More exactly, let $L$ be a formal language, $U$ the domain of discourse, and $I(U,L)$ the corresponding interpretation. If an interpretable string $s\in L$ contains a variable, a quantifier attached to that variable is a symbol expressing how many values in $U$ the variable can take. Depending on this quality, the valuation $[[s]]_I$ can be either true or false.

A variable with a quantifier attached to it is called a bound variable, otherwise, it is called a free variable.

Unlike different types of quantifiers in natural languages like “many”, “a lot”, “no”, “for some”, “a few”, logical calculi generally use two types of quantifiers:

existential quantifier \(\exists\): read “there exists”, symbolized by rotated letter “E”,

universal quantifier \(\forall\): read “for all” or “for every”.