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PAC learning conceptual graphs

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1453))

Abstract

This paper discusses the practical learnability of simple classes of conceptual graphs. We place ourselves in the well studied PAC learnability framework and describe the proof technique we use. We first prove a negative learning result for general conceptual graphs. We then establish positive results by restricting ourselves to classes in which basic operations are polynomial. More precisely, we first state a sufficient condition for the learnability of graphs having a polynomial projection operation. We then extend this result to disjunctions of graphs of bounded size.

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References

  1. A. Blumer, A. Ehrenfeucht, D. Haussler, and M. K. Warmuth. Learnability and the vapnik-chervonenkis dimension. J. ACM, pages 929–965, 1989.

    Google Scholar 

  2. R. J. Brachman and J. Schmolze. An overview of the kl-one knowledge representation system. Cognitive Science, 9: 171–216, 1985.

    Article  Google Scholar 

  3. M. Chein and M.L. Mugnier. Conceptual graphs: Fundamental notions. Revue d'Intelligence Artificielle, pages 365–406, 1992.

    Google Scholar 

  4. W. W. Cohen. Pac-learning non-determinate clauses. In Proc. of AAAI-94, pages 676–681, 1994.

    Google Scholar 

  5. W. W. Cohen and H. Hirsh. The learnability of Description Logic with equality constrain ts. Machine Learning, pages 169–199, 1994.

    Google Scholar 

  6. S. Dzeroski, S. Muggleton, and S. Russel. Pac-learning of determinate logic programs. In Proc. of the 5 th International Conference on Computational Theory, pages 128–137, 1992.

    Google Scholar 

  7. D. Genest. Document retrieval: An approach based on conceptual graphs. Rapport de Recherche LIRMM No 97296, 1998.

    Google Scholar 

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

    Article  MATH  Google Scholar 

  9. D. Haussler. Learning conjunctive concepts in structural domains. Machine Learning, 4: 7–40, 1989.

    Google Scholar 

  10. P. Jappy and O. Gascuel. On the conputational hardness of learning from structured symbolic data. In Proceedings of the 6th Internationl Conference on Ordinal and Symbolic Data Analysis, OSDA95, pages 128–143, 1995.

    Google Scholar 

  11. P. Jappy, R. Nock, and O. Gascuel. Negative robust learning results for horn clause programs. In Proc. of the 13 th International Conference on Machine Learning, 1996.

    Google Scholar 

  12. J.U. Kietz. Some lower bounds for the computational complexity of inductive logic programming. In European Conference on Machine Learning, ECML'93, pages 115–123, 1993.

    Google Scholar 

  13. R.K. Lindzay, B.G. Buchanan, E.A. Feigenbaum, and J. Lederberg. Dendral: a case study of the first expert system for scientific hypothesis formation. Artificial Intelligence, 61: 209–261, 1993.

    Article  Google Scholar 

  14. M. Liquière. Apprentissage à partir d'objets structurés. Conception et Réalisation. PhD thesis, Université de Montpellier II, 1990.

    Google Scholar 

  15. S.H. Muggleton. Inductive Logic Programming. Academic Press. New York, 1992.

    Google Scholar 

  16. S.H. Muggleton. Bayesian inductive logic programming. In COLT94, pages 3–11, 1994.

    Google Scholar 

  17. M.L. Mugnier and M. Chein. Polynomial algorithms for projection and matching. In Proc. of the 7th Workshop on Conceptual Structures, pages 68–76, 1992.

    Google Scholar 

  18. R.H. Richens. Preprogramming for mechanical translation. Mechanical Translation, 3, 1956.

    Google Scholar 

  19. R.L. Rivest. Learning decision lists. Machine Learning, pages 229–246, 1987.

    Google Scholar 

  20. E. Salvat and M.L. Mugnier. Sound and complete forward and backward chaining of graph rules. In Proceeding of the International Conference on Conceptual Structures, ICCS96, pages 248–262, 1996.

    Google Scholar 

  21. R. Shapire. The strength of weak learning. Machine Learning, 5(2), 1990.

    Google Scholar 

  22. E.Y. Shapiro. Algorithmic Program Debugging. Academic Press. New York, 1983.

    Google Scholar 

  23. J.F. Sowa. Conceptual Structures — Information Processinf in Mind and Machine. Addison-Wesley, 1984.

    Google Scholar 

  24. L. G. Valiant. A theory of the learnable. Communications of the ACM, pages 1134–1142, 1984.

    Google Scholar 

  25. L. G. Valiant. Learning disjunctions of conjunctions. In Proc. of the 9 th IJCAI, pages 560–566, 1985.

    Google Scholar 

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Marie-Laure Mugnier Michel Chein

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© 1998 Springer-Verlag Berlin Heidelberg

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Jappy, P., Nock, R. (1998). PAC learning conceptual graphs. In: Mugnier, ML., Chein, M. (eds) Conceptual Structures: Theory, Tools and Applications. ICCS 1998. Lecture Notes in Computer Science, vol 1453. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054923

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  • DOI: https://doi.org/10.1007/BFb0054923

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64791-1

  • Online ISBN: 978-3-540-68673-6

  • eBook Packages: Springer Book Archive

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