Autonomous vehicles face big challenges guaranteeing provable safety during driving. One of the major problems is the uncertainty arising from the perception of the surrounding environment, especially due to occlusions. Recent approaches to tackle these uncertainties either minimize collision risk probabilistically or assume worst-case vehicles coming out of occluded areas. The former does not provide any safety guarantees, while the latter tends to produce overly conservative driving behavior. Human drivers, however, can reason about possible traffic participants (TPs) in occlusions with the knowledge about the street, more importantly, with the continuous observation on the changes of the field of view when moving forward. In this paper, we present an approach that imitates this human-like intelligence and can reason about all the potential TPs in occlusions. By moving forward and propagating the initial knowledge with new observations, the approach can refine the possible states of the TPs in occlusions instead of always adopting a worst-case assumption. By planning w.r.t. the set-based occupancy prediction from the refined state intervals, the vehicle can drive more efficiently under occlusions while guaranteeing safety under reasonable assumptions. The proposed method is evaluated with numerical experiments showing that all the possible hidden TPs can be covered by our refined state intervals, and with that achieving significantly more driving efficiency under occlusions while being safe.