We believe that global inference makes better use of the information provided by P; in fact, as we show in Sec. 4, it does perform better than local inference. A standard way to perform global inference is to formulate it as an Integer Linear Programming (ILP) problem (Roth and Yih, 2004 ) and enforce transitivity rules as constraints. Then the ILP objective is formulated aŝ where {r m 3 } is selected based on the general transitivity proposed in<cite> (Ning et al., 2017)</cite> .