Conjunction and disjunction among conditional events

Abstract

We generalize, in the setting of coherence, the notions of conjunction and disjunction of two conditional events to the case of n conditional events. Given a prevision assessment on the conjunction of two conditional events, we study the set of coherent extensions for the probabilities of the two conditional events. Then, we introduce by a progressive procedure the notions of conjunction and disjunction for n conditional events. Moreover, by defining the negation of conjunction and of disjunction, we show that De Morgan’s Laws still hold. We also show that the associative and commutative properties are satisfied. Finally, we examine in detail the conjunction for a family F of three conditional events. To study coherence of prevision for the conjunction of the three conditional events, we need to consider the coherence for the prevision assessment on each conditional event and on the conjunction of each pair of conditional events in F.