## 1 Introduction
### Evidential Network  
Knowledge representation and uncertainty reasoning based on the network-based method began with research on early constrained networks, qualitative Markov trees [1], and qualitative Markovnetworks [2]. In the late 1980s and early 1990s, the Bayesian Network (BN) [3] and the value-based system (VBS) [4] greatly promoted the use of a network model for knowledge representation and uncertainty inference. However, BN and VBS cannot handle knowledge that is described as a belief function. [PERSON] put forward an axiomatic reasoning system in 1993 [5] that extracts an abstract mathematical model so as to represent information by expressing concepts and algorithms that are related to the value, and that provide a general framework for studying knowledge representation and reasoning in causal networks, including probability and belief functions. General information can then be decomposed from a generalized conditional-probability perspective. That same year, [PERSON], the author of the transitive belief model (TBM), proposed a generalized Bayesian theory (GBT) [6] under the framework of the TBM. By means of the Disjunctive Rule of Combination (DRC), where only one of the two independent evidences is known, the belief of both evidences can be calculated, which is to say that the belief function also has the same conditional belief function as the Bayesian formula. Based on these two basic theoretical achievements, some scholars began to explore the modeling and reasoning of evidence networks. In 1994, [PERSON] and [PERSON] first proposed the concept of evidential networks (EN) [7] and for the first time used the conditional belief function to represent the relationship between network nodes. This paper proposes the concept of using the evidential network with a conditional belief function (ENC) and offers the corresponding reasoning algorithm. By analyzing the characteristics of ENC, this paper also explores reasoning that may simplify the problem. [PERSON] and [PERSON] et al. proposed an understanding of the evidential network based on the qualitative Markov tree [8; 9]. [PERSON] and [PERSON] et al. by comparing and analyzing the similarities and differences between the evidence network and the VBS, pointed out that the main problem of evidential-network research is how to represent the independence of the belief function through the graph model. Based on the general belief function and the transitive belief function, a model of the directed belief network with the conditional belief function (DEVN) was proposed. The relationship between knowledge and conditions in the network was represented by a directed acyclic graph plus the belief function, and the EN reasoning was realized through DRC and GBT [10; 11; 12]. [PERSON] et al. obtained the causal graph through an explicit causal matching algorithm and then constructed the evidential network by using the basic concepts of the belief function. Expansion and marginalization were used in the reasoning process to solve the problem of job-satisfaction evaluation [13]. [PERSON] and [PERSON] published five consecutive articles from 2007-2009, combining Bayesian networks and evidence theory in order to solve the reliability problems in complex systems, which mainly involve incomplete and inaccurate information. Their reasoning mode is still used in Bayesian theory [14; 15; 16; 17; 18]. Trained as a [PERSON] student, [PERSON] developed a BeliefNet tool in 2008 that combines the synthesis, marginalization, expansion, and projection algorithms of the evidential network with inference algorithms such as binary syndication and hash tables [19]. In 2012, [PERSON] and [PERSON] used a dynamically-directed evidential network with conditional belief functions for a study on system reliability, indicating that the directed evidential network is moving toward a dynamic direction [20].