Conjunction, disjunction and iterated conditioning of conditional events

In R. Kruse (ed.), Advances in Intelligent Systems and Computing. Springer (2013)
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Abstract

Starting from a recent paper by S. Kaufmann, we introduce a notion of conjunction of two conditional events and then we analyze it in the setting of coherence. We give a representation of the conjoined conditional and we show that this new object is a conditional random quantity, whose set of possible values normally contains the probabilities assessed for the two conditional events. We examine some cases of logical dependencies, where the conjunction is a conditional event; moreover, we give the lower and upper bounds on the conjunction. We also examine an apparent paradox concerning stochastic independence which can actually be explained in terms of uncorrelation. We briefly introduce the notions of disjunction and iterated conditioning and we show that the usual probabilistic properties still hold.

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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.

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Giuseppe Sanfilippo
University of Palermo

Citations of this work

Square of opposition under coherence.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. 407-414.

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References found in this work

Conditionals Right and Left: Probabilities for the Whole Family.Stefan Kaufmann - 2009 - Journal of Philosophical Logic 38 (1):1-53.
The conditional in mental probability logic.Niki Pfeifer & G. D. Kleiter - 2010 - In Mike Oaksford & Nick Chater (eds.), Cognition and Conditionals: Probability and Logic in Human Thought. Oxford University Press. pp. 153--173.

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