Authors
Niki Pfeifer
Universität Regensburg
Giuseppe Sanfilippo
Università degli Studi di Palermo
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.
Keywords Centering  Coherence  p-entailment  Compound conditionals  Iterated conditionals  Counterfactuals
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References found in this work BETA

The Logic of Conditionals.Ernest Adams, Ernest W. Adams, Jaakko Hintikka & Patrick Suppes - 1974 - Journal of Symbolic Logic 39 (3):609-611.
Uncertainty and the de Finetti Tables.Jean Baratgin, David E. Over & Guy Politzer - 2013 - Thinking and Reasoning 19 (3-4):308-328.
A Primer of Probability Logic.Ernest Wilcox Adams - 1998 - Stanford: Csli Publications.

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