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

Giuseppe Sanfilippo
Università degli Studi di Palermo
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.
Keywords Conditional events   conditional random quantities  conjunction  iterated conditionals
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Conditionals Right and Left: Probabilities for the Whole Family.Stefan Kaufmann - 2009 - Journal of Philosophical Logic 38 (1):1-53.

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