w l is a parser with a scoring function s and a dependency d = (i, r, j), such that i is the position of the governor, j the position of the dependent, and r the dependency label, with 1 ≤ i, j ≤ l. We can define a new scoring function s + d in the following way: When running the parser on sentence S, with the scoring function s + d , one can be sure that dependency d will be part of the solution produced by the parser because the score of all its competing dependencies (i.e., dependencies of the form (i , r , j ) with different governors (i = i) or labels (r = r) and the same dependent (j = j)) are set to −∞.
the overall score of trees that have such competing dependencies cannot be higher than the trees that have our desired dependency.