 This problem of relating a set of statements to a set of observations and defining the corresponding probability was taken up by Carnap (1945, 1950). He distinguished two forms of probability: Probability\(_1\) or “degree of confirmation” \(P_1 (h ; e)\) is a logical relation between two sentences, a hypothesis h and a sentence e reporting a series of observations. Statements of this type are either analytical or contradictory. The second form, Probability\(_2\) or “relative frequency”, is the statistical concept. In the words of his student Solomonoff (1997):