Formally speaking, the argument classifiers attempt to assign labels to a set of arguments, S 1:M , indexed from 1 to M. Each argument S i can take any label from a set of argument labels, P, and the indexed set of arguments can take a set of labels, c 1:M ∈ P M .
if we assume that the argument classifier returns an estimated conditional probability distribution, Prob(S i = c i ), then, given a sentence, the inference procedure seeks a global assignment that maximizes the objective function denoted by Equation 2, which can be rewritten as follows, where the linguistic and structural constraints are represented by the filter F. this objective function reflects the expected number of correct argument predictions, subject to the constraints.