A New Approach to Updating Beliefs
Ronald Fagin, Joseph Y. Halpern

TL;DR
This paper introduces a novel definition of conditional belief for Dempster-Shafer belief functions, aligning it with the concept of conditional probability, and addresses limitations of previous definitions by providing a closed-form expression and extending to non-measurable sets.
Contribution
It proposes a new, well-founded approach to defining conditional belief functions that parallels conditional probability and extends to non-measurable sets, improving theoretical understanding.
Findings
Provides a closed-form expression for the new conditional belief
Connects belief functions with inner measures and conditional probabilities
Extends the concept of conditional probability to non-measurable sets
Abstract
We define a new notion of conditional belief, which plays the same role for Dempster-Shafer belief functions as conditional probability does for probability functions. Our definition is different from the standard definition given by Dempster, and avoids many of the well-known problems of that definition. Just as the conditional probability Pr (lB) is a probability function which is the result of conditioning on B being true, so too our conditional belief function Bel (lB) is a belief function which is the result of conditioning on B being true. We define the conditional belief as the lower envelope (that is, the inf) of a family of conditional probability functions, and provide a closed form expression for it. An alternate way of understanding our definition of conditional belief is provided by considering ideas from an earlier paper [Fagin and Halpern, 1989], where we connect belief…
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Taxonomy
TopicsBayesian Modeling and Causal Inference
