Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Artificial General Intelligence

The Journal of the Artificial General Intelligence Society

3 Issues per year

Open Access
Online
ISSN
1946-0163
See all formats and pricing
More options …

Formalization of Evidence: A Comparative Study

Pei Wang
Published Online: 2011-11-23 | DOI: https://doi.org/10.2478/v10229-011-0003-7

Formalization of Evidence: A Comparative Study

This article analyzes and compares several approaches of formalizing the notion of evidence in the context of general-purpose reasoning system. In each of these approaches, the notion of evidence is defined, and the evidence-based degree of belief is represented by a binary value, a number (such as a probability), or two numbers (such as an interval). The binary approaches provide simple ways to represent conclusive evidence, but cannot properly handle inconclusive evidence. The one-number approaches naturally represent inconclusive evidence as a degree of belief, but lack the information needed to revise this degree. It is argued that for systems opening to new evidence, each belief should at least have two numbers attached to indicate its evidential support. A few such approaches are discussed, including the approach used in NARS, which is designed according to the considerations of general-purpose intelligent systems, and provides novel solutions to several traditional problems on evidence.

Keywords: evidence; degree of belief; logic; probability; weight of evidence; revision; ignorance; evidential reasoning; general-purpose system

  • Achinstein, P., ed. 1983. The Concept of Evidence. Oxford: Oxford University Press.Google Scholar

  • Baroni, P., and Vicig, P. 2001. On the conceptual status of belief functions with respect to coherent lower probabilities. In Bishop, C., ed., Proceedings of the 6th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty; Lecture Notes In Computer Science, Vol. 2143. London: Springer-Verlag. 328-339.Google Scholar

  • Bonissone, P. P. 1987. Summarizing and propagating uncertain information with Triangular Norms. International Journal of Approximate Reasoning 1:71-101.CrossrefGoogle Scholar

  • Carnap, R. 1950. Logical Foundations of Probability. Chicago: The University of Chicago Press.Google Scholar

  • Cheeseman, P. 1988. An inquiry into computer understanding. Computational Intelligence 4:58-66.CrossrefGoogle Scholar

  • Clifford, W. K. 1877. The ethics of belief. Contemporary Review. Reprinted in The Ethics of Belief and Other Essays (Prometheus Books, 1999).Google Scholar

  • DeGroot, M. H. 1970. Optimal Statistical Decisions. New York: McGraw-Hill.Google Scholar

  • Dempster, A. P. 1967. Upper and lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics 38:325-339.CrossrefGoogle Scholar

  • Dubois, D., and Prade, H. 1982. A class of fuzzy measures based on triangular norms. International Journal of General Systems 8:43-61.CrossrefGoogle Scholar

  • Dubois, D., and Prade, H. 1994. Conditional objects as nonmonotonic consequence relationships. IEEE Transactions on Systems, Man, and Cybernetics 24:1724-1740.CrossrefGoogle Scholar

  • Fitelson, B., and Hawthorne, J. 2009. How Bayesian confirmation theory handles the Paradox of the Ravens. In Eells, E., and Fetzer, J., eds., Probability in Science. Chicago: Open Court. Forthcoming.Google Scholar

  • Good, I. J. 1950. Probability and the Weighing of Evidence. London: Griffin.Google Scholar

  • Good, I. J. 1985. Weight of evidence: a brief survey. In Bernardo, J.; DeGroot, M.; Lindley, D.; and Smith, A., eds., Bayesian Statistics 2. Amsterdam: North-Holland. 249-269.Google Scholar

  • Griggs, R. A., and Cox, J. R. 1982. The elusive thematic-materials effect in Wason's selection task. British Journal of Psychology 73:407-420.CrossrefGoogle Scholar

  • Halpern, J. Y., and Pucella, R. 2006. A logic for reasoning about evidence. Journal of Artificial Intelligence Research 26:1-34.Google Scholar

  • Hempel, C. G. 1965. Studies in the logic of confirmation. In Aspects of Scientific Explanation. New York: The Free Press. 3-46. Reprinted in The Concept of Evidence, Achinstein, P. (Ed), Oxford University Press, pp. 11-43, 1983.Google Scholar

  • Hume, D. 1748. An Enquiry Concerning Human Understanding. London.Google Scholar

  • Hutter, M. 2005. Universal Artificial Intelligence: Sequential Decisions based on Algorithmic Probability. Berlin: Springer.Google Scholar

  • Keynes, J. M. 1921. A Treatise on Probability. London: Macmillan.Google Scholar

  • Kyburg, H. E. 1983a. Recent work in inductive logic. In Lucey, K., and Machan, T., eds., Recent Work in Philosophy. Totowa, NJ: Rowman and Allanfield. 89-150.Google Scholar

  • Kyburg, H. E. 1983b. The reference class. Philosophy of Science 50:374-397.CrossrefGoogle Scholar

  • Kyburg, H. E. 1994. Believing on the basis of the evidence. Computational Intelligence 10:3-20.Google Scholar

  • McCarthy, J., and Hayes, P. J. 1969. Some philosophical problems from the standpoint of artificial intelligence. In Meltzer, B., and Michie, D., eds., Machine Intelligence 4. Edinburgh: Edinburgh University Press. 463-502.Google Scholar

  • McDermott, D. 1987. A critique of pure reason. Computational Intelligence 3:151-160.CrossrefGoogle Scholar

  • Milne, P. 1997. Bruno de Finetti and the logic of conditional events. The British Journal for the Philosophy of Science 48:195-232.CrossrefGoogle Scholar

  • Oaksford, M., and Chater, N. 1994. A rational analysis of the selection task as optimal data selection. Psychological Review 101:608-631.CrossrefGoogle Scholar

