IPMU 1990: Uncertainty in Knowledge Bases pp 1-13

# On Spohn's theory of epistemic beliefs

• Prakash P. Shenoy
1. Mathematical Theory Of Evidence
Part of the Lecture Notes in Computer Science book series (LNCS, volume 521)

## 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.

### Key words

Spohn's theory consistent epistemic state content of an epistemic state disbelief function Spohnian belief function Spohn's rules for belief revision A,α-conditionalization λ-conditionalization rule of combination for disbelief functions rule of subtraction for disbelief functions axioms for local computation of marginals

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