An epistemic model of the uncertainty associated with vague concepts is introduced. Label semantics theory is proposed as a framework for quantifying an agent’s uncertainty concerning what labels are appropriate to describe a given example. An interpretation of label semantics is then proposed which incorporates prototype theory by introducing uncertain thresholds on the distance between elements and prototypes for description labels. This interpretation naturally generates a functional calculus for appropriateness measures. A more general model with distinct threshold variables for different labels is discussed and we show how different kinds of semantic dependence can be captured in this model.