Reasoning about knowledge is one of the main concern in artificial intelligence and multi-agent Systems (MAS).
Researchers in a wide variety of disciplines have found that issues involving agents reasoning about other agents’ knowledge are of a great importance. Knowledge is considered as an important property to model intelligent systems. Formal theories and logics have been proposed to reason about knowledge of agents. Among of them, a logic of knowledge or the so called epistemic logic. The importance of epistemic logic comes from it suit- ability to be applied in a wide range of applications. In MAS, the epistemic logic is used to express statements on what the agent knows and what agent knows about the other agents. For example, «if agent1 sends a message S to agent2, then eventually, agent2 will know S», and agent1 knows that agent2 knows S. Several extensions of epistemic logic have been proposed in order to deal with specific type of applications. For example, several attempts have been proposed temporal epistemic logic to reason about the temporal evolution of knowledge by fusing pistemic logic framework into a kind of temporal logics. Although temporal epistemic logic is sufficient in a lot of applications, certain applications like robotics require a model of time and a model of how the continuous actions of agents evolving during the time. Also, temporal epistemic logic cannot specify time constraints to its knowledge.
On the other hand, hybrid automata have been proposed as a formal model of hybrid systems. They have also been approached to model group of agents situated in continuous dynamic environment. To specify and reason about the requirements of this model, we de ned a logic called RCTL in a previous work. However, a group of agents have to communicate and share their knowledge not only in timed systems but also in continuous dynamical systems. Thus, the main contribution of this paper is to define a new logic called epistemic region computational tree logic ERCTL that extends the logic RCTL, proposed by the author and others, by adding epistemic modalities. This extension allows us to specify epistemic requirements of agents situated in hybrid systems environment. To do so, the paper also extends the classical interpreted system used to mod- el MAS in epistemic logic by adding the operational semantics of hybrid automata in order to introduce the so-called hybrid interpreted system.