Abstract.
\n<\/em><\/p>\nAn\u00a0\u00a0empirical variable<\/b><\/i>\u00a0is 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\u00a0questions<\/i>\u00a0in natural language (where the inexact observations are partial answers). This leads to a topological conception of empirical variables,\u00a0as\u00a0maps from the state space into a topological<\/b>\u00a0space<\/b><\/i>. 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.<\/p>\n
A central tenet in empirical sciences is establishing\u00a0functional correlations<\/i><\/b>\u00a0between variables, with a view towards (1) establishing\u00a0<\/b>causality,<\/b><\/i>\u00a0 but also (2)\u00a0predicting<\/i>\u00a0the (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\u00a0inquisitive implication<\/i>: every partial answer to question Y is entailed by some partial answer to X.\u00a0 In this talk, I argue that\u00a0knowability of a dependency amounts to the<\/b>\u00a0continuity<\/i><\/b>\u00a0of the given functional correlatio<\/b>n. I give a\u00a0learning-theoretic justification<\/i>\u00a0of this claim,\u00a0connecting with\u00a0Kevin Kelly’s notion of\u00a0gradual learnabilit<\/i>y, then I give some concrete examples. Next, I present a\u00a0complete and decidable axiomatization<\/i><\/b>\u00a0of the logic of continuous dependence, and briefly skech the ideas behind the proofs.<\/p>\n
Further, I discuss the distinction between\u00a0knowing the dependence<\/b>\u00a0between X and Y, and\u00a0knowing how<\/b>\u00a0to 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\u00a0continuity versus uniform continuity<\/b>\u00a0of the underlying dependence map, and go on to propose an axiomatization of strongly known dependence, in the framework of\u00a0uniform spaces<\/i>\u00a0(-Andr\u00e8 Weil’s qualitative generalization of metric spaces).<\/p>\n
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.<\/p>\n
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.)<\/p>\n
See\u00a0here<\/a>\u00a0for the recording of the talk.<\/p>\n","protected":false},"excerpt":{"rendered":"Speaker: Alexandru Baltag
\nDate and Time: Thursday, May 14th 2020, 16:30-18:00, Amsterdam time.
\nVenue: online.
\nTitle: From known correlations to the logic of continuous dependence<\/p>\n
Abstract.<\/p>\n
An\u00a0\u00a0empirical variable\u00a0is 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 […]<\/p>\n","protected":false},"author":14,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"class_list":["post-4071","post","type-post","status-publish","format-standard","hentry","category-events"],"_links":{"self":[{"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/posts\/4071","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/users\/14"}],"replies":[{"embeddable":true,"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/comments?post=4071"}],"version-history":[{"count":2,"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/posts\/4071\/revisions"}],"predecessor-version":[{"id":4249,"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/posts\/4071\/revisions\/4249"}],"wp:attachment":[{"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/media?parent=4071"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/categories?post=4071"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/tags?post=4071"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}