Some theoretical properties of conditional probability assessments

Authors:
Veronica Biazzo;Angelo Gilio
Affiliations:
Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Catania, Italy;Dipartimento di Metodi e Modelli Matematici, Università “La Sapienza”, Roma, Italy
Venue:
ECSQARU'05 Proceedings of the 8th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Year:
2005

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Abstract

We consider a finite family of conditional events and, among other results, we prove a connection property for the set of coherent assessments on such family. This property assures that, for every pair of coherent assessments on the family, there exists (at least) a continuous curve C whose points are intermediate coherent probability assessments. We also consider the compactness property for the set of coherent assessments. Then, as a corollary of connection and closure properties, we obtain the theorem of extension for coherent conditional probabilities.