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SUMMARY:Logical Induction: a computable approach to logical non-omniscienc
 e - Adrià Garriga Alonso (University of Cambridge)
DTSTART:20180221T170000Z
DTEND:20180221T183000Z
UID:TALK101842@talks.cam.ac.uk
CONTACT:Adrià Garriga Alonso
DESCRIPTION:Link to slides: https://valuealignment.ml/talks/2018-02-21-log
 ical-induction.pdf\n\nIs P≠NP? Are there infinitely many twin primes? Th
 ese conjectures haven't been proven or disproven\, but we have quite a bit
  of "evidence" for them in the form of proven related sentences. For examp
 le\, the difference between any two consecutive primes is less than 7·10^
 7 (Zhang\, 2014).\n\nTo which degree should we believe in these logical se
 ntences? How should we update our beliefs based on the related evidence? O
 ne might turn to probability theory for answers. However\, the veracity of
  the sentences is implied by things we assume (the ZF/C axioms)\, rather t
 han any data we need to observe. Probability theory thus dictates we shoul
 d assign them probability 1 if they are true\, and 0 if they are false\, w
 hich is clearly impossible to do in general for a computable agent (read: 
 its program runs in a finite amount of time).\n\nIn this session we will t
 alk about Logical Induction (Garrabrant et al.\, 2016)\, a computable algo
 rithm for assigning probabilities to every logical statement in a formal l
 anguage. We will examine several desirable properties of the algorithm. Fo
 r example\, Logical Induction (almost quoting from their abstract):\n\n(1)
  learns to predict patterns of truth and falsehood in logical statements\,
  often long before having the resources to prove or disprove the statement
 s\, so long as the patterns can be written in polynomial time\,\n\n(2) lea
 rns to use appropriate statistical summaries to predict sequences of state
 ments whose truth values appear pseudorandom\n\n(3) learns to have accurat
 e beliefs about its own current beliefs\, in a manner that avoids the stan
 dard paradoxes of self-reference.\n\nFinally\, we will talk about its cons
 truction\, and its implications for solving the value alignment problem.\n
 \n\nReferences:\n\nLogical Induction (Scott Garrabrant\, Tsvi Benson-Tilse
 n\, Andrew Critch\, Nate Soares\, Jessica Taylor): https://arxiv.org/abs/1
 609.03543\n\nAbridged version: https://intelligence.org/files/LogicalInduc
 tionAbridged.pdf\n\nZhang\, Yitang. "Bounded gaps between primes." Annals 
 of Mathematics 179.3\n(2014): 1121-1174.\nhttp://annals.math.princeton.edu
 /wp-content/uploads/annals-v179-n3-p07-p.pdf\n
LOCATION: Cambridge University Engineering Department\, CBL Seminar room B
 E4-38.  For directions see http://learning.eng.cam.ac.uk/Public/Directions
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