An extension of process calculus for asynchronous communications between agents with epistemic states

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.