Definition:Bound Occurrence

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Let $\LL_1$ be the language of predicate logic.

Let $\mathbf A$ be a WFF of $\LL_1$.

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


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

Also see