Abstract
In both science and everyday life, we use the notion of evidence (e) confirming a hypothesis (h) or a prediction (d). Confirmation theory is an attempt to analyse this crucial notion of confirmation. The degree of confirmation of h given e is written C(h,e). Strictly speaking, the evidence e will be in addition to some background knowledge b. Thus we should really write C(h, e&b). The background knowledge will, however, often be omitted for ease of writing, but it should not be forgotten.
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
A. J. Ayer. Language, Truth and Logic, 2nd Edition. Gollancz, 1946. 15th Impression, 1962.
R. Camap. Logical Foundations of Probability. University of Chicago Press, 1950.2nd Edition, 1963.
R. Carnap. Inductive logic and inductive intuition. In The Problem of Inductive Logic, I. Lakatos, ed. pp. 258–267. North-Holland, 1964
L. J. Cohen. The Implications of Induction. Methuen, 1970.
L. J. Cohen. The Probable and the Provable. University Press, Oxford, 1977.
J. Cussens. Bayes and pseudo-Bayes estimates of conditional probability and their re- liability. In European Conference on Machine Learning (ECML-93), pp. 136–152. Springer-Verlag, 1993.
A. P. Dawid. The difficulty about conjunction. The Statistician, 36, 91–97, 1987.
B. De Finetti. Foresight: its logical laws, its subjective sources. In Studies in Sub-jective Probability, H. E. Kyburg and H. E. Smokier, eds. pp. 95–158. John Wiley, 1937.
B. De Finetti. Teoria delle Probabilità. Einaudi, 1970.
B. De Finetti. The role of `Dutch books’ and of `proper scoring rules’. British Journal for the Philosophy of Science, 32, 55–56, 1981.
J. Earman. Bayes or Bust? A Critical Examination ofBayesian Confirmation Theory. MIT Press, 1992.
A. W. F. Edwards. Likelihood. Cambridge University Press, 1972. Paperback Edition, 1984.
D. A. Gillies. A falsifying rule for probability statements. British Journal for the Philosophy of Science, 22, 231–261, 1971.
D. A. Gillies. Non-Bayesian confirmation theory and the principle of explanatory surplus. In PSA 1988, Vol. 2, pp. 373–380, 1989.
D. A. Gillies. The Turing—Good weight of evidence function and Popper’s measure of the severity of a test. British Journal for the Philosophy of Science, 41, 143–146, 1990.
D. A. Gillies. Intersubjective probability and confirmation theory. British Journal for the Philosophy of Science, 42, 513–533, 1991.
D. A. Gillies. Confirmation theory and machine learning. In Proceedings ofthe International Workshop on Inductive Logic Programming (ILP2), Japan, S. Muggleton and K. Furukawa, eds. pp. 40–51. ICOT Technical Memorandum: TM-1182, 1992.
D. A. Gillies. Philosophy of Science in the Twentieth Century. Four Central Themes. Blackwell, 1993.
C. Glymour. Theory and Evidence. Princeton University Press, 1980.
I. J. Good. A. M. Turings statistical work in world war II. Biometrika, 66, 393–396, 1979.
I. J. Good. Good Thinking. The Foundations of Probability and its Applications. Uni-versity of Minnesota Press, 1983.
I. J. Good. Weight of evidence: a brief survey. In Bayesian Statistics 2, Proceedings of the Second Valencia International Meeting, J. M. Bernardo, M. H. De Groott, D. V. Lindley and A. E M. Smith, eds. North-Holland, 1985.
I. Hacking. Logic of Statistical Inference. Cambridge University Press, 1965.
I. Hacking. Slightly more realistic personal probability. Philosophy of Science, 34, 311–325, 1967.
M. B. Hesse. The Structure of Scientific Inference. Macmillan, 1974.
A. Hodges. Alan Turing. The Enigma of Intelligence. Unwin, 1983. Paperback, 1987.
C. Howson. Must the logical probability of laws be zero? British Journal for the Philosophy of Science, 24, 153–182, 1973.
C. Howson and P. Urbach. Scientific Reasoning. The Bayesian Approach. Open Court, 1989.
D. Hume. An Enquiry concerning Human Understanding. Clarendon Press, Oxford, 1748, 1963.
H. Jeffreys. Theory of Probability. Oxford University Press, 1939.
J. M. Keynes. A Treatise on Probability. Macmillan, 1921, 1963.
I. Lakatos. Changes in the problem of inductive logic. In The Problem of Inductive Logic, I. Lakatos, ed. pp. 315–417. North-Holland, 1968.
S. Muggleton. A strategy for constructing new predicates in first order logic. In Proceedings of the Third European Working Session on Learning, D. Sleeman, ed. pp. 123–130. Pitman, 1988.
S. Muggleton, A. Srinivasan and M. Bain. Compression, significance and accuracy. In Proceedings of the Ninth International Machine Learning Conference,D. Sleeman and P. Edwards, eds. pp. 338–347. Morgan-Kaufmann, 1992.
J. Nicod. Foundations of Geometry and Induction. English translation by P. P. Wiener. Routledge and Kegan Paul, 1930.
K. R. Popper. The Logic of Scientific Discovery. Sixth Impression (Revised) of the 1959 English Translation, pp. 27–305. Hutchinson, 1934, 1972.
K. R. Popper. The Logic of Scientific Discovery. Sixth Impression (Revised) of the 1959 English Translation, pp. 309–464. Hutchinson, 1959, 1972.
K. R. Popper. Conjectures and Refutations. Routledge and Kegan Paul, 1963.
H. Putnam. Degree of confirmation and inductive logic. In Mathematics, Matter and Method. Philosophical Papers, Vol. 1, 2nd Edition, 1980, Chapter 17, pp. 270–292. Cambridge Uni-versity Press, 1963. Originally published in The Philosophy of Rudolf Carnap, P. A. Schilpp, ed. Open Court, 1963.
F. P. Ramsey. Truth and probability. In The Foundations of Mathematics and other Logical Essays, R. B. Braithwaite, ed. pp. 156–198. Routledge and Kegan Paul, 1926, 1931.
E P. Ramsey. Last Papers. In The Foundations of Mathematics and other Logical Es-says, R. B. Braithwaite, ed. pp. 212–269. Routledge and Kegan Paul, 1929, 1931.
G. Shafer. A Mathematical Theory of Evidence, Princeton University Press, 1976.
A. Srinivasan, S. Muggleton and M. Bain. The justification of logical theories based on data compression. In Machine Intelligence 13, K. Furukawa, D. Michie and S. Muggleton, eds. pp. 87–121. Oxford University Press, 1994.
L. Wittgenstein. Tractatus Logico-Philosophicus. English translation by D. E. Pears and B. F McGuinness. Routledge and Kegan Paul, 1963.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Gillies, D. (1998). Confirmation Theory. In: Smets, P. (eds) Quantified Representation of Uncertainty and Imprecision. Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1735-9_5
Download citation
DOI: https://doi.org/10.1007/978-94-017-1735-9_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5038-0
Online ISBN: 978-94-017-1735-9
eBook Packages: Springer Book Archive