Knowledge and Uncertainty

TL;DR

The paper discusses the role of knowledge and uncertainty in decision-making, emphasizing that measures of uncertainty aligning with real-valued functions must adhere to classical probability axioms to be meaningful in decision contexts.

Contribution

It explores the constraints on uncertainty measures imposed by decision-making requirements, demonstrating that real-valued uncertainty measures must satisfy probability axioms.

Findings

Uncertainty measures must satisfy classical probability axioms.

Real-valued utilities imply probability constraints.

Decision relevance constrains knowledge representation.

Abstract

One purpose -- quite a few thinkers would say the main purpose -- of seeking knowledge about the world is to enhance our ability to make good decisions. An item of knowledge that can make no conceivable difference with regard to anything we might do would strike many as frivolous. Whether or not we want to be philosophical pragmatists in this strong sense with regard to everything we might want to enquire about, it seems a perfectly appropriate attitude to adopt toward artificial knowledge systems. If is granted that we are ultimately concerned with decisions, then some constraints are imposed on our measures of uncertainty at the level of decision making. If our measure of uncertainty is real-valued, then it isn't hard to show that it must satisfy the classical probability axioms. For example, if an act has a real-valued utility U(E) if the event E obtains, and the same real-valued utility if the denial of E obtains, so that U(E) = U(-E), then the expected utility of that act must be U(E), and that must be the same as the uncertainty-weighted average of the returns of the act, p-U(E) + q-U('E), where p and q represent the uncertainty of E and-E respectively. But then we must have p + q = 1.