In the metavariable sense, a predicate variable can be used to define an axiom schema.
2.
In predicate logic, a "'universal quantification "'is a type of value of a predicate variable.
3.
If letters are used for predicate constants as well as for predicate variables, then there has to be a way of distinguishing between them.
4.
A " table " in an SQL database schema corresponds to a predicate variable; the contents of a table to a relation; key constraints, other constraints, and SQL queries correspond to predicates.
5.
Predicate variables should be distinguished from predicate constants, which could be represented either with a different ( exclusive ) set of predicate letters, or by their own symbols which really do have their own specific meaning in their domain of discourse : e . g . =, \ \ in, \ \ le, \.
6.
If " predicate variables " are only allowed to be bound to predicate letters of zero arity ( which have no arguments ), where such letters actually represent propositions, then such variables are actually "'propositional variables "', and any predicate logic which allows second-order quantifiers to be used to bind such propositional variables is a second-order predicate calculus, or second-order logic.
7.
If predicate variables are also allowed to be bound to predicate letters which are unary or have higher arity, and when such letters represent "'propositional functions "', such that the domain of the arguments is mapped to a range of different propositions, and when such variables can be bound by quantifiers to such sets of propositions, then the result is a higher-order predicate calculus, or higher-order logic.
8.
If these letters are not enough, then numerical subscripts can be appended, e . g . " X " 1, " X " 2, " X " 3, . . . However, if the predicate variables are not perceived ( or defined ) as actually belonging to the vocabulary of the predicate calculus, then they are actually predicate "'metavariables "', whereas the rest of the predicate letters are just called " predicate letters ".
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