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The relational algebra uses set union, set difference, and Cartesian product from set theory, and adds additional constraints to these operators to create new ones.. For set union and set difference, the two relations involved must be union-compatible—that is, the two relations must have the same set of attributes.
One common convention is to associate intersection = {: ()} with logical conjunction (and) and associate union = {: ()} with logical disjunction (or), and then transfer the precedence of these logical operators (where has precedence over ) to these set operators, thereby giving precedence over .
The problem of deciding whether for a given Datalog program there is an equivalent nonrecursive program (corresponding to a positive relational algebra query, or, equivalently, a formula of positive existential first-order logic, or, as a special case, a conjunctive query) is known as the Datalog boundedness problem and is undecidable.
A relation algebra (L, ∧, ∨, −, 0, 1, •, I, ˘) is an algebraic structure equipped with the Boolean operations of conjunction x∧y, disjunction x∨y, and negation x −, the Boolean constants 0 and 1, the relational operations of composition x•y and converse x˘, and the relational constant I, such that these operations and constants satisfy certain equations constituting an ...
In relational algebra, a selection (sometimes called a restriction to avoid confusion with SQL's use of SELECT) is a unary operation written as or () where: a {\displaystyle a} and b {\displaystyle b} are attribute names,
The most common numerical relational operators used in programming languages are shown below. Standard SQL uses the same operators as BASIC, while many databases allow != in addition to <> from the standard. SQL follows strict boolean algebra, i.e. doesn't use short-circuit evaluation, which is common to most languages below. E.g.
In relational algebra, a rename is a unary operation written as / where: . R is a relation; a and b are attribute names; b is an attribute of R; The result is identical to R except that the b attribute in all tuples is renamed to a. [1]
In relational algebra, if and are relations, then the composite relation is defined so that if and only if there is a such that and . [ note 1 ] This definition is a generalisation of the definition of functional composition .