Relational calculus is a nonprocedural formal query language.
Next, the formal definition of a tuple relational calculus expression is stated.
The Relational calculus expression for Query 1, [N.sub.1], is:
The "classical" interpretation of quantifiers such as [exists]x.[Psi](x) occurring in relational calculus expressions is that [Psi](x) is satisfied by some element of the database.
These corollaries give, among other things, an elementary proof that parity can not be defined using relational calculus with polynomial inequality constraints.
As in the case of relational calculus and algebra, we often consider queries that do not extend the active domain.
The choice of relational operators is conventional; the language is essentially the relational calculus with the addition of transitive closure.
Logicality, then, defined for Tarski the broadest notion of what constitutes a relational calculus. One might expect the lack of expressiveness with respect to first-order logic not to be of practical significance, since, if extra relational variables are admitted, projection can be expressed, and, by tupling, the restriction to three variables is overcome.
finding, object models, pruning, relational calculus, relational specifications, symmetry
Section 3 describes a general approach to safety for both relational calculus and Datalog query languages with and without negation.
Section 4 defines safe relational calculus queries with integer gap-order constraint databases, safe relational calculus queries with integer set order constraint databases, and the combination of these two languages.
Section 6 shows that the computational complexity in testing relational calculus with gap-order or set order, or stratified Datalog with gap-order or set order programs is safe in PTIME.