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International Conference on Algorithmic Learning Theory

ALT 2001: Algorithmic Learning Theory pp 283–298Cite as

Learning Recursive Functions Refutably

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2225))

Abstract

Learning of recursive functions refutably means that for every recursive function, the learning machine has either to learn this function or to refute it, i.e., 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. All these types are closed under union, though in different strengths. Also, these types are shown to be different with respect to their intrinsic complexity; two of them do not contain function classes that are “most difficult” to learn, while the third one does. Moreover, we present characterizations for these types of learning refutably. Some of these characterizations make clear where the refuting ability of the corresponding learning machines comes from and how it can be realized, in general.

For learning with anomalies refutably, we show that several results from standard learning without refutation stand refutably. Then we derive hierarchies for refutable learning. Finally, we show that stricter refutability constraints cannot be traded for more liberal learning criteria.

A full version of this paper is available as technical report (cf. [17]).

Supported in part by NUS grant number RP3992710.

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Author information

Authors and Affiliations

  1. School of Computing, National University of Singapore, 119260, Singapore

    Sanjay Jain

  2. Department of Computer Science, Sacred Heart University, Fairfield, CT, 06432-1000, USA

    Efim Kinber

  3. Department of Computer Science, University of Kaiserslautern, PO Box 3049, 67653, Kaiserslautern, Germany

    Rolf Wiehagen

  4. Institut für Theoretische Informatik, Med. Universität zu Lübeck, Wallstraβe 40, 23560, Lübeck, Germany

    Thomas Zeugmann

Authors
  1. Sanjay Jain
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  2. Efim Kinber
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  3. Rolf Wiehagen
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  4. Thomas Zeugmann
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Editor information

Editors and Affiliations

  1. IBM, Thomas J.Watson Research Center, Room 33-237, P.O.Box 218, 10598, Yorktown, NY, USA

    Naoki Abe

  2. Dept.of Electrical Engineering and Computer Science, Tufts University, 161 College Ave., 02155, Medford, MA, USA

    Roni Khardon

  3. Medizinische Universität zu Lübeck,Inst.für Theoretische Informatik, Wallstr.40, 23560, Lübeck, Germany

    Thomas Zeugmann

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© 2001 Springer-Verlag Berlin Heidelberg

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Jain, S., Kinber, E., Wiehagen, R., Zeugmann, T. (2001). Learning Recursive Functions Refutably. In: Abe, N., Khardon, R., Zeugmann, T. (eds) Algorithmic Learning Theory. ALT 2001. Lecture Notes in Computer Science(), vol 2225. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45583-3_22

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  • DOI: https://doi.org/10.1007/3-540-45583-3_22

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42875-6

  • Online ISBN: 978-3-540-45583-7

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