# Well-formed formula

The term refers to a logical formula logically meaningful expression, such as the formalized representation of a statement in logic, in general the presentation " logical forms by means of certain sign systems ". Notwithstanding found in Hans Reichenbach also logical formula ' as shorthand for, logically true formula ', that is a necessary true formula whose truth does not depend on the interpretation of the non-logical constants (see also tautology ( logic) ). A logical formula that has no syntax errors and can be assigned by an assignment of the non-logical constants of a specific truth value is also called well-formed formula (german, well formed formula ').

Logical formulas can be used in the divide of propositional logic ( propositional formula ) and the predicate logic ( predicate logic formula ). By type of statement can be simple (also: atomic, elementary ) formulas, different from compound formulas. Non -atomic formulas are distinguished in that they can be broken down into sub expressions and that the truth value of the whole formula on the values of partial formulas is functionally dependent. In predicate logic can additionally distinguish open and closed formulas by Willard Van Orman Quine. The open formulas contain unbound, ie free variables.