Qualitative and quantitative approaches to reasoning about uncertainty can lead to different logical systems for formalizing such reasoning . In the case of reasoning about relative likelihood, a standardqualitative approach using preordered preferential structures yields adramatically different logical system than a quantitative approach usingprobability measures . In fact, the standard preferential approach validatesprinciples of reasoning that are incorrect from a probabilistic point of view . In this paper we show that a natural modification of the preferentialapproach yields exactly the same logical system as a probablisticapproach–not using single probability measures, but rather sets of probabilitymeasures . The same preferential structures used in the study of non-monotonic logics and belief revision may be used in

Author(s) : Matthew Harrison-Trainor, Wesley H. Holliday, Thomas F. Icard III

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Keywords : reasoning - preferential - approach - logical - structures -

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