Incremental Concept Learning for

Important reenements of concept learning in the limit from positive data considerably restricting the accessibility of input data are studied. Let c be any concept; every innnite sequence of elements exhausting c is called positive presentation of c. In all learning models considered the learning machine computes a sequence of hypotheses about the target concept from a positive presentation of it. With iterative learning, the learning machine, in making a conjecture, has access to its previous conjecture and the latest data item coming in. In k-bounded example-memory inference (k is a priori xed) the learner is allowed to access, in making a conjecture, its previous hypothesis, its memory of up to k data items it has already seen, and the next element coming in. In the case of k-feedback identiication, the learning machine, in making a conjecture, has access to its previous conjecture, the latest data item coming in, and, on the basis of this information, it can compute k items and query the database of previous data to nd out, for each of the k items, whether or not it is in the database (k is again a priori xed). In all cases, the sequence of conjectures has to converge to a hypothesis correctly describing the target concept. Our results are manyfold. An innnite hierarchy of more and more powerful feedback learners in dependence on the number k of queries allowed to be asked is established. However, the hierarchy collapses to 1-feedback inference if only indexed families of inn-nite concepts are considered, and moreover, its learning power is then equal to learning in the limit. But it remains innnite for concept classes of only innnite r.e. concepts. Both k-feedback inference and k-bounded example-memory identiication are more powerful than iterative learning but incomparable to one another. Furthermore, there are cases where redundancy in the hypothesis space is shown to be a resource increasing the learning power of iterative learners. Finally, the union of at most k pattern languages is shown to be iteratively inferable.