The role of calculi in uncertain reasoning

Much of the controversy about methods for automated decision making has focused on specific calculi for combining beliefs or propagating uncertainty. We broaden the debate by (1) exploring the constellation of secondary tasks surrounding any primary decision problem, and (2) identifying knowledge engineering concerns that present additional representational tradeoffs. We argue on pragmatic grounds that the attempt to support all of these tasks within a single calculus is misguided. In the process, we note several uncertain reasoning objectives that conflict with the Bayesian ideal of complete specification of probabilities and utilities. In response, we advocate treating the uncertainty calculus as an object language for reasoning mechanisms that support the secondary tasks. Arguments against Bayesian decision theory are weakened when the calculus is relegated to this role. Architectures for uncertainty handling that take statements in the calculus as objects to be reasoned about offer the prospect of retaining normative status with respect to decision making while supporting the other tasks in uncertain reasoning.

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