Probabilistic Reasoning as a General Unifying Tool

Our starting point is the approach to probabilistic logic through coherence; but we give up de Finetti's idea of a conditional event E\H being a 3-valued entity, with the third value being just an undetermined common value for all ordered pairs (E,H). We let instead the "third" value of E\H suitably depend on the given pair. In this way we get, through a direct assignment of conditional probability, a general theory of probabilistic reasoning able to encompass other approaches to uncertain reasoning, such as fuzziness and default reasoning. We are also able to put forward a meaningful concept of conditional independence, which avoids many of the usual inconsistencies related to logical dependence. We give an example in which we put together different kinds of information and show how coherent conditional probability can act as a unifying tool.