Bjorndahl: The Epistemology of Nondeterminism. Logic, Probability, and Games Seminar @ Faculty House, Columbia U
Mar 29 @ 4:00 pm

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

Isaac Levi Conference and Memorial @ Columbia University, Philosophy rm tba
Sep 28 all-day

Conference Schedule

10AM       Teddy Seidenfeld – Conditional Probability, Conditionalization, and Total Evidence

11AM       Eleonora Cresto – Beyond Indeterminate Utilities. The Case of Neurotic Cake-Cutting

11:20AM  Ignacio Ojea Quintana – Unawareness and Levi’s Consensus as Common Ground

11:40AM  Rush Stewart – Uncertainty, Equality, Fraternity

1PM         Nils-Eric Sahlin – Levi’s Decision Theory: Lessons Learned

1:45PM    Wilfried Sieg – Scientific Theories as Set-Theoretic Predicates?

2:45PM    Panel Discussion – Learning from Levi

Abstracts available in attached documents under “Supporting material.”


A memorial service will be held at 5PM at St. Paul’s Chapel on the Columbia campus. Reception to follow on the 7th floor of Philosophy Hall.