Model Checking for Turn-Based Probability Epistemic Game Structure

In this paper, a turn-based probability epistemic game structure (TPEGS) is proposed to model knowledge preconditions for actions of system and environment firstly, which is an extension of turn-based synchronous game structures with probabilistic transition. Secondly, we introduce probability operator \( P_{\sim \lambda } \) into alternating temporal epistemic logic (ATEL) and define turn-based probability alternating-time temporal epistemic logic (tPATEL) for model checking the properties of TPEGS quantitatively. The probability of agents knowing some precondition before they implement an action can be expressed in tPATEL. Thirdly, we propose a method to compute probability for model checking verification problems of tPATEL based on DTMC and CTMC, and then analyze the time complexity of the method. Then, we are able to convert a part of tPATEL verification problems into the PATL ones by defining the knowledge formula \( K_{a} \phi ,\, E_{As} \phi \) and \( C_{As} \phi \) as atomic propositions. Finally, we study a flight procedure in STAS using PRISM-games to demonstrate the applicability of the above model checking framework and expand the application field of model checking.