Information can be uncertain. Uncertainty may arise because events depend on random elements or uncertainty may be due to incomplete knowledge. In any case, information can often be asserted only with a certain probability. In this chapter we show that information algebras provide a natural framework to describe uncertainty. We start by modeling uncertainty in information algebras by (generalized) random variables, taking values in information algebras. This extends the fundamental work of A. Dempster (Dempster, 1967) and G. Shafer (Shafer, 1976) to the framework of information algebras. In the following Section 7.2 we show, how generalized random variables arise in a natural way from assumption-based reasoning in information systems. This is an extension of the idea of “probaility of provability” introduced by Pearl (Pearl, 1988) and also discussed by (Laskey & Lehner, 1989). This idea has evolved into so-called probabilistic argumentation systems (Haenni, Kohlas & Lehmann, 2000). Closely related to such systems are structures called hints. The notion of a hint has been introduced in (Kohlas & Monney, 1995).
KeywordsSupport Function Simple Experiment Focal Element Basic Probability Assignment Argumentation System
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