Propositional dynamic logic (PDL) is a framework for reasoning about nondeterministic program executions (or, more generally, nondeterministic actions). In this setting, nondeterminism is taken as a primitive: a program is nondeterministic iff it has multiple possible outcomes. But what is the sense of “possibility” at play here? This talk explores an epistemic interpretation: working in an enriched logical setting, we represent nondeterminism as a relationship between a program and an agent deriving from the agent’s (in)ability to adequately measure the dynamics of the program execution. More precisely, using topology to capture the observational powers of an agent, we define the nondeterministic outcomes of a given program execution to be those outcomes that the agent is unable to rule out in advance. In this framework, determinism coincides exactly with continuity: that is, determinism is continuity in the observation topology. This allows us to embed PDL into (dynamic) topological (subset space) logic, laying the groundwork for a deeper investigation into the epistemology (and topology) of nondeterminism.
The seminar is concerned with applying formal methods to fundamental issues, with an emphasis on probabilistic reasoning, decision theory and games. In this context “logic” is broadly interpreted as covering applications that involve formal representations. The topics of interest have been researched within a very broad spectrum of different disciplines, including philosophy (logic and epistemology), statistics, economics, and computer science. The seminar is intended to bring together scholars from different fields of research so as to illuminate problems of common interest from different perspectives. Throughout each academic year, meetings are regularly presented by the members of the seminar and distinguished guest speakers.
details tba
02/08/2019 Faculty House, Columbia University
4:00 PM
03/29/2019 Faculty House, Columbia University
4:00 PM
04/19/2018 Faculty House, Columbia University
4:00 PM
Convergence to the truth is viewed with some ambivalence in philosophy of science. On the one hand, methods of inquiry that lead to the truth in the limit are prized as marks of scientific rationality. But an agent who, by using some method, expects to always converge to the truth seems to fail a minimum standard of epistemic modesty. This point was recently brought home by Gordon Belot in his critique of Bayesian epistemology. In this paper I will study convergence to the truth theorems within the framework of Edward Nelson’s radically elementary probability theory. This theory provides an enriched conceptual framework for investigating convergence and gives rise to an appropriately modest from of Bayesianism.
The seminar is concerned with applying formal methods to fundamental issues, with an emphasis on probabilistic reasoning, decision theory and games. In this context “logic” is broadly interpreted as covering applications that involve formal representations. The topics of interest have been researched within a very broad spectrum of different disciplines, including philosophy (logic and epistemology), statistics, economics, and computer science. The seminar is intended to bring together scholars from different fields of research so as to illuminate problems of common interest from different perspectives. Throughout each academic year, meetings are regularly presented by the members of the seminar and distinguished guest speakers.
details tba
02/08/2019 Faculty House, Columbia University
4:00 PM
03/22/2019 Faculty House, Columbia University
4:00 PM
04/19/2018 Faculty House, Columbia University
4:00 PM
Artificial intelligence (AI) promises to automate and scale solutions to perennial accessibility challenges (e.g., generating image descriptions for blind users). However, research shows that AI-bias disproportionately impacts people already marginalized based on their race, gender, or disabilities, raising questions about potential impacts in addition to AI’s promise. In this talk, Cynthia Bennett will overview broad concerns at the intersection of AI, disability, and accessibility. She will then share details about one project in this research space that led to guidance on human and AI-generated image descriptions that account for subjective and potentially sensitive descriptors around race, gender, and disability of people in images.
How does the brain cope with Complexity? How do we make decisions when confronted with practically infinite streams of information?
The conference showcases cutting edge research on these questions in Neuroscience and Psychology (neural mechanisms of cognitive control, exploration, decision-making, information demand, memory and creativity), Computer Science (artificial intelligence of curiosity and intrinsic motivation) and Economics (decision making and information demand). Alongside formal presentations, the conference will encourage ample interactions among faculty, students and postdocs through informal discussions and poster presentations.
Submissions for poster presentations and travel awards are due February 15, 2023. Please visit the call for submissions for complete requirements.
Event Information
Free and open to the public. Registration is required and will open shortly. All in-person attendees must follow Columbia’s COVID-19 policies. Visitors will be asked to provide proof of COVID-19 vaccination. Online attendees will receive a Zoom link. Please email events@zi.columbia.edu with any questions.