Conditional events and subjective probability in management of uncertainty

Subjective probability is the natural theoretical tool to model the uncertain knowledge and to revise beliefs. Based on de Finetti's coherence principle, this theory, which does not require to assume strictly positive probabilities for all conditioning events, provides the most general framework for checking consistency of conditional probability assessments. In this paper it is argued that, through the concept of generalized atom, a natural representation of the truth values of conditional events can be given. Moreover, some results on probabilistic consistency are obtained.