 Determined fragment. Let us say that an \(\mathbf{IFL}\) sentence \(\phi\) is determined if it satisfies: \(M \vDash(\phi \vee{\sim}\phi)\), for all models \(M\). The determined fragment of \(\mathbf{IFL}\) is the set of determined \(\mathbf{IFL}\) sentences. In the determined fragment contradictory negation is syntactically expressible by the strong negation. By the strong inexpressibility of contradictory negation, the determined fragment of \(\mathbf{IFL}\) has the same expressive power as \(\mathbf{FO}\). Membership in the determined fragment is a sufficient but not necessary condition for an \(\mathbf{IFL}\) sentence to have its contradictory negation expressible in \(\mathbf{IFL}\). The sentence \((\forall y)(\exists x/\forall y) x = y\) is not  determined;[43]  yet its contradictory negation \((\forall x)(\exists y) x \ne y\) is expressible in \(\mathbf{IFL}\).