Definition
Validity–Unsatisfiability Duality (Propositional Logic)
A formula
is valid if and only if its negation is unsatisfiable: In the language of models:
is valid when every interpretation is a model of , and is unsatisfiable when no interpretation is a model of .
Reason
One fact, two spellings
An interpretation
satisfies exactly when it falsifies : Validity says the left-hand side holds for every
; unsatisfiability of says the right-hand side holds for every . Since the two sides are equivalent for each single , the two universal claims coincide.