Hi, Vladimir!
In other words, epistemology seems too important to leave to non-mathematical methods.
It doesn't follow that a particular piece of mathematics is the way to go.
Is there another non-trivial mathematical account of how an agent can come to have accurate knowledge of its environment that is general enough to deserve the name 'epistemology'?
Is there another non-trivial mathematical account of how an agent can come to have accurate knowledge of its environment
Pretty much: Solomonoff Induction. That does most of the work in AIXI. OK, it won't design experiments for you, but there are various approaches to doing that...
I searched the posts but didn't find a great deal of relevant information. Has anyone taken a serious crack at it, preferably someone who would like to share their thoughts? Is the material worthwhile? Are there any dubious portions or any sections one might want to avoid reading (either due to bad ideas or for time saving reasons)? I'm considering investing a chunk of time into investigating Legg's work so any feedback would be much appreciated, and it seems likely that there might be others who would like some perspective on it as well.