For simplicity, we choose a setting that is similar to the one used in the exposition of the representation theorem, namely a binary data generating process, i.e., strings of 0's and 1's. A prediction rule determines a probability for the event, denoted \(Q^{1}_{t+1}\), that the next bit in the string is a 1, on the basis of a given string of bits with length \(t\), denoted by \(S_{t}\). Carnap and followers designed specific exchangeable prediction rules, mostly variants of the straight rule (Reichenbach 1938),  \[ P(Q^{1}_{t+1} \mid S_{n/t}) = \frac{n + 1}{t + 2} , \]  where \(S_{n/t}\) denotes a string of length \(t\) of which \(n\) entries are 1's. Carnap derived such rules from constraints on the probability assignments over the samples. Some of these constraints boil down to the axioms of probability. Other constraints, exchangeability among them, are independently motivated, by an appeal to so-called logical interpretation of probability.  Under this logical interpretation, the probability assignment must respect certain invariances under transformations of the sample space, in analogy to logical principles that constrain truth valuations over a language in a particular way.