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Non-Classical Probabilities for Decision Making in Situations of Uncertainty

Classical probability gives a quantitative representation of uncertainty over a given space of available events. It assigns to each event a value in the interval [0,1] interpreted as some agent’s subjective credence therein or, alternatively, its likelihood of occurrence. The space of events, here, is assumed to have an internal structure, where some events are simple and others compound. Overall, the different events can be arranged into a Boolean algebra, a set-theoretical structure with union, intersection and complementation. The probabilities that can be assigned to different events stand in various relations to each other. It seems incompatible, for instance, to assign a larger probability (or credence) to some specific event B than to some more general