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 )(Fx → Gx ) all the variables are bound. In (∀x )(F x → Gx ) & Gx 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. . 2011.

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