A bridge between probability and possibility in a comparative framework

Authors:
Giulianella Coletti;Romano Scozzafava;Barbara Vantaggi
Affiliations:
University of Perugia, Italy;University "La Sapienza", Rome, Italy;University "La Sapienza", Rome, Italy
Venue:
ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
Year:
2011

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Abstract

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.