Reflecting Inductive Inference Machines and Its Improvement by Therapy

Abstract

In a special sense, reflection means to think about its own capabilities. This phenomenon is studied in the field of Inductive Inference of Recursive Functions. The main statement in [Jan95] was, that reflection is possible iff it is not necessary at all. In the present paper this is weakened. Several notions of reflection are generalized and formalized. Here reflection is seen as a process in the limit too. Prototypical investigations are done to show some effects of additional requirements: finiteness and consistency. For finite learning each of the resulting reflective identification types has its own peculiarities, even two of these are incomparable. While for LIM and FIN reflection means restriction of learning power for total consistent learning this is not the case. The competence assessment should be used to improve the learning behaviour. Thus the idea of introducing a therapy in case of failure by changing the requirements is introduced and formalized. Based on this, some choice points while investigating therapy are worked out. So as reaction to incompetence it may be possible to use another strategy, change the space of hypothesis or to present the information in another way. Fixing such a choice, a couple of other questions is still open.