The use of multilegged arguments to increase confidence in safety claims for software-based systems: A study based on a BBN analysis of an idealized example

The work described here concerns the use of so-called multi-legged arguments to support dependability claims about software-based systems. The informal justification for the use of multi-legged arguments is similar to that used to support the use of multi-version software in pursuit of high reliability or safety. Just as a diverse, 1-out-of-2 system might be expected to be more reliable than each of its two component versions, so a two-legged argument might be expected to give greater confidence in the correctness of a dependability claim (e.g. a safety claim) than would either of the argument legs alone. Our intention here is to treat these argument structures formally, in particular by presenting a formal probabilistic treatment of ‘confidence’, which will be used as a measure of efficacy. This will enable claims for the efficacy of the multi-legged approach to be made quantitatively, answering questions such as ‘How much extra confidence about a system’s safety will I have if I add a verification argument leg to an argument leg based upon statistical testing?’ For this initial study, we concentrate on a simplified and idealized example of a safety system in which interest centres upon a claim about the probability of failure on demand. Our approach is to build a BBN (“Bayesian Belief Network”) model of a two-legged argument, and manipulate this analytically via parameters that define its node probability tables. The aim here is to obtain greater insight than is afforded by the more usual BBN treatment, which involves merely numerical manipulation. We show that the addition of a diverse second argument leg can, indeed, increase confidence in a dependability claim: in a reasonably plausible example the doubt in the claim is reduced to one third of the doubt present in the original single leg. However, we also show that there can be some unexpected and counter-intuitive subtleties here; for example an entirely supportive second leg can sometimes undermine an original argument, resulting overall in less confidence than came from this original argument. Our results are neutral on the issue of whether such difficulties will arise in real life - i.e. when real experts judge real systems

Higher-Order Defeat and Doxastic Resilience

It seems obvious that when higher-order evidence makes it rational for one to doubt that one’s own belief on some matter is rational, this can undermine the rationality of that belief. This is known as higher-order defeat. However, despite its intuitive plausibility, it has proved puzzling how higher-order defeat works, exactly. To highlight two prominent sources of puzzlement, higher-order defeat seems to defy being understood in terms of conditionalization; and higher-order defeat can sometimes place agents in what seem like epistemic dilemmas. This chapter draws attention to an overlooked aspect of higher-order defeat, namely that it can undermine the resilience of one’s beliefs. The notion of resilience was originally devised to understand how one should reflect the ‘weight’ of one’s evidence. But it can also be applied to understand how one should reflect one’s higher-order evidence. The idea is particularly useful for understanding cases where one’s higher-order evidence indicates that one has failed in correctly assessing the evidence, without indicating whether one has over- or underestimated the degree of evidential support for a proposition. But it is exactly in such cases that the puzzles of higher-order defeat seem most compelling

Visualizing Probabilistic Proof

The author revisits the Blue Bus Problem, a famous thought-experiment in law involving probabilistic proof, and presents simple Bayesian solutions to different versions of the blue bus problem. In addition, the author expresses his solutions in standard and visual formats, i.e. in terms of probabilities and natural frequencies

An Algebraic Opportunity to Develop Proving Ability

Set-based reasoning and conditional language are two critical components of deductive argumentation and facility with proof. The purpose of this qualitative study was to describe the role of truth value and the solution set in supporting the development of the ability to reason about classes of objects and use conditional language. This study first examined proof schemes – how students convince themselves and persuade others – of Algebra I students when justifying solutions to routine and non-routine equations. After identifying how participants learned to use set-based reasoning and conditional language in the context of solving equations, the study then determined if participants would employ similar reasoning in a geometrical context. As a whole, the study endeavored to describe a possible trajectory for students to transition from non-deductive justifications in an algebraic context to argumentation that supports proof writing. First, task-based interviews elicited how participants became absolutely certain about solutions to equations. Next, a teaching experiment was completed to identify how participants who previously accepted empirical arguments as proof shifted to making deductive arguments. Last, additional task-based interviews in which participants reasoned about the relationship between Varignon Parallelograms and Varignon Rectangles were conducted. The first set of task-based interviews found that a majority of participants displayed ritualistic proof schemes – they viewed equations as prompts to execute processes and solutions as results, or “answers.” Approximately half of participants employed empirical proof schemes; they described convincing themselves or others using a range of arguments that do not constitute valid proof. One particularly noteworthy finding was that no participants initially used deductive justifications to reach absolute certainty. Participants successfully adopted set-based reasoning and learned to use conditional language by progressively accommodating a series of understandings. They later utilized their new ways of reasoning in the geometrical context. Participants employed the implication structure, discriminated between necessary and sufficient conditions, and maintained a disposition of doubt toward empirical evidence. Finally, implications of these findings for pedagogues and researchers, as well as future directions for research, are discussed

A structured argumentation framework for detaching conditional obligations

We present a general formal argumentation system for dealing with the detachment of conditional obligations. Given a set of facts, constraints, and conditional obligations, we answer the question whether an unconditional obligation is detachable by considering reasons for and against its detachment. For the evaluation of arguments in favor of detaching obligations we use a Dung-style argumentation-theoretical semantics. We illustrate the modularity of the general framework by considering some extensions, and we compare the framework to some related approaches from the literature.Comment: This is our submission to DEON 2016, including the technical appendi

God and the external world

There are a number of apparent parallels between belief in God and belief in the existence of an external world beyond our experiences. Both beliefs would seem to condition one’s overall view of reality and one’s place within it – and yet it is difficult to see how either can be defended. Neither belief is likely to receive a purely a priori defence and any empirical evidence that one cites either in favour of the existence of God or the existence of the external world would seem to blatantly beg the question against a doubter. I will examine just how far this parallel can be pushed by examining some strategies for resisting external world scepticism