Consistency Conditions for Inductive Inference of Recursive Functions

  • Yohji Akama
  • Thomas Zeugmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4384)


A consistent learner is required to correctly and completely reflect in its actual hypothesis all data received so far. Though this demand sounds quite plausible, it may lead to the unsolvability of the learning problem.

Therefore, in the present paper several variations of consistent learning are introduced and studied. These variations allow a so-called δ–delay relaxing the consistency demand to all but the last δ data.

Additionally, we introduce the notion of coherent learning (again with δ–delay) requiring the learner to correctly reflect only the last datum (only the n − δth datum) seen.

Our results are threefold. First, it is shown that all models of coherent learning with δ–delay are exactly as powerful as their corresponding consistent learning models with δ–delay. Second, we provide characterizations for consistent learning with δ–delay in terms of complexity. Finally, we establish strict hierarchies for all consistent learning models with δ–delay in dependence on δ.


Consistency Condition Complexity Measure Recursive Function Inductive Inference Recursive Operator 
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 Berlin Heidelberg 2007

Authors and Affiliations

  • Yohji Akama
    • 1
  • Thomas Zeugmann
    • 2
  1. 1.Mathematical Institute, Tohoku University, Sendai Miyagi 980-8578Japan
  2. 2.Division of Computer Science, Hokkaido University, N-14, W-9, Sapporo 060-0814Japan

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