Skip to main content
SpringerLink
Log in

Inferability of Unbounded Unions of Certain Closed Set Systems

  • Conference paper
  • First Online:
New Frontiers in Artificial Intelligence (JSAI-isAI 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6284))

Included in the following conference series:

  • 804 Accesses

Abstract

In this article, we study inferability from positive data for the unbounded union of certain class of languages. In order to show inferability, we put an emphasis on a characteristic set of a given language. We consider a class of closed set systems such that there exists an algorithm for generating a characteristic set consisting of one element. Two concrete examples of closed set systems with such algorithms are given. Furthermore, we consider applications of these examples to the study of transaction databases.

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. Angluin, D.: Inductive Inference of Formal Languages from Positive Data. Information and Control 45, 117–135 (1980)

    Article  MathSciNet  Google Scholar 

  2. de Brecht, M., Kobayashi, M., Tokunaga, H., Yamamoto, A.: Inferability of Closed Set Systems From Positive Data. In: Washio, T., Satoh, K., Takeda, H., Inokuchi, A. (eds.) JSAI 2006. LNCS (LNAI), vol. 4384, pp. 265–275. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  3. Cox, D., Little, J., O’Shea, D.: Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra. Springer, Heidelberg (1992)

    Book  Google Scholar 

  4. Gold, E.M.: Language Identification in the Limit. Information and Control 10, 447–474 (1967)

    Article  MathSciNet  Google Scholar 

  5. Kameda, Y., Tokunaga, H., Yamamoto, A.: Learning bounded unionsof Noetherian closed set systems via characteristic sets. In: Clark, A., Coste, F., Miclet, L. (eds.) ICGI 2008. LNCS (LNAI), vol. 5278, pp. 98–110. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  6. Kapur, S., Bilardi, G.: On uniform learnability of language families. Information Processing Letters 44, 35–38 (1992)

    Article  MathSciNet  Google Scholar 

  7. Kobayashi, S.: Approximate Identification, Finite Elasticity and Lattice Structure of Hypothesis Space, Technical Report, CSIM 96-04, Dept. of Compt. Sci. and Inform. Math., Univ. of Electro-Communications (1996)

    Google Scholar 

  8. Lassez, J.L., Maher, M.J., Marriott, K.: Unification Revisited. In: Minker, J. (ed.) Foundations of Deductive Databases and Logic Programming, pp. 587–626. Morgan Kaufman, San Francisco (1988)

    Chapter  Google Scholar 

  9. Motoki, T., Shinohara, T., Wright, K.: The Correct Definition of Finite Elasticity: Corrigendum to Identification of Unions. In: Proceedings of COLT 1991, p. 375, 587–626. Morgan-Kaufman, San Francisco (1988)

    Google Scholar 

  10. Shinohara, T., Arimura, H.: Inductive Inference of Unbounded Unions of Pattern Languages From Positive Data. Theoretical Computer Science 241, 191–209 (2000)

    Article  MathSciNet  Google Scholar 

  11. Takamatsu, I., Kobayashi, M., Tokunaga, H., Yamamoto, A.: Computing Characteristic Sets of Bounded Unions of Polynomial Ideals. In: Satoh, K., Inokuchi, A., Nagao, K., Kawamura, T. (eds.) JSAI 2007. LNCS (LNAI), vol. 4914, pp. 318–329. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  12. Wright, K.: Identification of Unions of Languages Drawn from an Identifiable Class. In: Proc. of COLT 1989, pp. 328–388. Morgan-Kaufman, San Francisco (1989)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Information Sciences, Graduate School of Science and Engineering, Tokyo Metropolitan University, 1-1 Minami-Ohsawa, Hachioji-shi, 192-0397, Japan

    Yuichi Kameda & Hiroo Tokunaga

Authors
  1. Yuichi Kameda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hiroo Tokunaga
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. SRA Inc., Key Technology Laboratory, 2-32-8 Minami-Ikebukuro, Toyoshima-Ku, 171-8513, Tokyo, Japan

    Kumiyo Nakakoji

  2. National Institute of Information and Communications Technology, 3-5 Hikaridai, Seika-cho, Soraku-gun, 619-0289, Kyoto, Japan

    Yohei Murakami

  3. Department of English, Aoyama Gakuin University, 4-4-25 Shibuya, Shibuya-ku, 150-8366, Tokyo, Japan

    Elin McCready

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kameda, Y., Tokunaga, H. (2010). Inferability of Unbounded Unions of Certain Closed Set Systems. In: Nakakoji, K., Murakami, Y., McCready, E. (eds) New Frontiers in Artificial Intelligence. JSAI-isAI 2009. Lecture Notes in Computer Science(), vol 6284. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14888-0_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14888-0_25

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14887-3

  • Online ISBN: 978-3-642-14888-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation