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.