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RESEARCH PRODUCT
Conjunction, Disjunction and Iterated Conditioning of Conditional Events
Giuseppe SanfilippoAngelo Giliosubject
Theoretical computer scienceSettore MAT/06 - Probabilita' E Statistica MatematicaComputer scienceProbabilistic logicCoherence (philosophical gambling strategy)Conditional events conditional random quantities conjunction disjunction iterated conditionalsConjunction (grammar)Set (abstract data type)Regular conditional probabilitydisjunction; conditional events; conjunction; conditional random quantities; iterated conditionals.Iterated functionRepresentation (mathematics)Settore SECS-S/01 - StatisticaMathematical economicsEvent (probability theory)description
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-01-01 |