Skip to main content
SpringerLink
Log in

Learning with Refutation

  • Conference paper
  • First Online:
Algorithmic Learning Theory (ALT 1998)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1501))

Included in the following conference series:

  • 369 Accesses

Abstract

In their pioneering work, Mukouchi and Arikawa modeled a learning situation in which the learner is expected to refute texts which are not representative of L, the class of languages being identified. Lange and Watson extended this model to consider justified refutation in which the learner is expected to refute texts only if it contains a finite sample unrepresentative of the class L. Both the above studies were in the context of indexed families of recursive languages. We extend this study in two directions. Firstly, we consider general classes of recursively enumerable languages. Secondly, we allow the machine to either identify or refute the unrepresentative texts (respectively, texts containing finite unrepresentative samples). We observe some surprising difierences between our results and the results obtained for learning indexed families by Lange and Watson.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Ben-David. Can finite samples detect singularities of real-valued functions. In Symposium on the Theory of Computation, pages 390–399, 1992.

    Google Scholar 

  2. M. Blum. A machine-independent theory of the complexity of recursive functions. Journal of the ACM, 14:322–336, 1967.

    Article  MATH  MathSciNet  Google Scholar 

  3. J. Case, S. Jain, and S. Ngo Manguelle. Refinements of inductive inference by Popperian and reliable machines. Kybernetika, 30:23–52, 1994.

    MATH  MathSciNet  Google Scholar 

  4. J. Case and C. Lynes. Machine inductive inference and language identification. In M. Nielsen and E. M. Schmidt, editors, Proceedings of the 9th International Colloquium on Automata, Languages and Programming, volume 140 of Lecture Notes in Computer Science, pages 107–115. Springer-Verlag, 1982.

    Chapter  Google Scholar 

  5. M. Fulk. Prudence and other conditions on formal language learning. Information and Computation, 85:1–11, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  6. E. M. Gold. Language identification in the limit. Information and Control, 10:447–474, 1967.

    Article  MATH  Google Scholar 

  7. G. Grieser. Reflecting inductive inference machines and its improvement by therapy. In S. Arikawa and A. Sharma, editors, Algorithmic Learning Theory: Seventh International Workshop (ALT’ 96), volume 1160 of Lecture Notes in Artificial Intelligence, pages 325–336. Springer-Verlag, 1996.

    Google Scholar 

  8. K. P. Jantke. Reflecting ans self-confident inductive inference machines. In Algorithmic Learning Theory: Sixth International Workshop (ALT’ 95), volume 997 of Lecture Notes in Artificial Intelligence, pages 282–297. Springer-Verlag, 1995.

    Google Scholar 

  9. S. Kobayashi and T. Yokomori. On approximately identifying concept classes in the limit. In Algorithmic Learning Theory: Sixth International Workshop (ALT’ 95), volume 997 of Lecture Notes in Artificial Intelligence, pages 298–312. Springer-Verlag, 1995.

    Google Scholar 

  10. S. Kobayashi and T. Yokomori. Learning approximately regular languages with reversible languages. Theoretical Computer Science A, 174:251–257, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  11. S. Lange and P. Watson. Machine discovery in the presence of incomplete or ambiguous data. In S. Arikawa and K. Jantke, editors, Algorithmic learning theory: Fourth International Workshop on Analogical and Inductive Inference (AII’ 94) and Fifth International Workshop on Algorithmic Learning Theory (ALT’ 94), volume 872 of Lecture Notes in Artificial Intelligence, pages 438–452. Springer-Verlag, 1994.

    Google Scholar 

  12. Y. Mukouchi and S. Arikawa. Inductive inference machines that can refute hypothesis spaces. In K.P. Jantke, S. Kobayashi, E. Tomita, and T. Yokomori, editors, Algorithmic Learning Theory: Fourth International Workshop (ALT’ 93), volume 744 of Lecture Notes in Artificial Intelligence, pages 123–136. Springer-Verlag, 1993.

    Google Scholar 

  13. Y. Mukouchi and S. Arikawa. Towards a mathematical theory of machine discovery from facts. Theoretical Computer Science A, 137:53–84, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  14. E. Minicozzi. Some natural properties of strong identification in inductive inference. Theoretical Computer Science, pages 345–360, 1976.

    Google Scholar 

  15. Y. Mukouchi. Inductive inference of an approximate concept from positive data. In S. Arikawa and K. Jantke, editors, Algorithmic learning theory: Fourth International Workshop on Analogical and Inductive Inference (AII’ 94) and Fifth International Workshop on Algorithmic Learning Theory (ALT’ 94), volume 872 of Lecture Notes in Artificial Intelligence, pages 484–499. Springer-Verlag, 1994.

    Google Scholar 

  16. H. Rogers. Theory of Recursive Functions and Effective Computability. McGraw-Hill, 1967. Reprinted by MIT Press in 1987.

    Google Scholar 

  17. A. Sharma. A note on batch and incremental learnability. Journal of Computer and System Sciences, 1998. to appear.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of ISCS, National University of Singapore, Singapore, 119260

    Sanjay Jain

Authors
  1. Sanjay Jain
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. AG Künstliche Intelligenz - Expertensysteme, UniversitÄt Kaiserslautern, Postfach 3049, D-67653, Kaiserslautern, Germany

    Michael M. Richter

  2. Department of Computer Science, University of Maryland, College Park, MD, 20742, USA

    Carl H. Smith

  3. AG Algorithmischesn Lernen, UniversitÄt Kaiserslautern, Postfach 3049, D-67653, Kaiserslautern, Germany

    Rolf Wiehagen

  4. Graduate School of Information Science and Electrical Engineering Department of Informatics, Kyushu University, Kassuga, 816-8580, Japan

    Thomas Zeugmann

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Jain, S. (1998). Learning with Refutation. In: Richter, M.M., Smith, C.H., Wiehagen, R., Zeugmann, T. (eds) Algorithmic Learning Theory. ALT 1998. Lecture Notes in Computer Science(), vol 1501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49730-7_22

Download citation

  • DOI: https://doi.org/10.1007/3-540-49730-7_22

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65013-3

  • Online ISBN: 978-3-540-49730-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation