A traditional assurance case employs a positive argument in which reasoning steps, grounded on evidence and assumptions, sustain a top claim that has external significance. Human judgement is required to check the evidence, the assumptions, and the narrative justifications for the reasoning steps; if all are assessed good, then the top claim can be accepted. A valid concern about this process is that human judgement is fallible and prone to confirmation bias. The best defense against this concern is vigorous and skeptical debate and discussion in the manner of a dialectic or Socratic dialog. There is merit in recording aspects of this discussion for the benefit of subsequent developers and assessors. Defeaters are a means doing this: they express doubts about aspects of the argument and can be developed into subcases that confirm or refute the doubts, and can record them as documentation to assist future consideration. This report describes how defeaters, and multiple levels of defeaters, should be represented and assessed in Assurance 2.0 and its Clarissa/ASCE tool support. These mechanisms also support eliminative argumentation, which is a contrary approach to assurance, favored by some, that uses a negative argument to refute all reasons why the top claim could be false.

Dempster-Shafer Theory (DST) generalizes Bayesian probability theory, offering useful additional information, but suffers from a high computational burden. A lot of work has been done to reduce the complexity of computations used in information fusion with Dempster's rule. Yet, few research had been conducted to reduce the complexity of computations for the conjunctive and disjunctive decompositions of evidence, which are at the core of other important methods of information fusion. In this paper, we propose a method designed to exploit the actual evidence (information) contained in these decompositions in order to compute them. It is based on a new notion that we call focal point, derived from the notion of focal set. With it, we are able to reduce these computations up to a linear complexity in the number of focal sets in some cases. In a broader perspective, our formulas have the potential to be tractable when the size of the frame of discernment exceeds a few dozen possible states, contrary to the existing litterature. This article extends (and translates) our work published at the french conference GRETSI in 2019.