Bjorndahl: The Epistemology of Nondeterminism

The Epistemology of Nondeterminism
Adam Bjorndahl (Carnegie Mellon)
4:10 pm, Friday, March 29th, 2019
Faculty House, Columbia University

Abstract. 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.

Parikh: Buddha versus Popper

Buddha versus Popper: Do we live in the present or do we plan for the future?
Rohit Parikh (CUNY).
4:10 pm, Friday, February 22nd, 2019
Faculty House, Columbia University

Abstract. There are two approaches to life. The first one, which we are identifying with Sir Karl Popper, is to think before we act and to let our hypotheses die in our stead when the overall outcome is likely to be negative. We act now for a better future, and we think now which action will bring the best future. Both decision theory and backward induction are technical versions of this train of thought.  The second approach, which we will identify with the Buddha, is to live in the present and not allow the future to pull us away from living in the ever present  Now. The Buddha’s approach is echoed in many others who came after him, Jelaluddin Rumi, Kahlil Gibran, and even perhaps Jesus.  It occurs in many contemporary teachers like Eckhart Tolle and Thich Nhat Hanh.  We may call Popper’s approach “futurism” and the Buddha’s approach “presentism.”

In this talk, we will discuss various aspects of the discourse on presentism and futurism. The purpose is to contrast one with the other. We will not attempt to side with one against the other, and instead leave it as a future project to find a prescriptive action-guiding choice between the two. We merely conjecture that a better optimal choice between these two positions may be somewhere in between. (This is joint work with Jongjin Kim.)

Halpern: Actual Causality: A Survey

Actual Causality: A Survey
Joseph Halpern (Cornell University).
4:10 pm, Friday, December 7, 2018
Faculty House, Columbia University

Abstract. What does it mean that an event C “actually caused” event E? The problem of defining actual causation goes beyond mere philosophical speculation.  For example, in many legal arguments, it is precisely what needs to be established in order to determine responsibility.   (What exactly was the actual cause of the car accident or the medical problem?) The philosophy literature has been struggling with the problem of defining causality since the days of Hume, in the 1700s. Many of the definitions have been couched in terms of counterfactuals. (C is a cause of E if, had C not happened, then E would not have happened.) In 2001, Judea Pearl and I introduced a new definition of actual cause, using Pearl’s notion of structural equations to model counterfactuals.  The definition has been revised twice since then, extended to deal with notions like “responsibility” and “blame”, and applied in databases and program verification.  I survey the last 15 years of work here, including joint work with Judea Pearl, Hana Chockler, and Chris Hitchcock. The talk will be completely self-contained.

Nielsen: Speed-optimal Induction and Dynamic Coherence

Speed-optimal Induction and Dynamic Coherence
Michael Nielsen (Columbia University).
4:10 pm, Friday, November 16th, 2018
Faculty House, Columbia University

Abstract. A standard way to challenge convergence-based accounts of inductive success is to claim that they are too weak to constrain inductive inferences in the short run. We respond to such a challenge by answering some questions raised by Juhl (1994). When it comes to predicting limiting relative frequencies in the framework of Reichenbach, we show that speed-optimal convergence—a long-run success condition—induces dynamic coherence in the short run. This is joint work with Eric Wofsey.