kluwer, Dordrecht (1995)zbMATHGoogle Scholar
  18. 18.
    Toman, D.: Point-based Temporal Extensions of SQL. In: International Conference on Deductive and Object-Oriented Databases, pp. 103–121 (1997)Google Scholar
  19. 19.
    Toman, D.: Point-Based Temporal Extensions of SQL and Their Efficient Implementation. In: Etzion, O., Jajodia, S., Sripada, S. (eds.) Temporal Databases: Research and Practice, Springer LNCS State-of-the-Art Survey, pp. 211–237,(1998)Google Scholar
  20. 20.
    Toman, D.: Expiration of Historical Databases. In: International Symposium on Temporal Representation and Reasoning, pp. 128–135. IEEE Press, Los Alamitos (2001)Google Scholar
  21. 21.
    Toman, D.: Logical Data Expiration. In: Chomicki, J., Saake, G., van der Meyden, R. (eds.) Logics for Emerging Applications of Databases, vol. ch. 7. Springer, Heidelberg (2003)Google Scholar
  22. 22.
    Vardi, M.Y.: A Temporal Fixpoint Calculus. In: ACM Symposium on Principles of Programming Languages, pp. 250–259 (1988)Google Scholar
  23. 23.
    Vardi, M.Y., Wolper, P.: An Automata-Theoretic Approach to Automatic Program Verification. In: IEEE Symposium on Logic in Computer Science (1986)Google Scholar
  24. 24.
    Wolper, P.: Temporal Logic Can Be More Expressive. Information and Control 56(1/2), 72–99 (1983)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • David Toman
    • 1
  1. 1.School of Computer ScienceUniversity of WaterlooWaterlooCanada

Personalised recommendations