Structured safety arguments are widely applied in critical systems to demonstrate their safety and other attributes. Graphical formalisms such as Goal Structuring Notation (GSN) are used to represent these argument structures. However, they do not take into account the uncertainty that may exist in parts of these arguments. To address this issue, several frameworks for confidence assessment have been proposed. In this paper, a comparative study is carried out on three approaches based on Dempster-Shafer theory. We extract and compare the implicit logic at work in these works, and show that, to some extent, these current approaches fail to provide a consistent relationship between the informal statement of arguments, their logical model and the use of belief functions. We also propose recommendations to improve this consistency.