Probabilistic logic under coherence and default reasoning

In this paper we study a probabilistic logic based on the notion of coherence of de Finetti. We first recall the notion of coherence for precise conditional probability assessments, then we consider its generalization to the case of imprecise assessments. We examine conditional probabilistic knowledge bases associated with imprecise probability assessments defined on arbitrary families of conditional events. In our probabilistic logic the notion of probabilistic interpretation is directly defined in terms of precise conditional probability assessments. Then, we give in our approach new proofs of some results obtained in probabilistic default reasoning.