This paper investigates the possibility of performing automated reasoning in probabilistic knowledge bases when probabilities are expressed by means of linguistic quantifiers. Data are expressed in terms of ill-known conditional probabilities represented by linguistic terms. Each linguistic term is expressed as a prescribed interval of proportions. Then instead of propagating numbers, qualitative terms are propagated in accordance with the numerical interpretation of these terms. The quantified syllogism, modeling the chaining of probabilistic rules, is studied in this context. It is shown that a qualitative counterpart of this syllogism makes sense and is fairly independent of the thresholds defining the linguistically meaningful intervals, provided that these threshold values remain in accordance with the intuition. The inference power is less than a full-fledged probabilistic constraint propagation device but corresponds better to what could be thought of as commonsense probabilistic reasoning. Suggestions that may improve the inferencing power in the qualitative setting are proposed.