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. The term open sentence comes from considering the sentence (propositional function) as having a variable x with an unspecified domain of values, thus the variable x associated to the predicate letter is free.
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.
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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