A calculus for epistemic interactions

It plays a central role in intelligent agent systems to model agent's epistemic state and its change. To this end, some formal systems have been presented. Among them, epistemic logics focus on logic laws of different epistemic attributes (e.g., knowledge, belief, common knowledge, etc) and epistemic actions (e.g., public announcement, private announcement, asynchronous announcement, etc). All these systems do not involve the interactive behaviours between an agent and its environment. Through enriching the well-known $\pi$-calculus, this paper presents the e-calculus, which provides a concept framework to model epistemic interactions between agents with epistemic states. Unlike usual process calculus, all systems in the e-calculus are always arranged to run at an epistemic state. To formalize epistemic states abstractly, a group of postulates on them are presented. Moreover, based on these postulates, the behaviour theory of the e-calculus is developed in two different viewpoints.