Modelling uncertainty and inductive inference: A survey of recent non-additive probability systems

Abstract

Until recently, modelling uncertainty, especially subjective uncertainty judgments, was addressed by means of tools from the mathematical theory of probability. However, the discovery of systematic behavioral deviations with regard to the subjective expected utility model, together with the emergence of knowledge engineering (especially expert systems) have pointed out some limitations in the knowledge representation power of the standard additive theory. Motivated by such problems, new classes of set-functions have been proposed to model subjective uncertainty and are reviewed in this paper. Interpretive settings for these new models are proposed. The question of preserving notions of independence, conditioning etc… is discussed, with a view to develop new tools for inductive reasoning in the spirit of Bayes theorem. This discussion includes various approaches to inductive reasoning such as probability kinematics based on information measures, and the combination of uncertain or default information as studied in the field of Artificial Intelligence.