6533b856fe1ef96bd12b2889
RESEARCH PRODUCT
Iterated Conditionals, Trivalent Logics, and Conditional Random Quantities
Lydia CastronovoGiuseppe Sanfilipposubject
Settore MAT/06 - Probabilita' E Statistica MatematicaCoherence Conditional events Conditional random quantities Conditional previsions Conjoined and disjoined conditionals Iterated conditionals Compound probability theorem Lower and upper bounds Import-export principledescription
We consider some notions of iterated conditionals by checking the validity of some desirable basic logical and probabilistic properties, which are valid for simple conditionals. We consider de Finetti’s notion of conditional as a three-valued object and as a conditional random quantity in the betting framework. We recall the notions of conjunction and disjunction among conditionals in selected trivalent logics. Then, we analyze the two notions of iterated conditional introduced by Calabrese and de Finetti, respectively. We show that the compound probability theorem and other basic properties are not preserved by these objects, by also computing some probability propagation rules. Then, for each trivalent logic we introduce an iterated conditional as a suitable random quantity which satisfies the compound prevision theorem and some of the desirable properties. Finally, we remark that all the basic properties are satisfied by the iterated conditional mainly developed in recent papers by Gilio and Sanfilippo in the setting of conditonal random quantities.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2022-10-10 |