A Bridge between Probability and Possibility in a Comparative Framework

摘要

The paper studies the connection between comparative probability and comparative plausibility, with a particular emphasis on comparative possibility. We consider a comparative probability on an algebra and extend it to a different algebra. We prove that, in general, the upper extension of the given comparative probability is a comparative plausibility. By considering a suitable condition of weak logical independence between the two partitions related to the atoms of the two algebras, we prove that the upper ordinal relation is a comparative possibility. These results hold for comparative probability not necessarily representable by a numerical probability.