Verifying Computation Tree Logic of Knowledge via the Similar Reachability Graphs of Knowledge-oriented Petri Nets

Computation Tree Logic of Knowledge (CTLK) can specify many requirements of privacy or security of multi-agent systems (MAS). In our previous paper, we defined Knowledge-oriented Petri Nets (KPN) to model MAS. A KPN is a special Petri net in which some places are used to represent knowledge. Consequently, KPN can formally represent not only the interaction/collaboration process of multiple agents but also their epistemic evolutions. These epistemic evolutions are closely related to privacy and security of MAS. Then we defined the similar reachability graphs of KPN and constructed the equivalence classes of knowledge for each agent. We considered an epistemic operator K and designed its model checking algorithm based on similar reachability graph and equivalence class. In this paper, we design the model checking algorithm for another epistemic operator C. Additionally, we develop a related tool. Examples of privacy protocols illustrate the usefulness of our model and method.