Structured safety argument based on graphical representations such as GSN (Goal Structuring Notation) are used to justify the certification of critical systems. However, such approaches do not deal with uncertainties that might affect the merits of arguments. In the recent past, some authors proposed to model the confidence in such arguments using Dempster-Shafer theory. It enables us to determine the confidence degree in conclusions for some basic GSN patterns. In this paper, we refine this approach and improve the elicitation method for expert opinions used in previous papers.

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.

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.

Critical systems such as those developed in the aerospace, railway or automotive industries need official documents to certify their safety via convincing arguments. However, informal tools used in certification documents seldom cover the uncertainty that pervades safety cases. Several works use quantitative approaches based on belief functions to model and propagate confidence/uncertainty in the argument structures (particularly those using goal structuring notation). However the numerical uncertainty information is often a naive encoding of qualitative expert inputs. In this paper, we outline a qualitative substitute to Dempster-Shafer theory and suggest new qualitative confidence propagation models. We also propose a more faithful encoding of expert inputs.