A goal in approximate reasoning is the querying of fuzzy knowledge bases. This can be viewed as the estimation of the modalities of a proposition on the basis of vague propositions that can even be only partially true, partially necessary, or partially possible. In this article, we present a framework for an integrated theory of imprecision and uncertainty. First, we describe a tool to transform a proposition qualified by a partial degree of necessity (possibility) into a fuzzier, but true, proposition. Second, we show that the degree of truth of a proposition estimated from imprecise information is not necessarily unique but belongs to an interval where the lower bound is a necessity measure and the upper bound is a possibility measure. The theory of multiple-valued truths thus finds an interpretation in this integrated theory of uncertainty and imprecision.
