Changing the Inference Type – Keeping the Hypothesis Space

  • Frank Balbach
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2842)


In inductive inference all learning takes place in hypothesis spaces. We investigate for which classes of recursive functions learnability according to an inference type \(\mathcal{I}\) implies learnability according to a different inference type \(\mathcal{J}\) within the same hypothesis space.

Several classical inference types are considered. Among FIN, CONSCP, and CP the above implication is true, for all relevant classes, independently from the hypothesis space.

On the other hand, it is proved that for many other pairs \(\mathcal{(I,J)}\) hypothesis spaces exist that allow full \(\mathcal{I}\) learning power, but limit that of \(\mathcal{J}\) to finite classes.

Only in a few cases (e. g. LIM vs. CONS) the result does depend on the actual class to be learned.


Initial Segment Recursive Function Inductive Inference Total Function Inference Type 
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 2003

Authors and Affiliations

  • Frank Balbach
    • 1
  1. 1.Institut für Theoretische InformatikUniversität zu LübeckLübeckGermany

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