Bayesian networks (BNs) are powerful tools that are well-suited for reasoning about the uncertain consequences that can be inferred from evidence. Domain experts, however, typically do not have the expertise to construct BNs and instead resort to using other tools such as argument diagrams and mind maps. Recently, a structured approach was proposed to construct a BN graph from arguments annotated with causality information. As argumentative inferences may not be causal, we generalize this approach to include other types of inferences in this paper. Moreover, we prove a number of formal properties of the generalized approach and identify assumptions under which the construction of an initial BN graph can be fully automated