## From conditional events to conditional measures: a new axiomatic approach.(English)Zbl 1314.68306

Summary: 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.

### MSC:

 68T37 Reasoning under uncertainty in the context of artificial intelligence 60A05 Axioms; other general questions in probability 28E99 Miscellaneous topics in measure theory

### Keywords:

uncertainty measures; conditional events; conditioning
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