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Relational Calculus

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Encyclopedia of Database Systems

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Synonyms

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

Definition

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. Abiteboul S., Hull R., and Vianu V. Foundations of Databases: The Logical Level. Addison Wesley, Reading, MA, 1994.

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  2. Codd E.F. A relational model of data for large shared data banks. Commun. ACM, 13(6):377–387, 1970.

    MATH  Google Scholar 

  3. Codd E.F. Relational Completeness of Database Sublanguages. In Courant Computer Science Symposium 6: Data Base Systems, R. Rustin (ed.). Prentice-Hall, Englewood Cliffs, NJ, 1972, pp. 65–98.

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  4. Ullman J.D. Principles of Database and Knowledge-Base Systems Volume, I. Computer Science Press, Rockville, MD, 1988.

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Author information

Authors and Affiliations

  1. University of Pennsylvania, Philadelphia, PA, USA

    Val Tannen

Authors
  1. Val Tannen
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Editor information

Editors and Affiliations

  1. College of Computing, Georgia Institute of Technology, 266 Ferst Drive, 30332-0765, Atlanta, GA, USA

    LING LIU (Professor) (Professor)

  2. Database Research Group David R. Cheriton School of Computer Science, University of Waterloo, 200 University Avenue West, N2L 3G1, Waterloo, ON, Canada

    M. TAMER ÖZSU (Professor and Director, University Research Chair) (Professor and Director, University Research Chair)

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© 2009 Springer Science+Business Media, LLC

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Tannen, V. (2009). Relational Calculus. In: LIU, L., ÖZSU, M.T. (eds) Encyclopedia of Database Systems. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-39940-9_972

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