Assertion: predicate's variable | /r/HasProperty | bound by quantifier
Facets:
value: to such sets of propositions
type: OTHER
value: more precisely
type: DEGREE
value: on the same letter
type: LOCATION
Source sentences:
text: More precisely, a variable is only bound by a quantifier on the same letter; hence "x" is bound in "(x)Mx" but not in "(y)Mx", even though it is inside the scope of the quantifier in both cases.
text: Variables inside the scope of a quantifier are bound by that quantifier; otherwise they are free.
text: Therefore, propositional functions lack a truth-value; we can't tell whether the unfilled form " (blank) is human" is true or false until the blank (or free variable) is bound by a quantifier or replaced by a constant, that is, until the propositional function converted to a genuine proposition.
text: If predicate variables are also allowed to be bound to predicate letters which are unary or have higher arity, and when such letters represent propositional functions, such that the domain of the arguments is mapped to a range of different propositions, and when such variables can be bound by quantifiers to such sets of propositions, then the result is a higher-order predicate calculus, or higher-order logic.
text: First, the free variables may be bound by quantifiers; this is called generalization.