Algebraic Approach for Confidence Evaluation of Assurance Cases

This paper presents a preliminary study on a method to evaluate the confidence of assurance cases using an abstract algebra mapped to a partial order. Unlike conventional quantitative methods for confidence evaluation, our approach is purely qualitative and employs a small number of axioms. It does not rely on numerical parameters that are difficult to determine in practice. Furthermore, our method can be regarded as an abstraction over numerical methods that use probability. To illustrate that our method provides a rigorous foundation for the qualitative evaluation of assurance cases, we give a sufficient condition for a multi-legged argument to improve confidence. Finally, we use our method to evaluate a concrete goal structuring notation (GSN) diagram that argues that a computer simulation of a biological system is reliable. These findings suggest that methods based on abstract axioms are viable approaches for confidence evaluation of assurance cases.