Model Checking Epistemic and Probabilistic Properties of Multi-agent Systems

Model checking, a formal automatic verification method, has been widely used in multi-agent systems to verify specifications that contain qualitative properties (e.g safety and liveliness) and quantitative properties. Decision making processes based on inherent knowledge are necessary for agents to act appropriately, particularly in uncertain settings. In order to check epistemic (i.e knowledge) and measurable properties in multi-agent systems, we propose a new logic PCTLK, which uses probabilistic, epistemic, and temporal modal operators. We exploit Discrete-Time Markov Chains (DTMC), in which we are able to represent measurable properties with probability, to model uncertainty in multi-agent systems. We extend the formalism of interpreted systems by adding probabilistic features to suit DTMC models and to present the model checking algorithm for our logic. At the end of this paper, we simulate our algorithm using an example of online shopping.