Propagating Knowledge Strength Through Assurance Arguments using Three-Valued Logic to Assess Confidence in Claims

Assurance refers to the substantiation and scrutiny of claims about a system's capabilities and the risks associated with it. The assurance process involves formulating claims that capture stakeholders' interests in the system and building structured arguments to validate and verify the claims. The end goal is to determine if there are sufficient grounds for confidence in the claims, which requires a measure of confidence and a method for propagating it through the assurance argument. One common approach for propagating uncertainty through arguments is by use of probability theory and Bayesian Networks. However, the probability numbers used in such models do not capture uncertainties in the knowledge used to assign them. Many authors have therefore suggested alternative approaches based on extensions of probability theory, including Dempster-Shafer theory and subjective logic. However, such quantitative methods have been criticized based on ambiguity in interpretation and examples of seemingly inconsistent results. Another framework called Assurance 2.0 moves away from the focus on quantifying confidence and rather aims towards "indefeasible justification", meaning qualitative confidence that there are no overlooked or unresolved doubts that could change conclusions. In this paper, we propose to use the concept of knowledge strength as a practical way to assess confidence in claims. Specifically, a claim is considered true or false only if there is strong knowledge to substantiate it; otherwise, it is treated as uncertain.We then propagate confidence through the assurance arguments using three-valued logic. Inspired by Assurance 2.0, we emphasize the need for addressing doubts that could topple an argument and the need for incorporating counter evidence in the form of defeaters. Our proposed approach is demonstrated on an example of a machine-learning-based crack detection tool.

Keywords: Assurance, Strength of knowledge, Three-valued logic.