From Conditional Events to Conditional Measures: A New Axiomatic Approach |
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Authors: | G Coletti R Scozzafava |
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Affiliation: | (1) Dipartimento di Matematica e Informatica, Università di Perugia, 06100 Perugia, Italy;(2) Dipartimento di Metodi e Modelli Matematici, Università La Sapienza, Via Scarpa 16, 00161 Roma, Italy |
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Abstract: | Our starting point is a definition of conditional event EH 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 EH, it turns out that this function t(EH) 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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Keywords: | uncertainty measures conditional events conditioning |
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