Partial Learning of Recursively Enumerable Languages

This paper studies several typical learning criteria in the model of partial learning of r.e. sets in the recursion-theoretic framework of inductive inference. Its main contribution is a complete picture of how the criteria of confidence, consistency and conservativeness in partial learning of r.e. sets separate, also in relation to basic criteria of learning in the limit. Thus this paper constitutes a substantial extension to prior work on partial learning. Further highlights of this work are very fruitful characterisations of some of the inference criteria studied, leading to interesting consequences about the structural properties of the collection of classes learnable under these criteria. In particular a class is consistently partially learnable iff it is a subclass of a uniformly recursive family.