 His own primary attention during the later years of his career was to inductive logic, where he began by distinguishing two fundamentally different explicanda of the concept “probability”: (i) the idea of probability as relative frequency of some occurrence in a series of events or in a population, which he regarded as a legitimate and entirely empirical matter. He contrasted it with (ii) probability understood as an epistemic measure of our certainty or uncertainty about the empirical truth or adequacy of a statement. The latter was Carnap’s focus; at the outset he worked out a structural and logical conception of epistemic probability, influenced by Waismann and Keynes, as further explained in the supplement  Inductive Logic,  and progressed over the years toward a more “personalist” view, though never giving up the logical conception entirely. He worked closely with various students and associates on these problems, especially Richard Jeffrey, Yehoshua Bar-Hillel, and John Kemeny. See  section 8.2  below, see the supplement  Inductive Logic  for the details of his structural account of probability, and see the supplement  Methodology (Section 1)  for his probabilistic explication(s) of inductive confirmation. Ray J. Solomonoff’s work on universal inductive inference was also triggered by Carnap’s inductive logic. (Solomonoff studied with Carnap in Chicago. See Sterkenburg 2018 for a discussion and evaluation.)