Efficient Multi-agent Epistemic Planning: Teaching Planners About Nested Belief

In the absence of prescribed coordination, it is often necessary for individual agents to synthesize their own plans, taking into account not only their own capabilities and beliefs about the world but also their beliefs about other agents, including what each of the agents will come to believe as the consequence of the actions of others. To illustrate, consider the scenario where Larry and Moe meet on a regular basis at the local diner to swap the latest gossip. Larry has come to know that Nancy (Larry's daughter) has just received a major promotion in her job, but unbeknownst to him, Moe has already learned this bit of information through the grapevine. Before they speak, both believe Nancy is getting a promotion, Larry believes Moe is unaware of this (and consequently wishes to share the news), and Moe assumes Larry must already be aware of the promotion but is unaware of Moe's own knowledge of the situation. Very quickly we can see how the nesting of (potentially incorrect) belief can be a complicated and interesting setting to model. In this paper, we examine the problem of synthesizing plans in such settings. In particular, given a finite set of agents, each with: (1) (possibly incomplete and incorrect) beliefs about the world and about the beliefs of other agents; and (2) differing capabilities including the ability to perform actions whose outcomes are unknown to other agents; we are interested in synthesizing a plan to achieve a goal condition. Planning is at the belief level and as such, while we consider the execution of actions that can change the state of the world (ontic actions) as well as an agent's state of knowledge or belief (epistemic or more accurately doxastic actions, including communication actions), all outcomes are with respect to belief.