How do people and other systems make choices, and how ought they to? How do they cope with uncertainty, and react to new information? What is information, and how do agents obtain and reason with it?
Many formal frameworks exist in which such questions can be articulated precisely and answers proposed.
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Classical decision-theoretic models represent uncertainty about the world and constraints on rational choice in the context of such uncertainty.
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Game-theoretic analyses focus on multi-agent settings, with each decision-maker maintaining their own subjective model of the world and the agents it contains.
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Methods of knowledge/belief representation more common in computer science and linguistics are typically designed to formalize reasoning and communication, often making heavy use of the tools of modal logic.
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My interests span these disciplines, and my work directly engages with each of the corresponding modeling paradigms, frequently bridging between them. One of the guiding aims of my research is to bring these different approaches together in novel ways, offsetting the weaknesses of one with the strengths of another.
Below I summarize a few of the central branches of my research.
Topological Methods in Knowledge Representation
Topology is the abstract mathematics of spatial structure, sometimes described as "rubber-sheet geometry" because of its insensitivity to various stretching and squishing transformations. What could this have to do with knowledge?
Kantian Decision Making Under Uncertainty
At the center of the Kantian moral system lies the compelling idea that there is a fundamental distinction between the value of persons and the value of things—that human dignity cannot be assigned a price, and should never be traded off for material wealth. The apparent simplicity of this decision-theoretic imperative belies its uneasy relationship with uncertainty, which has received almost no attention in the literature.
Language-based Games
Games are situations where players have to think strategically about their choices in the context of other people thinking strategically about their choices. Epistemic logics, which provide succinct and powerful formalizations of concepts such as belief and knowledge, are ideal tools for studying such situations. The idea of a language-based game is to take this one step further: rather than using epistemic logics just to analyze games, we can employ these same logics to help define games.