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Manfred comments on Limited agents need approximate induction - Less Wrong
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Hm, I think we're talking past each other.
To give an example of what I mean, if a probabilistic programming language really implemented logical uncertainty, you could write a deterministic program that computes the last digit of the googolth prime number (possible outputs 0 through 9), and then use some getDistribution method on this deterministic program, and it would return the distribution {0.25 chance of 1, 0.25 chance of 3, 0.25 chance of 7, 0.25 chance of 9} (unless your computer actually has enough power to calculate the googolth prime).
I think your example is - at least theoretically - still within the reach of a probabilistic logic program, although the focus is entirely on approximation rather than conditioning (there are no observations). Of course, I doubt any existing inference engine would be able to help much with problems of that type, but the idea is still general enough to cover estimating intractable functions from the logic defining the solution.