In other words, precision is computed by reversing the roles of the key partition K(d) and the system partition S(d) used to compute recall for document d. If we wanted precision and recall to also play a symmetric role in the linguistically aware versions of these scoring metrics, it would be natural to define w L s in the same way as w L k , where E is the set of edges appearing in the maximum spanning tree defined over the mentions in S j .
there is a reason why it is undesirable for us to define w L s in this manner.