Physical Sciences and Mathematics Commons^™

On Learning Of Functions Refutably, Sanjay Jain, Efim Kinber, Rolf Wiehagen, Thomas Zeugmann

School of Computer Science & Engineering Faculty Publications

Learning of recursive functions refutably informally means that for every recursive function, the learning machine has either to learn this function or to refute it, that is to signal that it is not able to learn it. Three modi of making precise the notion of refuting are considered. We show that the corresponding types of learning refutably are of strictly increasing power, where already the most stringent of them turns out to be of remarkable topological and algorithmical richness. Furthermore, all these types are closed under union, though in different strengths. Also, these types are shown to be different with …