The chance that the sun will rise tomorrow revisited

Abstract

We propose a framework of the study of computable induction, which is a computable version of Solomonoff's universal induction. As a concrete example, we consider a problem of confirmation, such as the probability that the sun will rise tomorrow. Although we can not tell the exact probabilities, we can deduce the rate of the convergence up to a multiplicative constant, which is slightly faster than Laplace's result.