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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D. Angluin and C.H. Smith. Inductive inference: theory and methods. Computing Surveys, 15, 238–269, 1983.
J. Bell. Pragmatic logics. In Proceedings Second International Conference on Knowledge Representation and Reasoning KR’91, pp. 50–60, Morgan Kaufmann, San Mateo, 1991.
J. van Benthem. Reasoning in reverse. In [Flach and Kakas, 2000 ].
R. Carnap. Logical Foundations of Probability. Routledge Kegan Paul, London, 1950.
J. P. Delgrande. A formal approach to learning from examples. Int..1. Man-Machine Studies 26: 123–141, 1987.
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.
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.
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.
P.A. Flach. Conjectures: an inquiry concerning the logic of induction. PhD thesis, Tilburg University, 1995.
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.
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.
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.
P.A. Flach and I. Savnik. Database dependency discovery: a Machine Learning approach. AI Communications 12 (3): 139–160, 1999.
Flach and Lachiche, forthcoming] P.A. Flach and N. Lachiche. Confirmation-guided discovery of first-order rules with Tertius. Machine Learning,accepted for publication.
P.A. Flach and A.C. Kakas, editors. Abductive and inductive reasoning: essays on their relation and integration. Kluwer Academic Publishers, 2000.
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.
N.R. Hanson. The logic of discovery. J. Philosophy 55: 1073–1089, 1958.
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.
C.G. Hempel. A purely syntactical definition of confirmation. J. Symbolic Logic 6: 122–143, 1943.
C.G. Hempel. Studies in the logic of confirmation. Mind 54:1–26 (Part I); 54: 97–121 (Part II), 1945.
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.
S. Kraus, D. Lehmann and M. Magidor. Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence 44: 167–207, 1990.
N. Lachiche. Abduction and induction from a non-monotonic reasoning perspective. In [Flach and Kakas, 2000 ].
D. Lehmann and M. Magidor. What does a conditional knowledge base entail? Artificial Intelligence 55: 1–60, 1992.
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.
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.
S. Muggleton and L. De Raedt. Inductive Logic Programming: theory and methods. J. Logic Programming 19–20: 629–679, 1994.
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.
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.
W. Zadrozny. On rules of abduction. IBM Research Report, August 1991.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
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
Download citation
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