Description logics offer considerable expressive power for describing knowledge about static application domains while reasoning is still decidable. The dynamic description logic DDL is a family of dynamic extensions of description logics for representing and reasoning about knowledge of dynamic application domains. In order to provide effective reasoning mechanisms, systems of DDL investigated in the literatures assume that there is no general concept inclusion(GCI) contained in the knowledge base. In this paper, we build a system of dynamic description logic based on the tractable description logic DL-Lite${^{\rm pr}_{\rm R}}$, in such a way that all the knowledge described by DL-Lite${^{\rm pr}_{\rm R}}$ is supported by our system. A decision algorithm is provided for our system DDL-Lite${^{\rm pr}_{\rm R}}$.Termination and correctness of the algorithm are proved.