A method is described for handling the ambiguity and vagueness that is often found in quantifications - the semantically complex relations between nominal and verbal constituents. In natural language certain aspects of quantification are often left open; it is argued that the analysis of quantification in a model-theoretic framework should use semantic representations in which this may also be done. This paper shows a form for such a representation and how "ambiguous" representations are used in an elegant and efficient procedure for semantic analysis, incorporated in the TENDUM dialogue system. .