  We present a formal framework for the development of a family of
discriminative learning algorithms for Probabilistic Context-Free Grammars
(PCFGs) based on a generalization of criterion-H. First of all, we propose the
H-criterion as the objective function and the Growth Transformations as the
optimization method, which allows us to develop the final expressions for the
estimation of the parameters of the PCFGs. And second, we generalize the
H-criterion to take into account the set of reference interpretations and the
set of competing interpretations, and we propose a new family of objective
functions that allow us to develop the expressions of the estimation
transformations for PCFGs.
