View source for General validity

The property of a [[Logical formula|logical formula]] of being true for any interpretation of the non-logical symbols that it contains, that is, the predicate and propositional variables. Logical formulas with this property are called generally valid, identically true or tautologies. Every generally-valid formula expresses a [[Logical law|logical law]]. Instead of the words  "A is generally valid"  one often writes  " A" . The most important forms of logical formulas are propositional and predicate formulas. In the classical sense of logical operations (cf. [[Logical operation|Logical operation]]), the general validity of a propositional formula is verified by the construction of a [[Truth table|truth table]]: A formula is generally valid if and only if it takes the value T ( "true" ) for any truth values of the propositional variables. General validity of a predicate formula means truth in any [[Model (in logic)|model (in logic)]]. The set of generally-valid predicate formulas is undecidable, that is, there is no algorithm allowing one to decide whether an arbitrary predicate formula is generally valid or not. The [[Gödel completeness theorem|Gödel completeness theorem]] implies that all generally-valid predicate formulas, and only those, are derivable in classical predicate calculus.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  S.C. Kleene,   "Mathematical logic" , Wiley  (1967)</TD></TR></table>



====Comments====
The term  "universally valid logical formulauniversally valid"  is often used instead of  "generally valid" .