Since our constraints are intra-sentential, we formulate one ILP program for each sentence s in each training summary.
each ILP program contains 11×N s variables, where N s is the number of test instances formed from the concept pairs in s. there is one binary indicator variable x i,j,r for each relation class r of each test instance inst formed from concept i and concept j, which will be set to 1 by the ILP solver if and only if it thinks inst should belong to class r. Our objective is to maximize the linear combination of these variables and their corresponding probabilities given by the ensemble (see (3) below) subject to two types of constraints, the integrity constraints and the consistency constraints.