Skip to main content
SpringerLink
Log in
Book cover

International Conference on Inductive Logic Programming

ILP 2000: Inductive Logic Programming pp 253–264Cite as

New Conditions for the Existence of Least Generalizations under Relative Subsumption

  • Conference paper
  • First Online:

  • 237 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1866))

Abstract

Least common generalization under relative subsumption (LGRS) is a fundamental concept in Inductive Logic Programming. In this paper we give several new conditions for the existence of LGRSs. In previous researches the existence of LGRSs was guaranteed when a background theory is logically equivalent to conjunction of finitely many ground literals. Each of our conditions allows a background theory to have clauses with variables in it. The conditions are obtained using the bottom method (or the bottom generalization method), with which any clause subsuming a positive example relative to a background theory can be derived. We also compare the conditions with those for the existence of relative least generalizations under generalized subsumption (LGGSs).

This is a preview of subscription content, 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arikawa, S., Shinohara, T., and Yamamoto, A.:Learning Elementary Formal Systems, Theoretical Computer Science, Vol. 95, No. 1, pp. 97–113(1992).

    Article  MATH  MathSciNet  Google Scholar 

  2. Arimura, H.: Completeness of Depth-Bounded Resolution for Weakly Reducing Programs, in Nakata, I. and Hagiya, M. eds., Software Science and Engineering (World Scientific Series in Computer Science Vol.31), pp. 227–245(1991).

    Google Scholar 

  3. Buntine, W.: Generalized Subsumption and its Applications to Induction and Redundancy, Artificial Intelligence, Vol. 36, pp. 149–176(1988).

    Article  MATH  MathSciNet  Google Scholar 

  4. Ito, K. and Yamamoto, A.: Finding Hypotheses from Examples by Computing the Least Generalization of Bottom Clauses, in Proceedings of the First International Conference on Discovery Science (LNAI) 1532), pp. 303–314, Springer (1998).

    Google Scholar 

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

    Google Scholar 

  6. Lee, R. C. T.: A completeness theorem and a computer program for finding theorems derivable from given axioms, PhD Thesis, University of California, Berkeley, 1967.

    Google Scholar 

  7. Muggleton, S.: Inverse Entailment and Progol, New Generation Computing, Vol. 13, pp. 245–286(1995).

    Google Scholar 

  8. Muggleton, S. and Feng, C.: Efficient Induction of Logic Programs, in S. Arikawa and S. Goto and S. Ohsuga and T. Yokomori, ed., Proceedings of the First International Workshop on Algorithmic Learning Theory, pp. 368–381, JSAI (1990).

    Google Scholar 

  9. Niblett, T.: A Study of Generalization in Logic Programming, in D. Sleeman, ed., Proceedings of the 3rd European Workingsessions on Learning (EWSL-88), pp. 131–138(1988).

    Google Scholar 

  10. Nienhuys-Cheng, S.-H. and de Wolf, R.: Foundations of Inductive Logic Programming (LNAI 1228), Springer (1997).

    Google Scholar 

  11. Plotkin, G. D.: A Note on Inductive Generalization, in Machine Intelligence5, pp. 153–163, Edinburgh University Press (1970).

    MathSciNet  Google Scholar 

  12. Plotkin, G. D.: A Further Note on Inductive Generalization, in Machine Intelligence 6, pp. 101–124, Edinburgh University Press (1971).

    MathSciNet  MATH  Google Scholar 

  13. Plotkin, G. D.: Automatic Methods of Inductive Inference, PhD thesis, Edinburgh University (1971).

    Google Scholar 

  14. Reynolds, J. C.: Transformational Systems and the Algebraic Structure of Atomic Formulas, in Machine Intelligence5, pp. 135–151, Edinburgh University Press (1970).

    MathSciNet  Google Scholar 

  15. Shapiro, E.: Alternation and the Computational Complexity of Logic Programs, J. Logic Programming, Vol. 1, No. 1 (1984).

    Google Scholar 

  16. Shinohara, T.: Inductive Inference of Monotonic Formal Systems from Positive Data, New Generation Computing, Vol. 8, pp. 371–384(1991).

    MATH  Google Scholar 

  17. Yamamoto, A.: Representing Inductive Inference with SOLD-Resolution, in Proceedings of the IJCAI’97 Workshop on Abduction and Induction in AI, pp. 59–63 (1997).

    Google Scholar 

  18. Yamamoto, A.: Which Hypotheses Can Be Found with Inverse Entailment?, in Proceedings of the Seventh International Workshop on Inductive Logic Programming (LNAI 1297), pp. 296–308 (1997). The extended abstract is in Proceedings of the IJCAI’97 Workshop on Frontiers of Inductive Logic Programming, pp.19–-23 (1997).

    Google Scholar 

  19. Yamamoto, A.: An Inference Method for the Complete Inverse of Relative Sub-sumption, New Generation Computing, Vol. 17, No. 1, pp. 99–117(1999).

    Google Scholar 

  20. Yamamoto, A.: Revising the Logical Foundations of Inductive Logic Programming Systems with Ground Reduced Programs, New Generation Computing, Vol. 17, No. 1, pp. 119–127 (1999).

    Article  Google Scholar 

  21. Yamamoto, A.: Using Abduction for Induction based on Bottom Generalization, in A. Kakas and P. Flach (eds.) Abductive and Inductive Reasoning: Essays on their Relation and Integration, pp. 99–117 2000).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Technology and MemeMedia Laboratory, Hokkaido University, Japan

    Akihiro Yamamoto

  2. Information and Human Activity, PRESTO, JST MemeMedia Laboratory, N 13 W 8, Sapporo, 060-8628, Japan

    Akihiro Yamamoto

Authors
  1. Akihiro Yamamoto
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of York, Heslington, York, YO10 5DD, UK

    James Cussens  & Alan Frisch  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Yamamoto, A. (2000). New Conditions for the Existence of Least Generalizations under Relative Subsumption. In: Cussens, J., Frisch, A. (eds) Inductive Logic Programming. ILP 2000. Lecture Notes in Computer Science(), vol 1866. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44960-4_16

Download citation

  • DOI: https://doi.org/10.1007/3-540-44960-4_16

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67795-6

  • Online ISBN: 978-3-540-44960-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation