Definition:Free Variable/Predicate Logic

Definition

In predicate logic, a free variable is a variable which exists in a WFF only as free occurrences.

Also known as

A free variable is often referred to as an unknown, particularly in mathematical contexts.

In the field of logic, a free variable can also be referred to as a real variable.

However, this can be confused with a variable whose domain is the set of real numbers, so its use on $\mathsf{Pr} \infty \mathsf{fWiki}$ is discouraged.

The name arises in apposition to the name apparent variable, which is another name for bound variable.

Also see

• Definition:Free Occurrence: a somewhat more precise concept, recognising the fact that a variable may appear multiple times in an expression, and not necessarily always of the same category.