Goal structuring notation (GSN) is commonly proposed as a structuring tool for arguing about the high-level properties (e.g. safety) of a system. However, this approach does not include the representation of uncertainties that may affect arguments. Several works extend this framework using uncertainty propagation methods. The ones based on Dempster-Shafer Theory (DST) are of interest as DST can model incomplete information. However, few works relate this approach with a logical representation of relations between elements of GSN, which is actually required to justify the chosen uncertainty propagation schemes. In this paper, we improve previous proposals including a logical formalism added to GSN, and an elicitation procedure for obtaining uncertainty information from expert judgements. We briefly present an application to a case study to validate our uncertainty propagation model in GSN that takes into account both incomplete and conflicting information.