Variants of Partial Learning in Inductive Inference

Abstract

This thesis studies several variants of partial learning under the framework of inductive inference. In particular, the following learning criteria are examined: con fident partial learning, partially conservative learning, essentially class consistent partial learning, and iterative learning. Consistent partial learning of recursive functions is classifi ed according to the mode of data presentation; the two main types of data texts considered are canonical text and arbitrary text. The issue of consistent partial learning from incomplete texts is also given a brief treatment towards the end of the report. A further research direction taken up in this report is the investigation of the additional learning power conferred by oracles. It is shown that certain conditions on the computational degrees of oracles enable all recursive functions to be con fidently partially learnt. Similarly, it is proved that all PA-complete oracles are computationally strong enough to permit the essentially consistent inference of all recursive functions. Another question particularly relevant in the e ffort to construct class separation examples of various learning criteria is whether there is always a uniform e ffective procedure to fi nd a recursive function that is not learnt by a learner according to some criterion. The present work tries to address this question for the case of confi dent partial learning and consistent partial learning.