# Catalogue of Artificial Intelligence Techniques

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## Dempster-Shafer Theory

Aliases: Belief Functions

### Categories: Inference and Reasoning

Author(s): Judea Pearl

A theory of evidence potentially suitable for knowledge-based systems, especially when domain knowledge can be stated in categorical terms and the impact of each item of evidence described as an assignment of probabilities to a set of propositions. They include strict taxonomic hierarchies, terminological definitions and descriptions of deterministic systems (e.g., electronic circuits). The probability $m\left(A\right)$ attached to $A$ is the degree to which the evidence supports $A$, but $m\left(A\right)$ need not be $1-m\left(-A\right)$, since evidence can lend support to a hypothesis while having no direct bearing on its negation. These `basic probabilities' can be visualised as probability masses constrained within the subset (of worlds) with which they are associated, but free to move over every point there. From these basic probabilities we can derive upper and lower probabilities (Dempster) or belief functions and plausibilities (Shafer). The belief measure $Bel\left(A\right)$ is the probability that $A$ logically follows from the evidence, given that all items of evidence are non-contradictory. This notion of `belief' often behaves differently than $P\left(A\right)$, the probability that is true. Basic probabilities are combined using Dempster's Rule, which is valid for independent items of evidence.

### References:

• Pearl, J., Probabilistic Reasoning in Intelligent Systems: networks of plausible inference , Morgan Kaufmann, San Mateo, California, 1988.

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