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 also have introduced a new interpretation for extended vector annotations in EVALPSN, which is named before-after(bf)-EVALPSN. In this chapter, we review paraconsistent annotated logic programs EVALPSN/bf-EVALPSN from the view point of application to safety verification and process order control with simple examples. First, the background and overview of EVALPSN are introduced, and paraconsistent annotated logics and the basic annotated logic program are recapitulated as the formal background of EVALPSN with some simple examples. Then, 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 called transitive bf-inference rules are introduced, and this chapter is concluded with some remarks.