Definition
Tautology (Propositional Logic)
A propositional formula is a tautology (or valid) if it is true under every interpretation.
For an interpretation
, a formula is a tautology if Validity is often written
. It is the semantic counterpart of the verum : by validity as equivalence to verum, is a tautology exactly when . Dually, a tautology is never a contradiction, and its negation is unsatisfiable by the validity–unsatisfiability duality.