Sentence examples for predicate variable from inspiring English sources

In the wffs of a lower predicate calculus, every occurrence of a predicate variable is free.

Here x is said to be the argument of ϕ; a predicate (or predicate variable) with only a single argument is said to be a monadic, or one-place, predicate (variable).

In general, a predicate variable followed by any number of individual variables is a wff of the predicate calculus.

The atomic wffs are then simply those consisting of a predicate variable followed by a single individual variable.

Formation rule 1 is then replaced by: 1′.An expression consisting of a predicate variable or predicate constant of degree n followed by n terms is a wff.

The formation rules are: An expression consisting of a predicate variable of degree n followed by n individual variables is a wff.

In particular, in the second-order predicate calculus, quantification is permitted over both individual and predicate variables; hence, wffs such as (∃x)ϕx can be formed.

Formally, set theory can be derived by the addition of various special axioms to a rather modest form of LPC that contains no predicate variables and only a single primitive dyadic predicate constant to represent membership.

If x, y, z, … are used as individual variables (replaceable by names of individuals) and the symbols ϕ (phi), ψ (psi), χ (chi), … as predicate variables (replaceable by predicates), the formula ϕx is used to express the form of the propositions in question.

In the most straightforward of these, to which the most attention will be devoted in this discussion and which subsequently will be referred to simply as LPC, the wffs can be specified as follows: Let the primitive symbols be (1) x, y, … (individual variables), (2) ϕ, ψ, …, each of some specified degree (predicate variables), and (3) the symbols ∼, ∨, ∀, (, and ).

Assignments are next made to the predicate variables in the following way: if ϕ is monadic, there is assigned to it some subset of D (possibly the whole of D); intuitively this subset can be viewed as the set of all the objects in D that have the property ϕ.