Evidence, Proofs, and Derivations

The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical practice. Nonetheless, evidence, proof, and derivation are closely intertwined. This paper seeks to tease these concepts apart. It emphasizes the role of argumentation as a context shared by evidence, proofs, and derivations. The utility of argumentation theory, in general, and argumentation schemes, in particular, as a methodology for the study of mathematical practice is thereby demonstrated. Argumentation schemes represent an almost untapped resource for mathematics education. Notably, they provide a consistent treatment of rigorous and non-rigorous argumentation, thereby working to exhibit the continuity of reasoning in mathematics with reasoning in other areas. Moreover, since argumentation schemes are a comparatively mature methodology, there is a substantial body of existing work to draw upon, including some increasingly sophisticated software tools. Such tools have significant potential for the analysis and evaluation of mathematical argumentation. The first four sections of the paper address the relationships of evidence to proof, proof to derivation, argument to proof, and argument to evidence, respectively. The final section directly addresses some of the educational implications of an argumentation scheme account of mathematical reasoning

Formalism and judgement in assurance cases

This position paper deals with the tension between the desire for sound and auditable assurance cases and the current ubiquitous reliance on expert judgement. I believe that the use of expert judgement, though inevitable, needs to be much more cautious and disciplined than it usually is. The idea of assurance “cases ” owes its appeal to an awareness that all too often critical decisions are made in ways that are difficult to justify or even to explain, leaving the doubt (for the decision makers as well as other interested parties) that the decision may be unsound. By building a well-structured “case ” we would wish to allow proper scrutiny of the evidence and assumptions used, and of the arguments that link them to support a decision. A

Civil Procedure as a Critical Discussion

This Article develops a model for analyzing legal dispute resolution systems as systems for argumentation. Our model meshes two theories of argument conceived centuries apart: contemporary argumentation theory and classical stasis theory. In this Article, we apply the model to the Federal Rules of Civil Procedure as a proof of concept. Specifically, the model analyzes how the Federal Rules of Civil Procedure function as a staged argumentative critical discussion designed to permit judge and jury to rationally resolve litigants’ differences in a reasonable manner. At a high level, this critical discussion has three phases: a confrontation, an (extended) opening, and a concluding phase. Those phases are the umbrella under which discrete argumentation phases occur at points we call stases. Whenever litigants seek a ruling or judgment, they reach a stasis—a stopping or standing point for arguing procedural points of disagreement. During these stases, the parties make arguments that fall into predictable “commonplace” argument types. Taken together, these stock argument types form a taxonomy of arguments for all civil cases. Our claim that the Federal Rules of Civil Procedure function as a system for argumentation is novel, as is our claim that civil cases breed a taxonomy of argument types. These claims also mark the beginning of a broader project. Starting here with the Federal Rules of Civil Procedure, we embark on a journey that we expect to follow for several years (and which we hope other scholars will join), exploring our model’s application across dispute resolution systems and using it to make normative claims about those systems. From a birds-eye view, this Article also represents a short modern trek in a much longer journey begun by advocates in city states in and near Greece nearly 2500 years ago

Theory of Regulatory Compliance for Requirements Engineering

Regulatory compliance is increasingly being addressed in the practice of requirements engineering as a main stream concern. This paper points out a gap in the theoretical foundations of regulatory compliance, and presents a theory that states (i) what it means for requirements to be compliant, (ii) the compliance problem, i.e., the problem that the engineer should resolve in order to verify whether requirements are compliant, and (iii) testable hypotheses (predictions) about how compliance of requirements is verified. The theory is instantiated by presenting a requirements engineering framework that implements its principles, and is exemplified on a real-world case study.Comment: 16 page