Probabilistic Relations Among Logically Dependent Conditional Events

In this paper the concepts of partial and complete logical dependence among conditional events are studied and a comparison is made with some definitions given by other authors. Then, some logical and probabilistic relations are considered in the framework of coherent probabilistic assessments. A particular class of logically dependent conditional events is considered and, based on some results on coherence of precise and imprecise probability assessments, the probabilistic relations implied by logical dependence are studied. It is shown that logical dependence does not necessarily imply probabilistic relations. Finally, given two logically independent events, we examine the coherence of some probability assessments which are relevant to the property of stochastic independence.