I appreciate the links. I haven't read Gaifman's paper before, so I'll go ahead and read that.

Anyhow, I won't cotton to any method of assigning a logical probability that takes longer than just brute-forcing the right answer. For this particular problem I think a bottom-up approach is what you want to use.

I see the sentiment there, and that too is a valid approach. That said, after trying to use the bottom-up approach many times and failing, and after seeing others fail using bottom-up approaches, I think that if we can at least build a nonconstructive top-down theory, that would be a starting point. After all, Solomonoff Induction is completely top down, yet it's a very powerful theoretical tool.