  Qualitative and quantitative approaches to reasoning about uncertainty can
lead to different logical systems for formalizing such reasoning, even when the
language for expressing uncertainty is the same. In the case of reasoning about
relative likelihood, with statements of the form $\varphi\succsim\psi$
expressing that $\varphi$ is at least as likely as $\psi$, a standard
qualitative approach using preordered preferential structures yields a
dramatically different logical system than a quantitative approach using
probability measures. In fact, the standard preferential approach validates
principles of reasoning that are incorrect from a probabilistic point of view.
However, in this paper we show that a natural modification of the preferential
approach yields exactly the same logical system as a probabilistic
approach--not using single probability measures, but rather sets of probability
measures. Thus, the same preferential structures used in the study of
non-monotonic logics and belief revision may be used in the study of
comparative probabilistic reasoning based on imprecise probabilities.
