Abstract

The present paper deals with the learnability of indexed families of uniformly recursive languages from positive data under various postulates of naturalness. In particular, we consider set-driven and rearrangement-independent learners, i.e., learning devices whose output exclusively depends on the range and on the range and length of their input, respectively. The impact of set-drivenness and rearrangement-independence on the behavior of learners to their learning power is studied in dependence on the hypothesis space the learners may use. Furthermore, we consider the influence of set-drivenness and rearrangementindependence for learning devices that realize the subset principle to different extents. Thereby we distinguish between strong-monotonic, monotonic and weak-monotonic or conservative learning. The results obtained are twofold. First, rearrangement-independent learning does not constitute a restriction except the case of monotonic learning. Second, we prove that for all but on...

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