On some open problems in reflective inductive inference

In this paper we show that there exist classes of functions which can be learnt by a finite learner which reflects on its capability, but not learnable by a consistent learner which optimistically reflects on its capability. This solves the two mentioned open problems from [G. Grieser, Reflective inductive inference of recursive functions, Theoretical Computer Science A 397 (1–3) (2008) 57–69 (Special Issue on Forty Years of Inductive Inference. Dedicated to the 60th Birthday of Rolf Wiehagen)].