Predicate detection addresses the challenge of monitoring the state of a distributed system. This research is the first step to explore predicate detection with partial synchrony assumptions. We study the observability of computation and focus on predicate detection semantics in three partially synchronous models. A framework of the behavior of predicate detection is established in terms of partial synchrony, modalities permitted and the best detection semantics. This work forms a conceptualization of the problem space and leads to disciplined approaches to predicate detection in realistic systems by identifying the strongest possible semantics for each modality and partial synchrony assumption.