An Overview of Inconsistency-Tolerant Inferences in Prioritized Knowledge Bases

Abstract

The notion of priority is very important in the study of knowledge-based systems [Fagin et al., 1983] . In practice, knowledge bases are sometimes inconsistent, due to the presence of rules having exceptions, or because the available knowledge comes from several, not necessarily agreeing sources. When priorities attached to pieces of knowledge are available, the task of coping with inconsistency is greatly simplified, since conflicts have a better chance to be solved. Gardenfors [1988] has thus proved that upon arrival of a new piece of propositional information, any revision process of a belief set which satisfies natural requirements, is implicitly based on a priority ordering. Then the handling of priorities has been shown to be completely in agreement with possibilistic logic [Dubois and Prade, 1991] . One way of tackling inconsistency is to revise the knowledge base and restore consistency. However, as pointed out in [Benferhat et al., 1995a] , in the case of multiple sources of information, it does not always make sense to revise an inconsistent knowledge base since it comes down to destroying part of the knowledge. In the context of merging several knowledge bases, the introduction of priorities between pieces of information can be explained by the two following situations: Each partial knowledge base issued from a source of information is ‘flat’ (i.e. without any priority between items). But there is a complete pre-ordering between the sources of information according to their reliability. In this case, merging different sources of information leads to a prioritized knowledge base, where the priority level of each formula reflects the reliability of the source which supplies it. A particular case is when each piece of information is supported by a different source. All sources of information are equally reliable, but inside each partial knowledge base there exists a complete pre-ordering between pieces of information given by an expert, who rank-orders them according to their level of certainty or strength. Here again, the combination of the different sources of information gives a prioritized knowledge base, provided that the scales evaluating priority in each knowledge base are commensurate.