Reasoning about Knowledge and Belief

An agent operating in a complex environment can benefit from adapting its behavior to the situation at hand. The agent's choice of actions at any point in time can, however , be based only on its local knowledge and beliefs. When many agents are present, the success of one's agent's actions will typically depend on the actions of the other agents. These, in turn, are based on the other agents' own knowledge and beliefs. It follows that to operate effectively in a setting containing other agents, an agent must, in addition to its knowledge about the physical features of the outside world, consider its knowledge about other agent's knowledge. This line of reasoning can be extended to justify the need for using deeper levels of knowledge, of course. Moreover, the task of obtaining relevant knowledge and that of affecting the knowledge of other agents, become important goals in many applications. This crucial connection between knowledge and action is what makes knowledge and belief two of the most frequently used notions in everyday discourse. It also suggests that rigorous frameworks for reasoning about knowledge and belief can be of value when analyzing scenarios involving multiple agents. Philosophers have been concerned with epistemology, the study of knowledge, for thousands of years, going back to the great Chinese, Greek, and Indian thinkers. The focus of much of their analysis was on fundamental questions about the nature of knowledge: What can be known? When does someone know something? How does knowledge relate to truth and to belief? Rigorous logical treatment of knowledge and belief go back to the work of von Wright in the 1950's. It gained substantial grounding in Hintikka's seminal book Knowledge and Belief in 1962 [28], which based modal logics of knowledge on Kripke's possible-worlds semantic modeling of modal logics [30]. Hintikka's work was followed by a wave of research in the 1960's on logics for knowledge and belief and their proper axiomatizations, with a focus on the relationship between knowledge and belief [15, 31]. In the second half of the Twentieth century, researchers in different fields of science recognized the need to understand the role that knowledge and belief play in multi-agent systems and multi-agent interaction. In 1969, David K. Lewis published 622 15. Reasoning about Knowledge and Belief the book Conventions, which contained the first explicit definition of common knowledge among a set of agents (or individuals). Extensions of …