Replacing Limit Learners with Equally Powerful One-Shot Query Learners

Different formal learning models address different aspects of human learning. Below we compare Gold-style learning—interpreting learning as a limiting process in which the learner may change its mind arbitrarily often before converging to a correct hypothesis—to learning via queries—interpreting learning as a one-shot process in which the learner is required to identify the target concept with just one hypothesis. Although these two approaches seem rather unrelated at first glance, we provide characterizations of different models of Gold-style learning (learning in the limit, conservative inference, and behaviourally correct learning) in terms of query learning. Thus we describe the circumstances which are necessary to replace limit learners by equally powerful oneshot learners. Our results are valid in the general context of learning indexable classes of recursive languages. In order to achieve the learning capability of Gold-style learners, the crucial parameters of the query learning model are the type of queries (membership, restricted superset, or restricted disjointness queries) and the underlying hypothesis space (uniformly recursive, uniformly r. e., or uniformly 2-r. e. families). The characterizations of Gold-style language learning are formulated in dependence of these parameters.