On Conservative Learning of Recursively Enumerable Languages

Conservative partial learning is a variant of partial learning whereby the learner, on a text for a target language L, outputs one index e with L = W e infinitely often and every further hypothesis d is output only finitely often and satisfies \(L \not\subseteq W_d\). The present paper studies the learning strength of this notion, comparing it with other learnability criteria such as confident partial learning, explanatory learning, as well as behaviourally correct learning. It is further established that for classes comprising infinite sets, conservative partial learnability is in fact equivalent to explanatory learnability relative to the halting problem.