﻿ Validity

# Validity

In a formal logic or calculus is called a formula as generally valid if it is satisfied by any interpretation. The generality is thus a special case of satisfiability of a formula. While the mere satisfiability is already given when only a single -fulfilling interpretation - a so-called model - is, then, if a universal formula all interpretations models.

The central concept of interpretation for this explanation can be intuitively understood as a generalization of the variable assignment in propositional logic: Only by the assignment of the propositional variables of a propositional formula can be of the formula overall truth value attribute. In more complex logic assignments must also be made to the formal components of a formula, which determine the truth value of the whole formula. In predicate logic, for example, the user defines a universe and a mapping from predicate symbols to predicates ( in this universe) and function symbols to functions ( in this universe ). Can be determined only through this relation to a set of objects in an observed world, whether a formula is satisfiable and whether they might always fulfilled, so is generally valid.

The following table lists several closely related terms and synonyms. The columns and stand in a relation of equivalence, such as if and only generally valid if is unsatisfiable.

• Logic
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