# Definition:Bound Occurrence

## Definition

Let $\mathcal L_1$ be the language of predicate logic.

Let $\mathbf A$ be a WFF of $\mathcal L_1$.

Let $Q x$ be an occurrence of a quantifier in $\mathbf A$.

Any occurrence of the variable $x$ in the scope of $Q$ is called a bound occurrence.

## Also known as

Some authors gloss over the difference between:

a bound variable: a variable which exists in a WFF only as bound occurrences

and:

a bound occurrence of a variable which may otherwise exist as a free occurrence.