There is wide support in logic, philosophy, and psychology for the hypothesis that the probability of the indicative conditional of natural language, P(if A then B), is the conditional probability of B given A, P(B|A). We identify a conditional which is such that P(if A then B)=P(B|A) with de Finetti's conditional event, B|A. An objection to making this identification in the past was that it appeared unclear how to form compounds and iterations of conditional events. In this paper, we illustrate how to overcome this objection with a probabilistic analysis, based on coherence, of these compounds and iterations. We interpret the compounds and iterations as conditional random quantities which, given some logical dependencies, may reduce to conditional events. We show how the inference to B|A from A and B can be extended to compounds and iterations of both conditional events and biconditional events. Moreover, we determine the respective uncertainty propagation rules. Finally, we make some comments on extending our analysis to counterfactuals

Sanfilippo, G., Pfeifer, N., Over, D., Gilio, A. (2018). Probabilistic inferences from conjoined to iterated conditionals. INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 93, 103-118 [10.1016/j.ijar.2017.10.027].

Probabilistic inferences from conjoined to iterated conditionals

Sanfilippo, Giuseppe
;
2018-01-01

Abstract

There is wide support in logic, philosophy, and psychology for the hypothesis that the probability of the indicative conditional of natural language, P(if A then B), is the conditional probability of B given A, P(B|A). We identify a conditional which is such that P(if A then B)=P(B|A) with de Finetti's conditional event, B|A. An objection to making this identification in the past was that it appeared unclear how to form compounds and iterations of conditional events. In this paper, we illustrate how to overcome this objection with a probabilistic analysis, based on coherence, of these compounds and iterations. We interpret the compounds and iterations as conditional random quantities which, given some logical dependencies, may reduce to conditional events. We show how the inference to B|A from A and B can be extended to compounds and iterations of both conditional events and biconditional events. Moreover, we determine the respective uncertainty propagation rules. Finally, we make some comments on extending our analysis to counterfactuals
2018
Settore MAT/06 - Probabilita' E Statistica Matematica
Settore MAT/01 - Logica Matematica
Sanfilippo, G., Pfeifer, N., Over, D., Gilio, A. (2018). Probabilistic inferences from conjoined to iterated conditionals. INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 93, 103-118 [10.1016/j.ijar.2017.10.027].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/246700
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