In particular the constituent labels are highly ambiguous, firstly we don't know a priori how many there are, and secondly labels that appear high in a tree (e.g., an S category for a clause) rely on the correct inference of all the latent labels below them.
the probability of a derivation, e, is the product of the probabilities of its component rules, P (e) = c→e∈e P (e|c) .