Conventional upper bound constraint verification in grid workflow systems is based on the key assumption that an upper bound constraint only has two states: consistency and inconsistency. However, due to complexity of grid workflows and dynamic availability of participating grid services, this assumption is too restrictive as there may be some intermediate states. Therefore, in this paper, we introduce four states for an upper bound constraint. Namely, we treat conventional consistency as strong consistency and divide conventional inconsistency into weak consistency, weak inconsistency and strong inconsistency. Correspondingly, we develop their verification methods. For weak consistency, we present some algorithms on how to adjust it to strong consistency without triggering exception handling as in conventional work. For weak inconsistency, we analyse why it can rely on less costly exception handling than conventional work. The final evaluation demonstrates that our four-state approach can achieve better cost-effectiveness than the conventional two-state approach.