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.
In the realm of formal logic, these sentences may contain quantifiers. Within the specific context of first-order logic, a distinction is drawn between logically certain statements, sentences that hold true in every model, and tautologies (or, tautologically certain statements), which are a subset of the first-order logically certain statements.