Note that Algorithm 1 is only for the learning step of TempRel extraction; as for the inference step of this task, we consistently adopt the standard method by solving Eq. (1), as was done by (Bramsen et al., 2006; Chambers and Jurafsky, 2008; Denis and Muller, 2011; Do et al., 2012;<cite> Ning et al., 2017)</cite> .