Bayesian Network (BN) is a prominent model to deal with knowledge representation and inference in case of uncertain causalities.This paper discusses the essential difference between single-valued and multi-valued cases.It is pointed out that even a binary child variable can be either single-valued or multi-valued,while the existing compact representations and the corresponding inference algorithms applicable in single-valued cases cannot be simply applied in multi-valued cases.To overcome this problem and others,a new model named as DUCG (Dynamical Uncertain Causality Praph) is presented.By introducing a set of new concepts,DUCG is able to compactly and graphically represent complex conditional probability distributions (CPDs) in different modules,irrespective of whether the cases of the modules are single-valued or multi-valued.The simple connection among separately constructed modules composes a final DUCG.Once the evidence is observed,the first inference step is to simplify the DUCG regardless of queries by applying the 10 rules presented in this paper.The second step is to apply the event outspread algorithm presented in this paper to calculate the updated probabilities of the queries still in concern based on the simplified DUCG,regardless of whether the variables are singly or multiply connected.Sometimes,the qualitative solution can be found by only simplifying DUCG.Correspondingly,the accuracy of parameters is less important in DUCG.Moreover,DUCG enables people to represent the knowledge only in concern but not enough to represent CPDs.In other words,DUCG does not have to represent the joint probability distribution over a set of variables,although it is able to.This incompleteness of representation and flexiable conditional causalities represented in DUCG,in addition to that DUCG is able to deal with the directed cyclic graph (DCG) to be addressed in next paper,etc,makes DUCG beyound BN.The example of an alarm system detecting intruder illustrates the DUCG methodology.