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Logic programming provides a model for rule-based reasoning in expert systems. The advantage of this formal model is that it makes available many results from the semantics and proof theory of first-order predicate logic. A disadvantage is that in expert systems one often wants to use, instead of the usual two truth values, an entire continuum of "uncertainties" in between. That is, instead of the usual "qualitative" deduction, a form of "quantitative" deduction is required. We present andoi:10.1016/0743-1066(86)90003-8 fatcat:3hy3hyppmjg6xbtct6l6x6uhnm