Following Roth and Yih (2004) and Li et al.
(2013) in information extraction, we define the following log costs: ILP (Integer Logical Programming), a global inference is employed to achieve global optimization with the following objective function to maximize over a document as follows: while binary constraint (5) ensures that x<i,j,r> is binary value and equality constraint (6) ensures that exactly only one temporal relation can be assigned to each event mention pair.