Domain relational calculus; First-order query; Tuple relational calculus
The relational database model was proposed by Codd in  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  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  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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