If you can prove anything interesting about a system, that system is too simple to be interesting. Logic can't handle uncertainty, and doesn't scale at all to describing/modelling systems as complex as societies, brains, AIs, etc.
AIXI is simple, and if our universe happened to allow turing machines to calculate endlessly behind cartesian barriers, it could be interesting in the sense of actually working.
There have been a couple of brief discussions of this in the Open Thread, but it seems likely to generate more so here's a place for it.
The original paper in Nature about AlphaGo.
Google Asia Pacific blog, where results will be posted. DeepMind's YouTube channel, where the games are being live-streamed.
Discussion on Hacker News after AlphaGo's win of the first game.