Centering and Compound Conditionals Under Coherence

Gilio, Angelo; Over, David E.; Pfeifer, Niki and Sanfilippo, Giuseppe (2017): Centering and Compound Conditionals Under Coherence. In: Soft Methods for Data Science, Vol. 456: pp. 253-260

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 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.

• Item Type: Journal article
• Faculties: Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP)
• Subjects: 100 Philosophy and Psychology > 100 Philosophy; 500 Science > 510 Mathematics
• ISSN: 2194-5357
• Language: English