valid having the property that a well-formed formula, argument, argument form, or rule of inference has when it is logically correct in a certain respect. A well-formed formula is valid if it is true under every admissible reinterpretation of its non-logical symbols. (If truth-value gaps or multiple truth-values are allowed, ‘true’ here might be replaced by ‘non-false’ or takes a ‘designated’ truth-value.) An argument is valid if it is impossible for the premises all to be true and, at the same time, the conclusion false. An argument form (schema) is valid if every argument of that form is valid. A rule of inference is valid if it cannot lead from all true premises to a false conclusion. See also FREE LOGIC, MANY-VALUED LOGI. G.F.S.