A new framework for linguistic reasoning is proposed based on a random set model of the degree of appropriateness of a label. Labels are assumed to be chosen from a finite predefined set of labels and the set of appropriate labels for a value is defined as a random set-valued function from a population of individuals into the set of subsets of labels. Appropriateness degrees are then evaluated relative to the distribution on this random set where the appropriateness degree of a label corresponds to the probability that it is contained in the set of appropriate labels. This interpretation is referred to as label semantics. A natural calculus for appropriateness degrees is described which is weakly functional while taking into account the logical structure of expressions. Given this framework it is shown that a bayesian approach can be adopted in order to infer probability distributions on the underlying variable given constraints both in the form of linguistic expressions and mass assignments. In addition, two conditional measures are introduced for evaluating the appropriateness of a linguistic expression given other linguistic information.