Since Hanks and McDermott raised the problem of temporal projection (e.g. the Yale shooting problem) and showed that classical nonmonotonic logics failed to solve it, many solutions have been proposed. However, as indicated by some researchers, most of them are not completely satisfactory. In Zhang and Foo , we presented a theory of actions called the persistent set approach (PSA). In this paper, we extend our previous work to deal with temporal reasoning. Different from those minimality-based approaches, we propose a persistence-based formalization of actions within the situation calculus framework, and show that this gives natural and intuitive solutions to the problem of temporal projection in many cases. Explanations of some of the differences between persistence and minimality are given. We show that our approach also provides a unified framework for representing actions with disjunctive effects, while most of the current methods are inappropriate for dealing with these actions in the general case.