Three-valued Abstraction in Model Ckecking Probabiblistic Real-time Temporal Logic of Knowledge

Model checking in probabilistic real-time temporal logic of knowledge PTACTLK confronts the same challenge as in traditional model checking, that is the state space explosion problem. Abstraction is one of the most effective methods to alleviate the state space explosion problem, under the traditional framework of two-valued abstraction, the abstract model obtained using abstraction techniques is only the upper approximation of the original model. In this paper, we introduce three-valued abstraction into model checking probabilistic real-time temporal logic of knowledge, define the abstract model of a probabilistic real time interpreted system and present the three-valued semantics of PTACTLK on the abstract model. We prove that the abstract model obtained using the abstraction techniques is not only the upper approximation of the original model but also its lower approximation. At last, a simple communication protocol is adopted to illustrate the effectiveness of our abstraction techniques.