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 sometimes reduce to conditional events, given logical dependencies. We also show, for the first time, how to extend the inference of centering for conditional events, inferring B|A from the conjunction A and B, to compounds and iterations of both conditional events and biconditional events, B||A, and generalize it to n-conditional events.
Shared first authorship (all authors contributed equally to this work).
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Acknowledgments
We thank the anonymous referees for useful comments. We thank Villa Vigoni (Human Rationality: Probabilistic Points of View). N. Pfeifer is supported by his DFG project PF 740/2-2 (within the SPP1516). G. Sanfilippo is supported by the INdAM–GNAMPA Projects (2016 Grant U 2016/000391 and 2015 grant U 2015/000418).
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Gilio, A., Over, D.E., Pfeifer, N., Sanfilippo, G. (2017). Centering and Compound Conditionals Under Coherence. In: Ferraro, M., et al. Soft Methods for Data Science. SMPS 2016. Advances in Intelligent Systems and Computing, vol 456. Springer, Cham. https://doi.org/10.1007/978-3-319-42972-4_32
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DOI: https://doi.org/10.1007/978-3-319-42972-4_32
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