Lorini proposesLogic of Doxastic Attitude to address the problem of logical omnisci-ence in cognitive science;the article employs the"awareness"operator proposed by Levesque to distinguish explicit from implicit beliefs.In the field of artificial intelligence,decision making and knowledge representation,the accuracy of beliefs needs to be studied,which is not covered in Logic of Doxastic Attitude.In this regard,the paper tries to use fuzzy logic to characterize the probability of beliefs being true by introducing truth intervals,based on which a new logical framework is proposed and axioms are introduced,and the soundness of semantic models are fi-nally proved.