A logic is de ned that allows to express information about statistical probabilities and about degrees of belief in speci c propositions. By interpreting the twotypes of probabilities in one common probability space, the semantics given are well suited to model the in uence of statistical informationon the formation of subjective beliefs. Cross entropy minimization is a key element in these semantics,the use of which is justi ed by showingthat the resulting logicexhibits some very reasonable properties.