We can show that the FOL prior is not too different from the algorithmic prior, so it can’t perform too badly for problems where algorithmic induction does well. Partial theories which imply probabilities close to .9 but do not specify exact predictions will eventually have high probability; for example, a theory might specify that Q(x) is derived from an unspecified F(x) and G(x) (treated as random sources) getting OR’d together, making probabilities roughly .75; variations of this would bring things closer to .9.
This still may still assign simpler Q(j) to closer to 50% probability.
We can show that the FOL prior is not too different from the algorithmic prior, so it can’t perform too badly for problems where algorithmic induction does well. Partial theories which imply probabilities close to .9 but do not specify exact predictions will eventually have high probability; for example, a theory might specify that Q(x) is derived from an unspecified F(x) and G(x) (treated as random sources) getting OR’d together, making probabilities roughly .75; variations of this would bring things closer to .9.
This still may still assign simpler Q(j) to closer to 50% probability.