Argumentation systems and belief functions
Norbert Lehmann · reroDoc Digital Library · 2001
Uncertain knowledge can be represented in the framework of argumentation systems. In this framework, uncertainty is expressed using so-called assumptions. Depending on the setting of the assumptions, a given hypothesis of interest can be proved or falsified. The main goal of assumption-based reasoning is to determine the set of all supporting arguments for a given hypothesis. Such a supporting argument is a particular setting of assumptions. The assignment of probabilities to assumptions leads to the framework of probabilistic argumentation systems and allows an additional quantitative judgement of a given hypothesis. One possibility to compute the degree of support for a given hypothesis is to compute first the corresponding set of supporting arguments and then to derive the desired result. The problem of this approach is that the set of supporting arguments is sometimes very huge and can't be represented explicitly. This thesis proposes an alternative way for computing degrees of support which is often superior to the first approach. Instead of computing a symbolic result from which the numerical result is derived, we avoid symbolic computations right away. This can be done due to the fact that degree of support corresponds to the notion of normalized belief in Dempster-Shafer theory. We will show how a probabilistic argumentation system can be transformed into a set of independent mass functions. For efficient computations, the local computation framework of Shenoy is used. In this framework, computation is based on a message-passing scheme in a join tree. Four different architectures could be used for propagating potentials in the join tree. These architectures correspond to a complete compilation of the knowledge which allows to answer queries fast. In contrast, this thesis proposes a new method which corresponds to a partial compilation of the knowledge. This method is particularly interesting if there are only a few queries. In addition, it can prevent that the join tree has to be reconstructed in order to answer a given query. Finally, the language ABEL is presented. It allows to express probabilistic argumentations systems in a convenient way. We will show how several examples from different domains can be modeled using ABEL. These examples are also used to point out important aspects of the computational theory presented in the first chapters of this thesis.