Sherlock Holmes Doesn't Play Dice: The mathematics of uncertain reasoning when something may happen, that one is not even able to figure out

TL;DR

This paper explores an extended Evidence Theory that captures uncertainty from unknown potential events, contrasting it with traditional probability and information theories, and discusses its applications in social and life sciences.

Contribution

It introduces an extended version of Evidence Theory capable of representing uncertainty about unimagined events, expanding its applicability beyond conventional probability models.

Findings

Extended Evidence Theory expresses uncertainty about unforeseen events.

Comparison with imprecise and sub-additive probabilities highlights its unique features.

Potential applications in multi-agent systems are outlined.

Abstract

While Evidence Theory (also known as Dempster-Shafer Theory, or Belief Functions Theory) is being increasingly used in data fusion, its potentialities in the Social and Life Sciences are often obscured by lack of awareness of its distinctive features. In particular, with this paper I stress that an extended version of Evidence Theory can express the uncertainty deriving from the fear that events may materialize, that one is not even able to figure out. By contrast, Probability Theory must limit itself to the possibilities that a decision-maker is currently envisaging. I compare this extended version of Evidence Theory to sophisticated extensions of Probability Theory, such as imprecise and sub-additive probabilities, as well as unconventional versions of Information Theory that are employed in data fusion and transmission of cultural information. A further extension to multi-agent interaction is outlined.