Continuing with the dog example, the proposal is to estimate p(run | dog , subj) using a relative-frequency estimate of p(run | animal , subj) or an estimate based on a similar, suitably chosen class.
assuming this choice of class, p( dog | run, subj) would be approximated as follows: The following derivation shows that if p(v | c i , r) = k for each child c i of c , and Note that the proof applies only to a tree, since the proof assumes that c is partitioned by c and the sets of concepts dominated by each of the daughters of c , which is not necessarily true for a directed acyclic graph (DAG).