, A q are all of the occurrences of nonterminals in α, as they appear from left to right.
we can write d in the form ⇒ u j ) = 1 for each j with 0 ≤ j ≤ q, and further using the definition of p R and the inductive hypothesis, we can write As an easy corollary of Lemma 1, we have that R(G) is a consistent PCFG, as we can write 5 Consistency In this section we prove the main results of this paper, namely that all of the estimation methods discussed in Section 3 always provide consistent PCFGs.