Encyclopedia of Database Systems

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

Relational Calculus

  • Val TannenEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_972


Domain relational calculus; First-order query; Tuple relational calculus


The relational database model was proposed by Codd in [2] where he assumed that its “data sublanguage” would be based on the predicate calculus (FOL) and where he introduced various algebraic operations on relations. Only in [3] did he introduced the terms relational algebra and relational calculus.

Later, it became customary to talk about the domain relational calculus (detailed below), which is closely related to the syntax of first-order logic and has quantified variables ranging over individual constants, and about the tuple relational calculus which is in fact the one given by Codd in [3] and whose variables range over tuples of constants. The two calculi are equivalent, via easy back and forth translations. However, both calculi allow the formulation of domain dependentqueries which are inappropriate for database languages. While domain independence is undecidable, it is possible to...

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Recommended Reading

  1. 1.
    Abiteboul S, Hull R, Vianu V. Foundations of databases: the logical level. Reading: Addison Wesley; 1994.Google Scholar
  2. 2.
    Codd EF. A relational model of data for large shared data banks. Commun ACM. 1970;13(6):377–387.zbMATHCrossRefGoogle Scholar
  3. 3.
    Codd EF. Relational Completeness of Database Sublanguages. In: Rustin R, editor. Courant computer science symposium 6: data base systems. Englewood Cliffs: Prentice-Hall; 1972. p. 65–98.Google Scholar
  4. 4.
    Ullman JD. Principles of database and knowledge-base systems volume, I. Rockville: Computer Science Press; 1988.Google Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Department of Computer and Information ScienceUniversity of PennsylvaniaPhiladelphiaUSA

Section editors and affiliations

  • Val Tannen
    • 1
  1. 1.Dept. of Computer and Inf. ScienceUniv. of PennsylvaniaPhiladelphiaUSA