This is an impressive amount of work on logical uncertainty! I have to admit it's tough to see at first where all the definitions are heading. Could you expand the introductory section and give a heuristic example or two there?

Also, I worry about the possibility that $O{P}_{neg}P/poly$ might not contain any nontrivial problems of interest. Is there anything akin to calculating digits of pi which is known to lie in $O{P}_{neg}P/poly$?

P.S. Sorry for the delay in reading and responding; Nate, Benja and I were all at a conference overseas.