 An obvious way to obtain a global operation of partial meet contraction would be to use the same selection function for all sets to be contracted. However, with the standard way to obtain a partial meet contraction from a selection function, this is not possible, due to the way selection functions treat the empty set. The way selection functions have traditionally been defined, if \(A\bot p = \varnothing\), then \(\gamma(A\bot p ) = \{A\}\). As a consequence of this, if \(\gamma\) is a selection function for \(A\), and \(A \ne B\), then \(\gamma\) is not a selection function for \(B\). For let \(A\bot p = B\bot p = \varnothing\). For \(\gamma\) to be a function it must be the case that \(\gamma(A\bot p) = \gamma(B\bot p)\). For \(\gamma\) to be a selection function for \(A\) it must be case that \(\gamma(A\bot p) = \{A\}\), and in order for it to be a selection function for \(B\) it must be the case that \(\gamma(B\bot p) = \{B\}\). Since \(A \ne B\), this is impossible.