TY - JOUR

T1 - Probabilistic inferences from conjoined to iterated conditionals

AU - Sanfilippo, Giuseppe

AU - Gilio, Angelo

AU - Sanfilippo, Giuseppe

AU - Over, David E.

AU - Pfeifer, Niki

PY - 2018

Y1 - 2018

N2 - 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

AB - 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

KW - Centering

KW - Coherence

KW - Compound conditionals

KW - Counterfactuals

KW - Iterated conditionals

KW - p-Entailment

KW - Centering

KW - Coherence

KW - Compound conditionals

KW - Counterfactuals

KW - Iterated conditionals

KW - p-Entailment

UR - http://hdl.handle.net/10447/246700

M3 - Article

VL - 93

SP - 103

EP - 118

JO - International Journal of Approximate Reasoning

JF - International Journal of Approximate Reasoning

SN - 0888-613X

ER -