Dear all,
We will have our next LIRa session on Thursday, May 14th. Our speaker is Alexandru Baltag. You will receive the zoom link and a reminder of the guidelines for online sessions the day before the talk. After the talk, we will continue the discussion with (online) drinks, as usual. You can find the details below.
Speaker: Alexandru Baltag
Date and Time: Thursday, May 14th 2020, 16:30-18:00, Amsterdam
time.
Venue: online.
Title: From known correlations to the logic of continuous dependence
Abstract.
An empirical variable is one whose exact value might not be
knowable, and instead only inexact approximations can be observed.
Examples are in natural sciences, economics etc (where the inexact
observations are some form of measurements), but also in the semantics
of questions in natural language (where the inexact observations are
partial answers). This leads to a topological conception of empirical
variables, as maps from the state space into a topological space.
Here, the exact value of the variable is represented by the output of
the map, while the open neighborhoods of this value represent the
knowable approximations of the exact answer.
A central tenet in empirical sciences is establishing functional
correlations between variables, with a view towards (1)
establishing causality, but also (2) predicting the (approximate)
value of a hard-to-measure variable Y when given (approximate)
value(s) of easier-to-measure variable X. In interrogative terms, this
is related to inquisitive implication: every partial answer to
question Y is entailed by some partial answer to X. In this talk, I
argue that knowability of a dependency amounts to the continuity of
the given functional correlation. I give a learning-theoretic
justification of this claim, connecting with Kevin Kelly\'s notion
of gradual learnability, then I give some concrete examples. Next, I
present a complete and decidable axiomatization of the logic of
continuous dependence, and briefly skech the ideas behind the proofs.
Further, I discuss the distinction between knowing the
dependence between X and Y, and knowing how to determine Y (with
any desired accuracy) from X: the later is a stronger notion of
knowability, that requires the ability to find the accuracy that is
needed for X-measurements (to determine Y with the given accuracy). I
formalize this distinction in terms of continuity versus uniform
continuity of the underlying dependence map, and go on to propose an
axiomatization of strongly known dependence, in the framework
of uniform spaces (-Andrè Weil\'s qualitative generalization of
metric spaces).
Time-permitting, I may go back to the problem of learning true causal
relations from observed functional correlations. I will end with a
number of open questions, some technical and some conceptual.
This is ongoing joint work with Johan van Benthem, embodied in a
follow-up draft to our joint work on the Logic of Functional
Dependence, presented at a previous LIRa seminar. (But my presentation
will be self-contained.)
Hope to see you there!
The LIRa team