Oooh, I remember now. You are talking about that discussion we had a while ago. OK. Yeah, so,"learning" in that context means you're given a bunch of atoms as

Oooh, I remember now. You are talking about that discussion we had a while ago. OK. Yeah, so,"learning" in that context means you're given a bunch of atoms as examples and you learn a logic programs that entails those atoms. "Atoms" here in the logical sense, of atomic formulae (not in the Prolog sense, where "atoms" are constants). Ultimately, a sound and complete inductive algorithm like the one in Louise, is capable of learning any program, given one or more example atoms it entails, but in practice some programs are harder to learn than others. This is more so if a program must essentially be executed before it can be learned. Which, for the Ackermann fucntion, is a bit of a problem, given it's very expensive. So "learning" can't be done in a PAC-Learning sense, of learning from randomly chosen examples, because then you end up with combinatorial explosion and fast. So this "learning" I show in the Ackermann example is more like teaching: I chose, manually, an example that I know is informative and that the learner can use to learn. Btw, I like necromancing old converstations too :D