 Various contributions are specifically devoted to problems related to relevancy. Consider some of the conditional assertions in the Nixon Diamond: \(\mathbf{K}\) = {Quaker \(\nc\) Pacifist, Republican \(\nc\) ¬Pacifist}. It seems desirable to derive e.g. Quaker \(\wedge\) worker \(\nc\) Pacifist since in view of \(\mathbf{K}\), being a worker is irrelevant to the assertion Quaker \(\nc\) Pacifist. Intuitively speaking, Quaker \(\nc\) ¬worker should fail in which case Rational Monotony yields Quaker \(\wedge\) worker \(\nc\) Pacifist in view of Quaker \(\nc\) Pacifist. Hence, prima facie we may want to proceed as follows: let \(\nc^{R}\) be the result of intersecting all rational consequence relations \(\nc\) that extend \(\mathbf{K}\) (in the sense that the conditional assertions in \(\mathbf{K}\) hold for \(\nc\)). Unfortunately it is not the case that Quaker \(\wedge\) worker \(\nc^{R}\) Pacifist. The reason is simply that there are rational consequence relations for which Quaker \(\nc\) ¬worker and whence Rational Monotony does not yield the desired Quaker \(\wedge\) worker \(\nc\) Pacifist. Moreover, it has been shown that \(\nc^R\) is identical to the preferential closure \(\nc^P\). 