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.

Castronovo, L., Sanfilippo, G. (2022). Iterated Conditionals, Trivalent Logics, and Conditional Random Quantities. In F. Dupin de Saint-Cyr, M. Öztürk-Escoffier, N. Potyka (a cura di), Scalable Uncertainty Management, 15th International Conference, SUM 2022, Paris, France, October 17–19, 2022, Proceedings (pp. 47-63) [10.1007/978-3-031-18843-5_4].

Iterated Conditionals, Trivalent Logics, and Conditional Random Quantities

Castronovo, Lydia
;
Sanfilippo, Giuseppe
2022-10-10

Abstract

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.
10-ott-2022
Settore MAT/06 - Probabilita' E Statistica Matematica
978-3-031-18842-8
978-3-031-18843-5
Castronovo, L., Sanfilippo, G. (2022). Iterated Conditionals, Trivalent Logics, and Conditional Random Quantities. In F. Dupin de Saint-Cyr, M. Öztürk-Escoffier, N. Potyka (a cura di), Scalable Uncertainty Management, 15th International Conference, SUM 2022, Paris, France, October 17–19, 2022, Proceedings (pp. 47-63) [10.1007/978-3-031-18843-5_4].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/572907
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