Logical and Probabilistic Models of Belief Change

Lecturer: Eric Pacuit (website)
Meeting Times: 5:15pm-6:45pm
Location: Rutgers University
Meeting Room: Honors S126

Course Description

Reasoning about the knowledge and beliefs of a single agent or group of agents is an interdisciplinary concern spanning computer science, game theory, philosophy, linguistics and statistics. 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, the theory of subjective probability, but there are many variants, such as the Dempster-Shafer belief functions and conditional probability systems). 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 beliefs of a group of agents, and how these beliefs may change over time. There are two central questions that I will address is this course: 1. What is the precise relationship between the different formalisms describing an agent's beliefs (e.g., what is the relationship between an agent's graded beliefs and full beliefs?); and 2. How should a agent change her beliefs in response to new evidence?

In this course, I will introduce the main formalisms that can describe an agents' beliefs and how those beliefs change over time. Rather than focusing solely on the technical details of a specific formalism, I will pay special attention to the key foundational questions (of course, introducing formal details as needed). There are two goals of this course. The first is to explain the relationship between logical and probabilistic models of belief. The second is to explore the many technical and conceptual issues that arise when studying how agents' beliefs change over time. In addition to introducing the key formal frameworks, this course will introduce the fundamental conceptual questions that drive much of the research in {\em formal epistemology}.

Day 1: Formal models of belief (revision)

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Day 2: Bayesian models, updating probabilities

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Day 3: Updating probabilities

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TBA

Day 4: Meta-information, Iterated revision

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Day 5: Iterated Belief Revision and Agreement Theorems

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TBA