Communication and Inference through Situations

In this paper, we show how to use common knowledge computationally in solving problems involving cooperation of multiple agents, when common knowledge is available. We will explain why a procedural approach to common knowledge is better suited to solving multiple-agent problems than a static one. We show, even if one can never prove that common knowledge has been attained ([Halpern and Moses, 1990]), that assuming it has been attained is often safe and efficacious. The ability to detect fairly reliably when certain conditions are not met suffices as a guideline for when to assume something is common knowledge. In principle, the problem of when one has individual knowledge is about as difficult. We use the situation oriented programming language PROSIT. By combining reasoning about situations and in situations, PROSIT makes possible an especially intuitive and simple solution of hypothetical reasoning problems involving common knowledge ([Nakashima and Tutiya, 1991]). 1 Introduction Treatment of common knowledge is important in connection with multi-agent systems. When several or many agents cooperate to solve a problem that cannot be solved by any single one, it is essential for them to have models of other agents and to communicate with one another. In treating such systems, we need abstractions of a higher level than individual knowledge/beliefs, namely the knowledge/belief of groups of agents. Indeed , [Levesque et al., 1986] claims that the concept of joint intention is necessary to formalize problem solving by a group. In this paper, we will show that • common knowledge can be used algorithmically in solving problems cooperatively, and • common knowledge is assumed rather than established. To represent common knowledge, we use the framework of situation theory, which has been developed to provide a powerful logical foundation for analyzing information flow when partiality of information is crucial ([Barwise, 1989], [Devlin, 1991]), as it is in distinguishing between individual and common knowledge. We will compare our model of common knowledge with Barwise's ([Barwise, 1989a]) and show why his model is not the best to make use of common knowledge in inference. We then apply our model to the three wisemen problem. 1.1 Situation Theory Fundamental notions of situation theory include item of information (called an infon) and situation (a part of the world capable of making an infon a fact). A typical infon would be that a particular relation holds (alternatively, does not hold) of particular objects. For instance, the information …