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Consistency Conditions for Inductive Inference of Recursive Functions

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Book cover New Frontiers in Artificial Intelligence (JSAI 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4384))

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Abstract

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.

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Authors and Affiliations

  1. Mathematical Institute, Tohoku University, Sendai Miyagi 980-8578, Japan

    Yohji Akama

  2. Division of Computer Science, Hokkaido University, N-14, W-9, Sapporo 060-0814, Japan

    Thomas Zeugmann

Authors
  1. Yohji Akama
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  2. Thomas Zeugmann
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Editor information

Takashi Washio Ken Satoh Hideaki Takeda Akihiro Inokuchi

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Akama, Y., Zeugmann, T. (2007). Consistency Conditions for Inductive Inference of Recursive Functions. In: Washio, T., Satoh, K., Takeda, H., Inokuchi, A. (eds) New Frontiers in Artificial Intelligence. JSAI 2006. Lecture Notes in Computer Science(), vol 4384. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69902-6_22

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  • DOI: https://doi.org/10.1007/978-3-540-69902-6_22

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69901-9

  • Online ISBN: 978-3-540-69902-6

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