This paper provides a systematic study of incremental learning from noise-free and from noisy data, thereby distinguishing between learning from only positive data and from both positive and negative data. Our study relies on the notion of noisy data introduced in [22]. The basic scenario, named iterative learning, is as follows. In every learning stage, and algorithmic learner takes as input one element of an information sequence for a target concept and its previously made hypothesis and outputs a new hypothesis. The sequence of hypotheses has to converge to a hypothesis describing the target concept correctly.
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