If we assume that the classifiers return a score score(S i = c i ) that corresponds to the likelihood of argument S i being labeled c i then, given a sentence, the unaltered inference task is solved by maximizing the overall score of the arguments, In the presence of global constraints derived from linguistic information and structural considerations, our system seeks to output a legitimate labeling that maximizes this score.
it can be thought of as if the solution space is limited through the use of a filter function, F, which eliminates many argument labelings from consideration.