Combination calculi for uncertainty reasoning: representing uncertainty using distributions

There are many different methods for incorporating notions of uncertainty in evidential reasoning. A common component to these methods is the use of additional values, other than conditional probabilities, to assert current degrees of belief and certainties in propositions. Beginning with the viewpoint that these values can be associated with statistics of multiple opinions in an evidential reasoning system, we categorize the choices that are available in updating and tracking these multiple opinions. In this way, we develop a matrix of different uncertainty calculi, some of which are standard, and others are new. The main contribution is to formalize a framework under which different methods for reasoning with uncertainty can be evaluated. As examples, we see that both the “Kalman filtering” approach and the “Dempster–Shafer” approach to reasoning with uncertainty can be interpreted within this framework of representing uncertainty by the statistics of multiple opinions.