The analogy between Solomonoff induction and a simplicity prior on logical sentences is not perfect.
EDIT: What I mean is: and so I’m not sold that the reasons Solomonoff induction uses an exponential distribution also applies to logical sentences.
For example, in thought experiment 1, it is totally allowed that there are only 3 options. If this was solomonoff induction, there are always an infinite number of programs that fit the data. But in thought experiment 1, the only options realio trulio are A, B and C. There are no bad consequences if you give them probabilities proportional to a power law—or at least not the same bad consequences.
The analogy between Solomonoff induction and a simplicity prior on logical sentences is not perfect.
EDIT: What I mean is: and so I’m not sold that the reasons Solomonoff induction uses an exponential distribution also applies to logical sentences.
For example, in thought experiment 1, it is totally allowed that there are only 3 options. If this was solomonoff induction, there are always an infinite number of programs that fit the data. But in thought experiment 1, the only options realio trulio are A, B and C. There are no bad consequences if you give them probabilities proportional to a power law—or at least not the same bad consequences.