Conditional Objects as Possibilistic Variables

The interpretation of basic conditionals as three-valued objects initiated by de Finetti has been mainly developed and extended by Gilio and Sanfilippo and colleagues, who look at (compound) conditionals as probabilistic random quantities. Recently, it has been shown that this approach ends up providing a Boolean algebraic structure for the set of conditional objects. In this paper, we show how that this probabilistic-based approach can also be developed within the possibilistic framework, where conditionals are attached with possibilistic variables instead: variables attached with a (conditional) possibility distribution on its domain of plain events. The possibilistic expectation of these variables now provides a means of extending the original possibility distribution on events to (compound) conditional objects. Our main result shows that this possibilistic approach leads to exactly the same underlying Boolean algebraic structure for the set of conditionals.