Uncertain Information

• Authors: Jürg Kohlas;Christian Eichenberger
• Venue: Formal Theories of Information
• Year: 2009

In the previous chapter Information Algebra, an algebraic structure capturing the idea that pieces of information refer to precise questions and that they can be combined and focussed on other questions is presented and discussed. A prototype of such information algebras is relational algebra. But also various kind of logic systems induce information algebras. In this chapter, this framework will be used to study uncertain information . It is often the case that a piece of information is known to be valid under certain assumptions, but it is not altogether sure that these assumptions really hold. Varying the assumptions leads to different information. Given such an uncertain body of information, assumption-based reasoning permits to deduce certain conclusions or to prove certain hypotheses under some assumptions. This kind of assumption-based inference can be carried further if the varying likelihood of different assumptions is described by a probability measure on the assumptions. Then, it is possible to measure the degree of support of a hypothesis by the probability that the assumptions supporting the hypothesis hold. A prototype system of such a probabilistic argumentation system based on propositional logic is described in [3]. Another example will be described in Section 2 of this chapter. It is shown that this way to model uncertain information leads to a theory which generalizes the well-known Dempster-Shafer theory [6, 19].