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.

Also see

 * Definition:Occurrence (Formal Systems)
 * Definition:Free Occurrence, the complementary notion
 * Definition:Alphabetic Substitution


 * Definition:Bound Variable: a variable which occurs as a bound occurrence