Understanding and Evaluating Assurance Cases

Assurance cases are a method for providing assurance for a system by giving an argument to justify a claim about the system, based on evidence about its design, development, and tested behavior. In comparison with assurance based on guidelines or standards (which essentially specify only the evidence to be produced), the chief novelty in assurance cases is provision of an explicit argument. In principle, this can allow assurance cases to be more finely tuned to the specific circumstances of the system, and more agile than guidelines in adapting to new techniques and applications. The first part of this report (Sections 1-4) provides an introduction to assurance cases. Although this material should be accessible to all those with an interest in these topics, the examples focus on software for airborne systems, traditionally assured using the DO-178C guidelines and its predecessors. A brief survey of some existing assurance cases is provided in Section 5. The second part (Section 6) considers the criteria, methods, and tools that may be used to evaluate whether an assurance case provides sufficient confidence that a particular system or service is fit for its intended use. An assurance case cannot provide unequivocal "proof" for its claim, so much of the discussion focuses on the interpretation of such less-than-definitive arguments, and on methods to counteract confirmation bias and other fallibilities in human reasoning

An Epistemic Framing Analysis of Upper Level Physics Students' Use of Mathematics

Mathematics is central to a professional physicist's work and, by extension, to a physics student's studies. It provides a language for abstraction, definition, computation, and connection to physical reality. This power of mathematics in physics is also the source of many of the difficulties it presents students. Simply put, many different activities could all be described as "using math in physics". Expertise entails a complicated coordination of these various activities. This work examines the many different kinds of thinking that are all facets of the use of mathematics in physics. It uses an epistemological lens, one that looks at the type of explanation a student presently sees as appropriate, to analyze the mathematical thinking of upper level physics undergraduates. Sometimes a student will turn to a detailed calculation to produce or justify an answer. Other times a physical argument is explicitly connected to the mathematics at hand. Still other times quoting a definition is seen as sufficient, and so on. Local coherencies evolve in students' thought around these various types of mathematical justifications. We use the cognitive process of framing to model students' navigation of these various facets of math use in physics. We first demonstrate several common framings observed in our students' mathematical thought and give several examples of each. Armed with this analysis tool, we then give several examples of how this framing analysis can be used to address a research question. We consider what effects, if any, a powerful symbolic calculator has on students' thinking. We also consider how to characterize growing expertise among physics students. Framing offers a lens for analysis that is a natural fit for these sample research questions. To active physics education researchers, the framing analysis presented in this dissertation can provide a useful tool for addressing other research questions. To physics teachers, we present this analysis so that it may make them more explicitly aware of the various types of reasoning, and the dynamics among them, that students employ in our physics classes. This awareness will help us better hear students' arguments and respond appropriately

Sifting the Commonplace: Topoi and the Grounds for Argument in Classical and Modern Rhetoric

This dissertation is a reminder that how we consider reasoning to work and its end is very much bound up with how we think about people, what they are, what they can be, and how they do and should live together. Part of the end of the human being is to understand, to understand the Good or God and thus understand herself and her relation to others and her obligation to others; this is something we see in Aristotle\u27s somewhat-spiritual understanding of Ethics and the Human Being. Focusing on reasoning (and its connection to being) in general, instead of accenting the limitations and conditionings of the human capacity to know, is part of the means of securing the road for this end, which is especially important, as understanding, which is of and by being, is bound up with morality and moral development. Also, bound up with understanding and how human beings should convey it and build it up are rhetoric and dialectic, which are meant to get to the same end, Good or God, together. It is a fundamental contention of this project that rhetoric and dialectic cannot or should not be separated, nor these separated from substance, for rhetoric and dialectic easily become instruments of abuse in isolation, as in, for example, a rigid formalism of the self or a rigid formalism of philosophy. I will focus on dialectical aspects of reasoning and understanding here. Situating Aristotle\u27s discussion of how reasoning operates in a discussion prompted by Toulmin\u27s Uses of Argument, this dissertation shows how Aristotle attempts to avoid the lure of formalism by grounding reasoning and its evaluation in the real (which he understands as the connection among mind, world, and language)