Using answer set programming to model multi-agent scenarios involving agents' knowledge about other's knowledge

One of the most challenging aspects of reasoning, planning, and acting in a multi-agent domain is reasoning about what the agents know about the knowledge of their fellows, and to take it into account when planning and acting. In the past this has been done using modal and dynamic epistemic logics. In this paper we explore the use of answer set programming (ASP), and reasoning about action techniques for this purpose. These approaches present a number of theoretical and practical advantages. From the theoretical perspective, ASP's property of non-monotonicity (and several other features) allow us to express causality in an elegant fashion. From the practical perspective, recent implementations of ASP solvers have become very efficient, outperforming several other systems in recent SAT competitions. Finally, the use of ASP and reasoning about action techniques allows for the adaptation of a large body of research developed for single-agent to multi-agent domains. We begin our discussion by showing how ASP can be used to find Kripke models of a modal theory. We then illustrate how both the muddy children, and the sum-and-product problems can be represented and solved using these concepts. We describe and implement a new kind of action, which we call "ask-and-truthfully-answer," and show how this action brings forth a new dimension to the muddy children problem.