# Logical formula

The term logical formula denotes a logically meaningful expression, e.g. B. the formalized representation of a statement in logic, generally the representation of "logical forms by means of certain systems of signs". In contrast, Hans Reichenbach also uses 'logical formula' as a short form for 'logically true formula', i.e. a necessarily true formula, the truth of which does not depend on the interpretation of the non-logical constants ( see also tautology (logic) ). Has a logical formula that no syntax errors and a specific truth value can be assigned by an assignment of the non-logical constants, is also well-formed formula ( engl. , Well formed formula ').

Logical formulas can be divided into those of propositional logic ( propositional logic formula ) and those of predicate logic ( predicate logic formula ). According to the type of statement, simple (also: atomic, elementary) formulas are distinguished from compound formulas. Non-atomic formulas are characterized by the fact that they can be broken down into sub-expressions and that the truth value of the overall formula is functionally dependent on the values ​​of the sub-formulas. In predicate logic, according to Willard Van Orman Quine, one can also distinguish between open and closed formulas. The open formulas contain unbound, i.e. free variables .