Next, the probabilities Pðr i j F i ,pÞ are combined with the probabilities Pðfr 1 : : : n gjpÞ for a set of roles appearing in a sentence given a predicate, using the following formula: Pðr 1 : : : n jF 1 : : : n , pÞ , Pðfr 1 : : : n gjpÞ Y i Pðr i jF i , pÞ Pðr i jpÞ This approach, described in more detail in Gildea and Jurafsky (2002), allows interaction among the role assignments for individual constituents while making certain independence assumptions necessary for efficient probability estimation.
we assume that sets of roles appear independent of their linear order and that the features F of a constituent are independent of other constituents' features given the constituent's role.