Abstract
Our starting point is a definition of conditional event E❘H which differs from many seemingly “similar” ones adopted in the relevant literature since 1935, starting with de Finetti. In fact, if we do not assign the same “third” value u (“undetermined”) to all conditional events, but make it depend on E❘H, it turns out that this function t(E❘H) can be taken as a general conditional uncertainty measure, and we get (through a suitable – in a sense, “compulsory” – choice of the relevant operations among conditional events) the “natural” axioms for many different (besides probability) conditional measures.
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Coletti, G., Scozzafava, R. From Conditional Events to Conditional Measures: A New Axiomatic Approach. Annals of Mathematics and Artificial Intelligence 32, 373–392 (2001). https://doi.org/10.1023/A:1016786121626
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DOI: https://doi.org/10.1023/A:1016786121626