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Probabilistic inferences from conjoined to iterated conditionals

Authors :
Sanfilippo, Giuseppe
Pfeifer, Niki
Over, David E.
Gilio, Angelo
Source :
International Journal of Approximate Reasoning, volume 93, pages 103 - 118, 2018
Publication Year :
2017

Abstract

There is wide support in logic, philosophy, and psychology for the hypothesis that the probability of the indicative conditional of natural language, $P(\textit{if } A \textit{ then } B)$, is the conditional probability of $B$ given $A$, $P(B|A)$. We identify a conditional which is such that $P(\textit{if } A \textit{ then } B)= P(B|A)$ 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.

Details

Database :
arXiv
Journal :
International Journal of Approximate Reasoning, volume 93, pages 103 - 118, 2018
Publication Type :
Report
Accession number :
edsarx.1701.07785
Document Type :
Working Paper
Full Text :
https://doi.org/10.1016/j.ijar.2017.10.027