This reminds me of the proposal which tsvi posted, in which logical induction predicts logic using actions as input to the traders, much as AIXI predicts observations and rewards by treating actions as input to the environment. This allows predictions to be well-defined in cases which would otherwise be divide-by-zero errors, though without providing any obvious guarantees about what predictions will look like in such cases.
This reminds me of the proposal which tsvi posted, in which logical induction predicts logic using actions as input to the traders, much as AIXI predicts observations and rewards by treating actions as input to the environment. This allows predictions to be well-defined in cases which would otherwise be divide-by-zero errors, though without providing any obvious guarantees about what predictions will look like in such cases.