Approximate Reasoning Using Logico-symbolic Valuations

The knowledge given by an expert in order to construct a Knowledge Based System is often not very precise and contains uncertainty. In many cases, the expert prefers to express the uncertainty in a qualitative form rather than in a quantitative one . In this paper, we present a model of the uncertainty (and/or the lack of precision) in qualitative form. A symbolic approach in a context of a many-valued logic is proposed.We also present, all necessary tools to represent and to manage the uncertain and imprecise knowledge in an Expert System. Contrary to machines, Men can manage perfectly uncertain and imprecise knowledge. The following sentences are fully understandable by them: they are about 200 young people. the temperature is very high. a very large suite. coughing occurs quite frequently. One of the most important problems encounted during the realization of expert systems is that the knowledge representation is often chosen independently from its management. But, the representation does not have any significance which allows us to determine if the related knowledge is represented correctly or not. So, we have to study the doublet (use of the knowledge, use of it’s representation) especially when we manage uncertainty and imprecision. There are several mathematical formalisms and tools to represent such expert knowledge (probabilistic logic to represent the uncertainty, default logic to represent the lack of knowledge, fuzzy logic to represent the imprecision, etc...). We have introduced [1, 2] fundamental concepts of a many-valued logic to represent the knowledge, using linguistic valuations to translate both uncertainty and imprecision. A mechanism to manage the given knowledge in a symbolic way, avoiding computations is also proposed in [1, 2].