Learning Recursive Functions Refutably

  • Sanjay Jain
  • Efim Kinber
  • Rolf Wiehagen
  • Thomas Zeugmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2225)


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.


Learning Machine Accumulation Point Partial Function Recursive Function Inductive Inference 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Sanjay Jain
    • 1
  • Efim Kinber
    • 2
  • Rolf Wiehagen
    • 3
  • Thomas Zeugmann
    • 4
  1. 1.School of ComputingNational University of SingaporeSingapore
  2. 2.Department of Computer ScienceSacred Heart UniversityFairfieldUSA
  3. 3.Department of Computer ScienceUniversity of KaiserslauternKaiserslauternGermany
  4. 4.Institut für Theoretische InformatikMed. Universität zu LübeckLübeckGermany

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