Validity (logic)
In a formal logic or calculus, a formula is said to be universally valid or valid if it is satisfied by any interpretation. Thus general validity is a special case of the satisfiability of a formula. Whereas mere satisfiability is already given if only one satisfying interpretation - a so-called model - can be found, in the case of a universally valid formula all interpretations are models.
The concept of interpretation, which is central to this explanation, can intuitively be understood as a generalization of the assignment of variables in propositional logic: Only through the assignment of the propositional variables of a propositional logic formula can a truth value be ascribed to the formula as a whole. In more complex logics, assignments must also be made to the formal components of a formula, which determine the truth value of the formula as a whole. In predicate-logic, for example, there is a definition of a universe and an assignment of predicate-symbols to predicates (on this universe) and of function-symbols to functions (on this universe). Only by this reference to a set of objects in a world under consideration it can be determined whether a formula can be fulfilled and whether it is possibly always fulfilled, i.e. whether it is generally valid.
The following table lists some closely related terms and synonyms. The columns 
and ¬ 
are in an equivalence relation, e.g. is general if and only if ¬ unsatisfiable.
See also
- Universals Problem
- Tautology
- Objectivity
- This
- Antithesis
- Synthesis
