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.

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

Slides

The main reading for the course include the following papers:

The main reading for the course include the following papers:

- W. Holliday, Epistemic Logic and Epistemology, Handbook of Formal Philosophy, Springer, forthcoming
- E. Pacuit, Dynamic Epistemic Logic I: Modeling Knowledge and Belief, Philosophy Compass, 2013
- E. Pacuit, Dynamic Epistemic Logic II: Logics of Information Change, Philosophy Compass, 2013

Slides

On the Margin of Error argument: Inexact Knowledge

On Fitch's Paradox: Fitch's Paradox of Knowability

On Fitch's Paradox and the Dynamics of Knowability: What One May Come to Know, Actions that Make Us Know, Everything is Knowable On the Puzzle of the Gifts: Information Dynamics and Uniform Substitution

On the Margin of Error argument: Inexact Knowledge

On Fitch's Paradox: Fitch's Paradox of Knowability

On Fitch's Paradox and the Dynamics of Knowability: What One May Come to Know, Actions that Make Us Know, Everything is Knowable On the Puzzle of the Gifts: Information Dynamics and Uniform Substitution

Slides

On the Brandenbruger-Keisler Paradox: An Impossibility Theorem on Beliefs in Games, Understanding the Brandenburger-Keisler Paradox

On the Agreeing to Disagree Theorem: Agreeing to Disagree, Agreeing to Disagree: The Non-Probabilistic Case, Approximating Common Knowledge with Common Belief

On the Brandenbruger-Keisler Paradox: An Impossibility Theorem on Beliefs in Games, Understanding the Brandenburger-Keisler Paradox

On the Agreeing to Disagree Theorem: Agreeing to Disagree, Agreeing to Disagree: The Non-Probabilistic Case, Approximating Common Knowledge with Common Belief

Slides

On the Absent Minded Driver: On the Interpretation of Decision Problems with Imperfect Recall

On Common Knowledge of Rationality and Backwards Induction: Substantive Rationality and Backwards Induction

On the Absent Minded Driver: On the Interpretation of Decision Problems with Imperfect Recall

On Common Knowledge of Rationality and Backwards Induction: Substantive Rationality and Backwards Induction

Slides

On iterated belief revision: Iterated Belief Revision, When is an example a counterexample?

On quantified epistemic logic: Roles, Rigidity, and Quantification in Epistemic Logic

On iterated belief revision: Iterated Belief Revision, When is an example a counterexample?

On quantified epistemic logic: Roles, Rigidity, and Quantification in Epistemic Logic