Intuitively, the tree enumerates all possible argument sequences that start with the predicate, have zero or more intervening arguments, and end with the word and label of interest, w:l. The probability of w:l given the predicate is the sum of the probabilities of all branches in this tree, i.e., of all possible sequences that end with w:l. In reality, we do not have the computational power to explore all possible sequences, so we must limit the tree somehow.
we only ask the PRNSFM for its top k predictions at each branch point, and we only explore sequences with a maximum length of T .