  It plays a central role in intelligent agent systems to model agent's
epistemic state and its change. Asynchrony plays a key role in distributed
systems, in which the messages transmitted may not be received instantly by the
agents. To characterize asynchronous communications, asynchronous announcement
logic (AAL) has been presented, which focuses on the logic laws of the change
of epistemic state after receiving information.
  However AAL does not involve the interactive behaviours between an agent and
its environment. Through enriching the well-known pi-calculus by adding the
operators for passing basic facts and applying the well-known action model
logic to describe agents' epistemic states, this paper presents the e-calculus
to model epistemic interactions between agents with epistemic states. The
e-calculus can be adopted to characterize synchronous and asynchronous
communications between agents. To capture the asynchrony, a buffer pools is
constructed to store the basic facts announced and each agent reads these facts
from this buffer pool in some order. Based on the transmission of link names,
the e-calculus is able to realize reading from this buffer pool in different
orders. This paper gives two examples: one is to read in the order in which the
announced basic facts are sent (First-in-first-out, FIFO), and the other is in
an arbitrary order.
