On Spohn's theory of epistemic beliefs
 Prakash P. Shenoy
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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 DempsterShafer theory of belief functions. One implication of this is that we have a readymade algorithm for propagating disbelief functions using only local computation.
 Title
 On Spohn's theory of epistemic beliefs
 Book Title
 Uncertainty in Knowledge Bases
 Book Subtitle
 3rd International Conference on Information Processing and Management of Uncertainty in KnowledgeBased Systems, IPMU '90 Paris, France, July 2–6, 1990 Proceedings
 Pages
 pp 113
 Copyright
 1991
 DOI
 10.1007/BFb0028091
 Print ISBN
 9783540543466
 Online ISBN
 9783540475804
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 521
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Spohn's theory
 consistent epistemic state
 content of an epistemic state
 disbelief function
 Spohnian belief function
 Spohn's rules for belief revision
 A,αconditionalization
 λconditionalization
 rule of combination for disbelief functions
 rule of subtraction for disbelief functions
 axioms for local computation of marginals
 Industry Sectors
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 Editors
 Authors

 Prakash P. Shenoy ^{(1)}
 Author Affiliations

 1. School of Business, University of Kansas, 660452003, Lawrence, KS, USA
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