Combining symbolic and numerical methods for defeasible reasoning

AI has stimulated a rapid development of methods for both quantitative and symbolic uncertainty management. As a consequence many proposals have been made for logic-based reasoning in the face of limited knowledge as well as descriptions of a variety of techniques for reasoning about belief and ignorance. However work on quantitative methods has also been substantial, yielding significant theoretical results. Since the methods appear to address different needs, an eclectic position has emerged which argues that the methods need to be integrated in some way. The authors discuss how this may be achieved. They outline two approaches which require considerable further work but may eventually provide a basis for coping with the ill-defined nature of practical problem solving and the vagueness of knowledge. Representing logical inference and numerical uncertainty calculation procedures as object level theories manipulated by a meta-interpreter appears to be a promising approach to combining quantitative and symbolic methods for reasoning under and about, uncertainty