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Logical Characterisations of Inductive Learning

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Abductive Reasoning and Learning

Part of the book series: Handbook of Defeasible Reasoning and Uncertainty Management Systems ((HAND,volume 4))

Abstract

This chapter aims to develop a logical account of inductive reasoning, one of the most important ways to synthesise new knowledge. Induction provides an idealised model for empirical sciences, where one aims to develop general theories that account for phenomena observed in controlled experiments. It also provides an idealised model for cognitive processes such as learning concepts from instances. The advent of the computer has suggested new inductive tasks such as program synthesis from examples of input-output behaviour and knowledge discovery in databases, and the application of inductive methods to artificial intelligence problems is an active research area, which has displayed considerable progress over the last decades.

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References

  1. D. Angluin and C.H. Smith. Inductive inference: theory and methods. Computing Surveys, 15, 238–269, 1983.

    Article  Google Scholar 

  2. J. Bell. Pragmatic logics. In Proceedings Second International Conference on Knowledge Representation and Reasoning KR’91, pp. 50–60, Morgan Kaufmann, San Mateo, 1991.

    Google Scholar 

  3. J. van Benthem. Reasoning in reverse. In [Flach and Kakas, 2000 ].

    Google Scholar 

  4. R. Carnap. Logical Foundations of Probability. Routledge Kegan Paul, London, 1950.

    Google Scholar 

  5. J. P. Delgrande. A formal approach to learning from examples. Int..1. Man-Machine Studies 26: 123–141, 1987.

    Article  Google Scholar 

  6. L. De Raedt and M. Bruynooghe. A theory of clausal discovery. In Proceedings Thirteenth International Conference on Artificial Intelligence IJCAI’93, pp. 1058–1063. Morgan Kaufmann, San Mateo, 1993.

    Google Scholar 

  7. Flach, 1990] P.A. Flach. Inductive characterisation of database relations. In Proceedings International Symposium on Methodologies for Intelligent Systems ISMIS’90,Z.W. Ras, M. Zemankowa and M.L. Emrich (eds.), pp. 371–378. North-Holland, Amsterdam.

    Google Scholar 

  8. P.A. Flach. Predicate invention in Inductive Data Engineering. In Proceedings European Conference on Machine Learning ECML’93, P.B. Brazdil (ed.), pp. 83–94. Lecture Notes in Artificial Intelligence 667, Springer-Verlag, Berlin, 1993.

    Google Scholar 

  9. P.A. Flach. Conjectures: an inquiry concerning the logic of induction. PhD thesis, Tilburg University, 1995.

    Google Scholar 

  10. P.A. Flach. Rationality postulates for induction. In Proceedings Theoretical Aspects of Rationality and Knowledge TARK’96, Yoav Shoham (ed.), pp. 267–281. Morgan Kaufmann, San Mateo, 1996.

    Google Scholar 

  11. P.A. Flach. Comparing consequence relations. In Proceedings Sixth International Conference on Knowledge Representation and Reasoning KR’98, A.G. Cohn, L. Schubert and S.C. Shapiro (eds.), pp. 180–189. Morgan Kaufmann, San Mateo, 1998.

    Google Scholar 

  12. P.A. Flach. Knowledge representation for inductive learning. In Proceedings Symbolic and Quantitative Approaches to Reasoning and Uncertainty ECSQARU’99, A. Hunter and S. Parsons (eds.), pp. 160–167. Lecture Notes in Artificial Intelligence 1638, Springer-Verlag, Berlin, 1999.

    Google Scholar 

  13. P.A. Flach and I. Savnik. Database dependency discovery: a Machine Learning approach. AI Communications 12 (3): 139–160, 1999.

    Google Scholar 

  14. Flach and Lachiche, forthcoming] P.A. Flach and N. Lachiche. Confirmation-guided discovery of first-order rules with Tertius. Machine Learning,accepted for publication.

    Google Scholar 

  15. P.A. Flach and A.C. Kakas, editors. Abductive and inductive reasoning: essays on their relation and integration. Kluwer Academic Publishers, 2000.

    Google Scholar 

  16. D.M. Gabbay. Theoretical foundations for non-monotonic reasoning in expert systems. In Logics and Models of Concurrent Systems, K.R. Apt (ed.), pp. 439–457. Springer-Verlag, Berlin, 1985.

    Google Scholar 

  17. N.R. Hanson. The logic of discovery. J. Philosophy 55: 1073–1089, 1958.

    Article  Google Scholar 

  18. N. Helft. Induction as nonmonotonic inference. In Proceedings First International Conference on Knowledge Representation and Reasoning KR’89, pp. 149–156. Morgan Kaufmann, San Mateo, 1989.

    Google Scholar 

  19. C.G. Hempel. A purely syntactical definition of confirmation. J. Symbolic Logic 6: 122–143, 1943.

    Article  Google Scholar 

  20. C.G. Hempel. Studies in the logic of confirmation. Mind 54:1–26 (Part I); 54: 97–121 (Part II), 1945.

    Google Scholar 

  21. R.E. Jennings, C.W. Chan and M.J. Dowad. Generalised inference and inferential modelling. In Proceedings Twelfth International Joint Conference on Artificial Intelligence IJCAT 91, pp. 1046–1051. Morgan Kaufmann, 1991.

    Google Scholar 

  22. S. Kraus, D. Lehmann and M. Magidor. Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence 44: 167–207, 1990.

    Article  Google Scholar 

  23. N. Lachiche. Abduction and induction from a non-monotonic reasoning perspective. In [Flach and Kakas, 2000 ].

    Google Scholar 

  24. D. Lehmann and M. Magidor. What does a conditional knowledge base entail? Artificial Intelligence 55: 1–60, 1992.

    Article  Google Scholar 

  25. D. Makinson. General theory of cumulative inference. In Proceedings Second International Workshop on Non-Monotonic Reasoning, M. Reinfrank, J. de Kleer, M.L. Ginsberg and E. Sandewall (eds.), pp. 1–18. Lecture Notes in Artificial Intelligence 346, Springer-Verlag, Berlin, 1989.

    Google Scholar 

  26. J. S. Mill. A System of Logic, Reprinted in The Collected Works of John Stuart Mill, J.M. Robson (ed.), Routledge and Kegan Paul, London, 1843.

    Google Scholar 

  27. S. Muggleton and L. De Raedt. Inductive Logic Programming: theory and methods. J. Logic Programming 19–20: 629–679, 1994.

    Article  Google Scholar 

  28. S. Muggleton and W. Buntine. Machine invention of first-order predicates by inverting resolution. In Proceedings Fifth International Conference on Machine Learning, J. Laird (ed.), pp. 339–352. Morgan Kaufmann, San Mateo, 1988.

    Google Scholar 

  29. A. Tarski. Über den Begriff der logischen Folgering, Actes du Congrès Int. de Philosophie Scientifique 7:1–11, 1936. Translated into English as On the concept of logical consequence. In Logic, Semantics, Metamathematics, A. Tarski, pp. 409–420, Clarendon Press, Oxford, 1956.

    Google Scholar 

  30. W. Zadrozny. On rules of abduction. IBM Research Report, August 1991.

    Google Scholar 

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Flach, P.A. (2000). Logical Characterisations of Inductive Learning. In: Gabbay, D.M., Kruse, R. (eds) Abductive Reasoning and Learning. Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1733-5_4

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  • DOI: https://doi.org/10.1007/978-94-017-1733-5_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5560-6

  • Online ISBN: 978-94-017-1733-5

  • eBook Packages: Springer Book Archive

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