Reasoning about the knowledge and beliefs of a single agent or group of agents is an interdisciplinary concern spanning computer science, mathematics, game theory and philosophy. Inspired, in part, by issues in these different "application" areas, many different notions of knowledge and belief have been identified and analyzed in the formal epistemology literature. The main challenge is not to argue that one particular account of belief or knowledge is primary, but, rather, to explore the logical space of definitions and identify interesting relationships between the different notions. A second challenge (especially for students) is to keep track of the many different formal frameworks used in this broad literature (typical examples include modal logics of knowledge and belief or the theory of subjective probability, but there are many variants). This foundational course will introduce students to key methodological, conceptual and technical issues that arise when designing a formalism to make precise intuitions about the knowledge and beliefs of a group of agents.
The course will serve as a introduction to epistemic logic and Bayesian epistemology; however, we will not follow the standard textbook presentation of this material. For example, as found in Reasoning about Knowledge by Fagin, Halpern, Moses and Vardi, Dynamic Epistemic Logic by van Ditmarsch, van der Hoek and Kooi or Modal Logic for Open Minds by van Benthem. Rather than focusing on the technical details of a specific formalism, we will focus on the key foundational questions (of course, introducing formal details as needed). There are good reasons for taking an "issue-oriented" approach to introducing formal models of knowledge and belief (especially at a summer school such as ESSLLI). Many of the recent developments concerning formal models of knowledge and belief have been driven by analyzing concrete examples. These range from toy examples, such as the infamous muddy children puzzle to philosophical quandaries, such as the knowability paradox or the surprise examination paradox, to everyday examples of social interaction. Different formal frameworks are then judged, in part, on how well they conform to the analyst's intuitions about the relevant set of examples. Thus, in order to appreciate the usefulness and limits of the different formal frameworks, it is important to understand the issues that motivate the key technical developments.