In this foundational course we will treat some well-known puzzles about knowledge and belief in detail. We focus on modelling knowledge, belief, ignorance and in particular the dynamics of such epistemic attitudes. In addition, we will discuss common knowledge and common belief and their dynamics, and on probability and knowledge. We will do all this without going into formal logical details. This is because the goal of this course is motivational: it attempts to justify and clarify the need for logical modelling of such puzzling phenomena.
Puzzles treated include: Muddy Children, Sum and Product, One Hundred Prisoners, Surprise Examination, Monty Hall Problem, Judy Benjamin problem, the Preface Paradox, the Lottery Paradox, the Coordinated Attack Problem, and the Brandenburg-Kreisler Paradox.
The course should help to make technical courses on modal logic and Bayesian epistemology more accessible. Logical syntax and semantics will only rarely be presented. The strong focus is on meta-level analysis, i.e., explanations in words and with structures, not with formulas. 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 literature on artificial intelligence and formal epistemology. A main challenge is not to argue that one particular account of belief or knowledge is primary, but, rather, to explore the entire spectrum of definitions and to identify interesting relationships between the different notions. This foundational course will introduce students to key methodological and conceptual issues that arise when making precise intuitions about the knowledge and beliefs of a group of agents.
Rather than focusing on the technical details of a specific formalism, we will focus on the key foundational questions. There are good reasons for this. 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, and to everyday examples of social interaction, such as informational cascades.