- bound variable
- A variable
*x*is bound in a formula if it is within the scope of a quantifier (in first-order logic, (∀*x*) or (∃*x*)). Intuitively this means that as the formula is evaluated and*x*in this occurrence is assigned to an object, the quantified expression in which it occurs is evaluated with respect to that object. If a variable is not bound it is free. In (∀*x*)(F*x*→ G*x*) all the variables are bound. In (∀*x*)(F*x*→ G*x*) & G*x*the final occurrence of the variable*x*is free, so the expression is an open sentence or predicate . To turn it into a closed sentence one must either replace the variable with a constant or closed term referring to a thing, or extend the scope of the initial quantifier, or introduce another quantifier: (*x*)(F*x*G*x*) & (∃*x*)(G*x*), for example.

*Philosophy dictionary.
Academic.
2011.*