Open formula
An open formula is a formula that contains at least one free variable.[citation needed] Some educational resources use the term "open sentence",[1][unreliable source?] but this use conflicts with the definition of "sentence" as a formula that does not contain any free variables.
An open formula does not have a truth value assigned to it, in contrast with a closed formula which constitutes a proposition and thus can have a truth value like true or false. An open formula can be transformed into a closed formula by applying quantifiers or the specification of the domain of individuals for each free variable x, y, z....
For example, when reasoning about natural numbers, the formula "x+2 > y" is open, since it contains the free variables x and y. In contrast, the formula "∃y ∀x: x+2 > y" is closed, and has truth value true.
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