# Relational Calculus

**DOI:**https://doi.org/10.1007/978-1-4614-8265-9_972

## Synonyms

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

## 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 dependent*queries which are inappropriate for database languages. While domain independence is undecidable, it is possible to...

## Recommended Reading

- 1.Abiteboul S, Hull R, Vianu V. Foundations of databases: the logical level. Reading: Addison Wesley; 1994.Google Scholar
- 2.Codd EF. A relational model of data for large shared data banks. Commun ACM. 1970;13(6):377–387.zbMATHCrossRefGoogle Scholar
- 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.Ullman JD. Principles of database and knowledge-base systems volume, I. Rockville: Computer Science Press; 1988.Google Scholar