Comparing the ambiguity reduction abilities of probabilistic context-free grammars

We present a measure for evaluating Probabilistic Context Free Grammars (PCFG) based on their ambiguity resolution capabilities.Probabilities in a PCFG can be seen as a filtering mechanism: For an ambiguous sentence, the trees bearing maximum probability aresingle out, while all others are discarded. The level of ambiguity is related to the size of the singled out set of trees. Under our measure, a grammar is better than other if the first one has reduced the level of ambiguity in a higher degree. The measure we present is computed over a finite sample set of sentence because, as we show, it can not be computed over the set of sentences accepted by the grammar.