The reliability of reasoning with unreliable rules and propositions
In this paper, the well known mathematical theory of evidence (Shafer, 1976) will be considered from a point of view which is different from usual. Simple belief functions (hints) will be regarded as arguments which are not fully reliable (Kohlas, 1989). This implies that the construction of argumentation chains for a particular hypothesis will have limited reliability. Since there are usually many different ways to argue in favour of a hypothesis, the problem to be addressed is to determine the overall reliability of the arguments.
The point of view adopted here places the model of reasoning with unreliable arguments into the framework of combinatorial reliability theory as developed for the study of technical systems composed of unreliable components (see also Provan, 1990). Most approaches proposed so far for the combination of evidence could be qualified as “forward chaining” methods because all available information is combined to obtain an overall result. In contrast, the method favored in this paper is “backward chaining”. In fact, starting with a hypothesis, arguments for it are looked for, searching for subhypotheses or subgoals, for which in turn further arguments may be developed. This permits to obtain sequentially refined bounds on the credibility of the hypothesis. In this way, in many cases it becomes possible to avoid the tedious task to combine all hints, even those which do not contribute much to the judgment of the hypothesis.
As an example of an idea inherited from reliability theory, the so-called factorization method can be mentionned. It can be regarded as a mechanism for reasoning with assumptions and represents an alternative procedure to the well known Markov tree approach (Shafer et al., 1986) for the elimination of disturbing dependencies between evidences.
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