Formal representations of uncertainty∗

The recent development of uncertainty theories that account for the notion of belief is linked to the emergence, in the XXth century, of Decision Theory and Artificial Intelligence. Nevertheless, this topic was dealt with very differently by each area. Decision Theory insisted on the necessity to found representations on the empirical observation of individuals choosing between courses of action, regardless of any other type of information. Any axiom in the theory should be liable of empirical validation. Probabilistic representations of uncertainty can then be justified with a subjectivist point of view, without necessary reference to frequency. Degrees of probability then evaluate to what extent an agent believes in the occurrence of an event or in the truth of a proposition. In contrast, Artificial Intelligence adopted a more introspective approach aiming at formalizing intuitions, reasoning processes, through the statement of reasonable axioms, often without reference to probability. Actually, until the nineties Artificial Intelligence essentially focused on purely qualitative and ordinal (in fact, logical) representations.