Quantifying Confidence of Safety Cases with Belief Functions

Abstract

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.

Uncertainty Elicitation and Propagation in GSN Models of Assurance Cases

“…Thus, we deduce that this GSN represent a conjunctive type where all sub-goals are needed to support (G 1 ). As seen in [10], C-Arg tends to propagate the premises that support the conclusion with the least weight, increasing along with it the uncertainty level. Thus, we can explain why we go from acceptable premises with very high confidence (G 6 , G 7 ), high confidence (G 5 ) and for sure (G 4 ) to a tolerable top goal (G 1 ) with low confidence (Dec = 0.692, Conf = 0.384).…”

“…In [10], we provided a recursive equation to compute m n ∩ (∅) for n premises when we know m n−1 ∩ (∅):…”

A Qualitative Counterpart of Belief Functions with Application to Uncertainty Propagation in Safety Cases

“…Two types of information are collected from experts about a statement A: A so-called decision and a level of confidence associated to it. Then, these pieces of information are numerically encoded, and transformed to belief and disbelief degrees in the sense of Shafer (see also [7]). More precisely:…”

“…In this approach each formula in a knowledge base is viewed as a simple support function and combined with other formulas in the knowledge base. Besides, the application of belief functions to argument structures has been studied in [2,10,7] to build models for uncertainty propagation. For instance in [7], we assign mass functions to logical expressions such as facts p i , ¬p i , and rules p i ⇒ C, ¬p i ⇒ ¬C, (∧ n i=1 p i ) ⇒ C and (∧ n i=1 ¬p i ) ⇒ ¬C, in order to deduce the belief on the conclusions C and ¬C.…”

“…In order to address the issue of incomplete information, Dempster-Shafer theory (DST) is also proposed. In the latter case, argument trees can be modelled in classical logic using if-then rules [6,7].…”