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Minimal Generalizations under OI-Implication

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Book cover Foundations of Intelligent Systems (ISMIS 2002)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2366))

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Abstract

The adoption of the object identity bias for weakening implication has lead to the definition of OI-implication, a generalization model for clausal spaces. In this paper, we investigate on the generalization hierarchy in the space ordered by OI-implication. The decidability of this relationship and the existence of minimal generalizations in the related search space is demonstrated. These results can be exploited for constructing refinement operators for incremental relational learning.

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References

  1. L Badea and M. Stanciu. Refinement operators can be (weakly) perfect. In S. Džeroski and P. Flach, editors, Proceedings of the 9th International Workshop on Inductive Logic Programming, volume 1634 of LNAI, pages 21–32. Springer, 1999.

    Google Scholar 

  2. F. Esposito, N. Fanizzi, S. Ferilli, and G. Semeraro. A generalization model based on OI-implication for ideal theory refinement. Fundamenta Informaticae, 47:15–33, 2001.

    MATH  MathSciNet  Google Scholar 

  3. F. Esposito, N. Fanizzi, S. Ferilli, and G. Semeraro. OI-implication: Soundness and refutation completeness. In B. Nebel, editor, Proceedings of the 17th International Joint Conference on Artificial Intelligence, pages 847–852, Seattle, WA, 2001.

    Google Scholar 

  4. G. Gottlob. Subsumption and implication. Information Processing Letters, 24(2):109–111, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  5. G. Gottlob and C.G. Fermüller. Removing redundancy from a clause. Artificial Intelligence, 61:263–289, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  6. P. Idestam-Almquist. Generalization of clauses under implication. Journal of Artificial Intelligence Research, 3:467–489, 1995.

    MATH  Google Scholar 

  7. R. Khardon. Learning function-free Horn expressions. Machine Learning, 37(3):241–275, December 1999.

    Google Scholar 

  8. Jörg-Uwe Kietz. A comparative study of structural most specific generalisations used in machine learning. In Proceedings of the Third International Workshop on Inductive Logic Programming, pages 149–164, Ljubljana, Slovenia, 1993. J. Stefan Institute Technical Report IJS-DP-6707.

    Google Scholar 

  9. S.-H. Nienhuys-Cheng and R. de Wolf. Foundations of Inductive Logic Programming, volume 1228 of LNAI. Springer, 1997.

    Google Scholar 

  10. M. Schmidt-Schauss. Implication of clauses is undecidable. Theoretical Computer Science, 59:287–296, 1988.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Università degli Studi di Bari, Via E. Orabona 4, I-70125, Bari, Italy

    Nicola Fanizzi & Stefano Ferilli

Authors
  1. Nicola Fanizzi
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  2. Stefano Ferilli
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Editor information

Editors and Affiliations

  1. UFR d’Informatique, Université Claude Bernard Lyon I, 8, boulevard Niels Bohr, 69622, Villeurbanne Cedex, France

    Mohand-Saïd Hacid

  2. Dept. of Computer Science College of IT, University of North Carolina, Charlotte, NC, 28223, USA

    Zbigniew W. Raś

  3. Băt. L. Equipe de Recherche en Ingénierie des Connaissances, Université Lumière Lyon 2, 5, avenue Pierre Mendes-France, 69676, Bron Cedex, France

    Djamel A. Zighed

  4. LRI, Université Paris Sud, Băt. 490, 91405, Orsay Cedex, France

    Yves Kodratoff

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© 2002 Springer-Verlag Berlin Heidelberg

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Fanizzi, N., Ferilli, S. (2002). Minimal Generalizations under OI-Implication. In: Hacid, MS., Raś, Z.W., Zighed, D.A., Kodratoff, Y. (eds) Foundations of Intelligent Systems. ISMIS 2002. Lecture Notes in Computer Science(), vol 2366. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48050-1_17

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  • DOI: https://doi.org/10.1007/3-540-48050-1_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43785-7

  • Online ISBN: 978-3-540-48050-1

  • eBook Packages: Springer Book Archive

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