Abstract
This paper is about Spohn's theory of epistemic beliefs. The main ingredients of Spohn's theory are (i) a functional representation of an epistemic state called a disbelief function, and (ii) a rule for revising this function in light of new information. The main contribution of this paper is as follows. First, we provide a new axiomatic definition of an epistemic state and study some of its properties. Second, we state a rule for combining disbelief functions that is mathematically equivalent to Spohn's belief revision rule. Whereas Spohn's rule is defined in terms of the initial epistemic state and some features of the final epistemic state, the rule of combination is defined in terms of the initial epistemic state and the incremental epistemic state representing the information gained. Third, we state a rule of subtraction that allows one to recover the addendum epistemic state from the initial and final epistemic states. Fourth, we study some properties of our rule of combination. One distinct advantage of our rule of combination is that besides belief revision, it can also be used to describe an initial epistemic state for many variables when this information is provided in the form of several independent epistemic states each involving a small number of variables. Another advantage of our reformulation is that we are able to demonstrate that Spohn's theory of epistemic beliefs shares the essential abstract features of probability theory and the Dempster-Shafer theory of belief functions. One implication of this is that we have a ready-made algorithm for propagating disbelief functions using only local computation.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Dempster, A. P. (1968), A generalization of Bayesian inference, Journal of Royal Statistical Society, Series B, 30, 205–247.
Dubois, D. and Prade, H. (1988), Possibility Theory: An Approach to Computerized Processing of Uncertainty, Plenum Publishing Company, New York.
Dubois, D. and Prade, H. (1990), Epistemic entrenchment and possibilistic logic, unpublished manuscript.
Gardenfors, P. (1988), Knowledge in Flux: Modeling the Dynamics of Epistemic States, MIT Press, Cambridge, MA.
Geiger, D. and Pearl, J. (1990), On the logic of causal models, Uncertainty in Artificial Intelligence 4, Shachter, R., Levitt, T., Lemmer, J and Kanal, L., eds., 3–14, North-Holland.
Ginsberg, M. L. (1984), Non-monotonic reasoning using Dempster's rule, Proceedings of the Third National Conference on Artificial Intelligence (AAAI-84), 126–129, Austin, TX.
Hunter, D. (1988), Graphoids, semi-graphoids, and ordinal conditional functions, unpublished manuscript.
Hunter, D. (1990), Parallel belief revision, Uncertainty in Artificial Intelligence 4, Shachter, R., Levitt, T., Lemmer, J and Kanal, L., eds., 241–252, North-Holland.
Jeffrey, R. C. (1983), The Logic of Decision, 2nd edition, Chicago University Press
Pearl, J. (1988), Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, Morgan-Kaufmann.
Pearl, J. (1989). Probabilistic semantics for nonmonotonic reasoning: A survey, Proceedings of the First International Conference on Principles of Knowledge Representation and Reasoning, Toronto, Canada, pp. 505–516.
Shafer, G. (1976), A Mathematical Theory of Evidence, Princeton University Press, Princeton, NJ.
Shafer, G. (1984), The problem of dependent evidence, School of Business Working Paper No. 164, University of Kansas, Lawrence, KS.
Shafer, G. (1987), Belief functions and possibility measures, in Analysis of Fuzzy Information, volume I: Mathematics and Logic, Bezdek, J. C. (ed.), 51–84, CRC Press.
Shenoy, P. P. (1989), A valuation-based language for expert systems, International Journal of Approximate Reasoning, 3(5), 359–416.
Shenoy, P. P. (1989b), On Spohn's rule for revision of beliefs, School of Business Working Paper No. 213, University of Kansas, Lawrence, KS. To appear in International Journal of Approximate Reasoning in 1991.
Shenoy, P. P. and Shafer, G. (1988), An axiomatic framework for Bayesian and belief-function propagation, Proceedings of the Fourth Workshop on Uncertainty in Artificial Intelligence, 307–314, Minneapolis, MN.
Shenoy, P. P. and Shafer, G. (1990), Axioms for probability and belief-function propagation, Uncertainty in Artificial Intelligence 4, Shachter, R., Levitt, T., Lemmer, J and Kanal, L., eds., 169–198, North-Holland.
Spohn, W. (1988), Ordinal conditional functions: A dynamic theory of epistemic states, in Harper, W. L. and Skyrms, B. (eds.), Causation in Decision, Belief Change, and Statistics, II, 105–134, D. Reidel Publishing Company.
Spohn, W. (1990), A general non-probabilistic theory of inductive reasoning, Uncertainty in Artificial Intelligence 4, Shachter, R., Levitt, T., Lemmer, J and Kanal, L., eds., 149–158, North-Holland.
Verma, T. and Pearl, J. (1990), Causal networks: Semantics and expressiveness, Uncertainty in Artificial Intelligence 4, Shachter, R., Levitt, T., Lemmer, J and Kanal, L., eds., 69–78, North-Holland.
Zadeh, L. A. (1978), Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1, 3–28.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Shenoy, P.P. (1991). On Spohn's theory of epistemic beliefs. In: Bouchon-Meunier, B., Yager, R.R., Zadeh, L.A. (eds) Uncertainty in Knowledge Bases. IPMU 1990. Lecture Notes in Computer Science, vol 521. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028091
Download citation
DOI: https://doi.org/10.1007/BFb0028091
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54346-6
Online ISBN: 978-3-540-47580-4
eBook Packages: Springer Book Archive