  • Pearl, J. 1988. Probabilistic Reasoning in Intelligent Systems. San Mateo, California: Morgan Kaufmann Publishers.Google Scholar

  • Pearl, J. 1990. Jeffrey's rule, passage of experience, and Neo-Bayesianism. In Kyburg, H. E.; Loui, R. P.; and N., C. G., eds., Knowledge Representation and Defeasible Reasoning. Amsterdam: Kluwer Academic Publishers. 245-265.Google Scholar

  • Peirce, C. S. 1878. The probability of induction. Popular Science Monthly 12:705-718. Reprinted in The Essential Peirce, Vol. 1, N. Houser and C. Kloesel, eds., Bloomington, IN: Indiana University Press (1992), 155-169.Google Scholar

  • Popper, K. R. 1959. The Logic of Scientific Discovery. New York: Basic Books.Google Scholar

  • Reiter, R. 1987. Nonmonotonic reasoning. Annual Review of Computer Science 2:147-186.CrossrefGoogle Scholar

  • Rescher, N. 1958. A theory of evidence. Philosophy of Science 25(1):83-94.CrossrefGoogle Scholar

  • Shafer, G. 1976. A Mathematical Theory of Evidence. Princeton, New Jersey: Princeton University Press.Google Scholar

  • Smets, P., and Kennes, R. 1994. The transferable belief model. Artificial Intelligence 66:191-234.CrossrefGoogle Scholar

  • Smets, P. 1991. The transferable belief model and other interpretations of Dempster-Shafer's model. In Bonissone, P. P.; Henrion, M.; Kanal, L. N.; and Lemmer, J. F., eds., Uncertainty in Artificial Intelligence 6. Amsterdam: North-Holland. 375-383.Google Scholar

  • Solomonoff, R. J. 1964. A formal theory of inductive inference. Part I and II. Information and Control 7(1-2):1-22,224-254.CrossrefGoogle Scholar

  • Tversky, A., and Kahneman, D. 1974. Judgment under uncertainty: heuristics and biases. Science 185:1124-1131.Google Scholar

  • Tversky, A., and Kahneman, D. 1983. Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment. Psychological Review 90:293-315.CrossrefGoogle Scholar

  • Walley, P. 1991. Statistical Reasoning with Imprecise Probabilities. London: Chapman and Hall.Google Scholar

  • Walley, P. 1996a. Inferences from multinomial data: learning about a bag of marbles. Journal of the Royal Statistical Society, Series B 58:3-57.Google Scholar

  • Walley, P. 1996b. Measures of uncertainty in expert systems. Artificial Intelligence 83:1-58.CrossrefGoogle Scholar

  • Wang, P. 1993. Belief revision in probability theory. In Proceedings of the Ninth Conference on Uncertainty in Artificial Intelligence, 519-526. Morgan Kaufmann Publishers, San Mateo, California.Google Scholar

  • Wang, P. 1994a. A defect in Dempster-Shafer Theory. In Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence, 560-566. Morgan Kaufmann Publishers, San Mateo, California.Google Scholar

  • Wang, P. 1994b. From inheritance relation to nonaxiomatic logic. International Journal of Approximate Reasoning 11(4):281-319.CrossrefGoogle Scholar

  • Wang, P. 1995a. Non-Axiomatic Reasoning System: Exploring the Essence of Intelligence. Ph.D. Dissertation, Indiana University.Google Scholar

  • Wang, P. 1995b. Reference classes and multiple inheritances. International Journal of Uncertainty, Fuzziness and and Knowledge-based Systems 3(1):79-91.Google Scholar

  • Wang, P. 1996a. Heuristics and normative models of judgment under uncertainty. International Journal of Approximate Reasoning 14(4):221-235.CrossrefGoogle Scholar

  • Wang, P. 1996b. The interpretation of fuzziness. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 26(4):321-326.CrossrefGoogle Scholar

  • Wang, P. 2001a. Abduction in non-axiomatic logic. In Working Notes of the IJCAI workshop on Abductive Reasoning, 56-63.Google Scholar

  • Wang, P. 2001b. Confidence as higher-order uncertainty. In Proceedings of the Second International Symposium on Imprecise Probabilities and Their Applications, 352-361.Google Scholar

  • Wang, P. 2001c. Wason's cards: what is wrong? In Proceedings of the Third International Conference on Cognitive Science, 371-375.Google Scholar

  • Wang, P. 2004. The limitation of Bayesianism. Artificial Intelligence 158(1):97-106.CrossrefGoogle Scholar

  • Wang, P. 2005. Experience-grounded semantics: a theory for intelligent systems. Cognitive Systems Research 6(4):282-302.CrossrefGoogle Scholar

  • Wang, P. 2006. Rigid Flexibility: The Logic of Intelligence. Dordrecht: Springer.Google Scholar

  • Wason, P. C., and Johnson-Laird, P. N. 1972. Psychology of Reasoning: Structure and Content. Cambridge, Massachusetts: Harvard University Press.Google Scholar

  • Zadeh, L. A. 1975. The concept of a linguistic variable and its application to approximate reasoning. Information Sciences 8:199-249, 8:301-357, 9:43-80.CrossrefGoogle Scholar

About the article


Published Online: 2011-11-23

Published in Print: 2009-12-01


Citation Information: Journal of Artificial General Intelligence, ISSN (Online) 1946-0163, DOI: https://doi.org/10.2478/v10229-011-0003-7.

Export Citation

This content is open access.

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Hanns Sommer and Lothar Schreiber
Journal of Artificial General Intelligence, 2012, Volume 3, Number 1
[2]
Yingjin Xu and Pei Wang
Synthese, 2012, Volume 187, Number S1, Page 43

Comments (0)

Please log in or register to comment.
Log in