A Framework to Reason about the Knowledge of Agents in Continuous Dynamic Systems

Applying formal methods to a group of agents provides a precise and unambiguous definition of their behaviors, as well as verify properties of agents against implementations. Hybrid automaton is one of the formal approaches that are used by several works to model a group of agents. Several logics have been proposed, as extension of temporal logics to specify and hence verify those quantitative and qualitative properties of systems modeled by hybrid automaton. However, when it comes to agents, one needs to reason about the knowledge of other agents participating in the model. For this purpose, epistemic logic can be used to specify and reason about the knowledge of agents. But this logic assumes that the model of time is discrete. This paper proposes a novel framework that formally specifies and verifies the epistemic behaviors of agents within continuous dynamics. To do so, the paper first extends the hybrid automaton with knowledge. Second, the paper proposes a new logic that extends epistemic logic with quantitative real time requirement. Finally, the paper shows how to specify several properties that can be verified within our framework. Keywords—Epistemic logic; Reasoning; Hybrid Automata; Agents