Extremes in the degrees of inferability

AbstractMost theories of learning consider inferring a function f from either (1) observations about f or, (2) questions about f. We consider a scenario whereby the learner observes f and asks queries to some set A. If I is a notion of learning then I[A] is the set of concept classes I-learnable by an inductive inference machine with oracle A. A and B are I-equivalent if I[A] = I[B]. The equivalence classes induced are the degrees of inferability. We prove several results about when these degrees are trivial, and when the degrees are omniscient (i.e., the set of recursive function is learnable)