This post is a second look at The Definability of Truth in Probabilistic Logic, a preprint by Paul Christiano and other Machine Intelligence Research Institute associates, which I first read and took notes on a little over one year ago.
In particular, I explore relationships between Christiano et al’s probabilistic logic and stumbling blocks for self-reference in classical logic, like the liar’s paradox (“This sentence is false”) and in particular Löb’s theorem.
The original motivation for the ideas in this post was an attempt to prove a probabilistic version of Löb’s theorem to analyze the truth-teller sentences (“This sentence is [probably] true”) of probabilistic logic, an idea that came out of some discussions at a MIRIx workshop that I hosted in Seattle.
Meditations on Löb’s theorem and probabilistic logic [LINK]
A post on my own blog following a MIRIx workshop from two weekends ago.
http://qmaurmann.wordpress.com/2014/08/10/meditations-on-l-and-probabilistic-logic/
Reproducing the intro:
This post is a second look at The Definability of Truth in Probabilistic Logic, a preprint by Paul Christiano and other Machine Intelligence Research Institute associates, which I first read and took notes on a little over one year ago.
In particular, I explore relationships between Christiano et al’s probabilistic logic and stumbling blocks for self-reference in classical logic, like the liar’s paradox (“This sentence is false”) and in particular Löb’s theorem.
The original motivation for the ideas in this post was an attempt to prove a probabilistic version of Löb’s theorem to analyze the truth-teller sentences (“This sentence is [probably] true”) of probabilistic logic, an idea that came out of some discussions at a MIRIx workshop that I hosted in Seattle.