Probabilistic inferences from conjoined to iterated conditionals

International Journal of Approximate Reasoning 93:103-118 (2018)
  Copy   BIBTEX

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.

Other Versions

No versions found

Similar books and articles

Centering and compound conditionals under coherence.A. Gilio, Niki Pfeifer & Giuseppe Sanfilippo - 2017 - In M. B. Ferraro, P. Giordani, B. Vantaggi, M. Gagolewski, P. Grzegorzewski, O. Hryniewicz & María Ángeles Gil (eds.), Soft Methods for Data Science. pp. 253-260.

Analytics

Added to PP
2021-03-15

Downloads
460 (#62,927)

6 months
132 (#38,243)

Historical graph of downloads
How can I increase my downloads?

Author Profiles

Niki Pfeifer
Universität Regensburg
Giuseppe Sanfilippo
University of Palermo