 According to Quine (1954), an inclusive quantificational logic should evaluate every universally quantified formula of the form \(\forall x A\) to be vacuously true in a model \(\langle D, I\rangle\) in which \(D\) is empty, and it should evaluate every existentially quantified formula of the form \(\exists x A\) to be false in such a model. \(\forall xPx \rightarrow \exists xPx\) and \(\exists x(Px \rightarrow Px)\) are therefore not valid on the expanded model theory. However, it is quite a delicate matter to provide a compositional amendment of the Tarskian definition of truth in a model \(\langle D, I \rangle\) under an assignment \(s\) that delivers Quine’s  verdicts.[7]