Encyclopedia of Database Systems

2018 Edition
| Editors: Ling Liu, M. Tamer Özsu

Temporal Algebras

  • Abdullah Uz TanselEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_387


Bitemporal algebras; Historical algebras; Transaction-time algebras; Valid-time algebras


Temporal algebra is a generic term for an algebra defined for a data model that organizes temporal data. A temporal data model may support valid-time (the time over which a data value is valid), transaction-time (time when a data value is recorded in the database), or both (bitemporal). So an algebra can be defined for each case, a valid-time relational algebra, a transaction-time relational algebra, or a bitemporal relational algebra, respectively. For the relational data model, temporal algebras include the temporal versions of relational algebra operations in addition to new operations for manipulating temporal data like time-slice, rollback, temporal coalesce, temporal restructuring operations, and others. For a temporal algebra, it is desirable to be closed (common algebras are closed), a consistent extension of the relational algebra, and to reduce to relational algebra...

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

Recommended Reading

  1. 1.
    Böhlen MH, Jensen CS, Snodgrass RT. Temporal statement modifiers. ACM Trans Database Syst. 2000;25(4):407–56.zbMATHCrossRefGoogle Scholar
  2. 2.
    Böhlen MH, Snodgrass RT, Soo MD. Coalescing in temporal databases. In: Proceedings of the 22nd International Conference on Very Large Data Bases; 1996. p. 180–91.Google Scholar
  3. 3.
    Clifford J, Croker A. The historical relational data model (HRDM) and algebra based on lifespans. In: Proceedings of the 3rd International Conference on Data Engineering; 1987. p. 528–37.Google Scholar
  4. 4.
    Clifford J, Croker A, Tuzhilin A. On completeness of historical data models. ACM Trans Database Syst. 1993;19(1):64–116.CrossRefGoogle Scholar
  5. 5.
    Clifford J, Tansel A.U. On an algebra for historical relational databases: two views. In: Proceedings of the ACM SIGMOD International Conference on Management of Data; 1985. p. 247–65.CrossRefGoogle Scholar
  6. 6.
    Gadia SK. A homogeneous relational model and query languages for temporal databases. ACM Trans Database Syst. 1988;13(4):418–48.MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Gadia SK, Nair SS. Algebraic identities and query optimization in a parametric model for relational temporal databases. IEEE Trans Knowl Data Eng. 1998;10(5):793–807.CrossRefGoogle Scholar
  8. 8.
    Jensen CS, Soo MD, Snodgrass RT. Unifying temporal data models via a conceptual model. Inf Syst. 1994;19(7):513–47.CrossRefGoogle Scholar
  9. 9.
    Lorentzos NA, Johnson RG. Extending relational algebra to manipulate temporal data. Inf Syst. 1988;13(3):289–96.zbMATHCrossRefGoogle Scholar
  10. 10.
    McKenzie E, Snodgrass RT. Evaluation of relational algebras incorporating the time dimension in databases. ACM Comput Surv. 1991;23(4):501–43.CrossRefGoogle Scholar
  11. 11.
    Soo MD, Jensen C, Snodgrass RT. 1An algebra for TSQL2. In: Snodgrass RT, editor. TSQL2 temporal query language. Norwell: Kluwer; 1995. p. 505–46.CrossRefGoogle Scholar
  12. 12.
    Tansel AU. Adding time dimension to relational model and extending relational algebra. Inf Syst. 1986;11(4):343–55.zbMATHCrossRefGoogle Scholar
  13. 13.
    Tansel AU. Temporal relational data model. IEEE Trans Knowl Database Eng. 1997;9(3):464–79.CrossRefGoogle Scholar
  14. 14.
    Tansel AU, Arkun ME, Ozsoyoglu G. Time-by-example query language for historical databases. IEEE Trans Softw Eng. 1989;15(4):464–78.zbMATHCrossRefGoogle Scholar
  15. 15.
    Tansel AU, Eren-Atay C. Nested bitemporal relational algebra. In: Proceedings of the 21st International Symposium on Computer and Information Sciences; 2006. p. 622–33.CrossRefGoogle Scholar
  16. 16.
    Tansel AU, Tin E. Expressive power of temporal relational query languages. IEEE Trans Knowl Data Eng. 1997;9(1):120–34.CrossRefGoogle Scholar
  17. 17.
    Tuzhilin A, Clifford J. A temporal relational algebra as basis for temporal relational completeness. In: Proceedings of the 16th International Conference on Very Large Data Bases; 1990. p. 13–23.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Baruch College, CUNYNew YorkUSA

Section editors and affiliations

  • Richard T. Snodgrass
    • 1
  • Christian S. Jensen
    • 2
  1. 1.University of ArizonaTucsonUSA
  2. 2.Aalborg UniversityAalborg ØstDenmark