We have already proposed a paraconsistent annotated logic program called EVALPSN. In EVALPSN, an annotation called an extended vector annotation is attached to each literal. In order to deal with before-after relation between two time intervals, we introduce a new interpretation for extended vector annotations in EVALPSN, which is named Before-after(bf) EVALPSN.In this chapter, we introduce the bf-EVALPSN and its application to real-time process order control and its safety verification with simple examples. First, the background and overview of EVALPSN are introduced, and paraconsistent annotated logic as the formal background of EVALPSN and EVALPSN itself are recapitulated with simple examples. Then, after bf-EVALPSN is formally defined, how to implement and apply bf-EVALPSN to real-time intelligent process order control and its safety verification with simple practical examples. Last, unique and useful features of bf-EVALPSN are introduced, and conclusions and remarks are provided.