These sentences may contain quantifiers, unlike sentences of propositional logic. In the context of first-order logic, a distinction is maintained between logical validities, sentences that are true in every model, and tautologies (or, tautological validities), which are a proper subset of the first-order logical validities.
These sentences may contain quantifiers, unlike sentences of propositional logic. In the context of first-order logic, a distinction is made between logical certainties, sentences that are true in every model, and tautologies (or, tautological certainties), which are a proper subset of the first-order logically certain statements.