A Bayesian network (BN) is a graphical model of uncertainty that is especially well suited to legal arguments. It enables us to visualize and model dependencies between different hypotheses and pieces of evidence and to calculate the revised probability beliefs about all uncertain factors when any piece of new evidence is presented. Although BNs have been widely discussed and recently used in the context of legal arguments, there is no systematic, repeatable method for modeling legal arguments as BNs. Hence, where (...) BNs have been used in the legal context, they are presented as completed pieces of work, with no insights into the reasoning and working that must have gone into their construction. This means the process of building BNs for legal arguments is ad hoc, with little possibility for learning and process improvement. This article directly addresses this problem by describing a method for building useful legal arguments in a consistent and repeatable way. The method complements and extends recent work by Hepler, Dawid, and Leucari (2007) on object-oriented BNs for complex legal arguments and is based on the recognition that such arguments can be built up from a small number of basic causal structures (referred to as idioms). We present a number of examples that demonstrate the practicality and usefulness of the method. (shrink)

Bayesian models of legal arguments generally aim to produce a single integrated model, combining each of the legal arguments under consideration. This combined approach implicitly assumes that variables and their relationships can be represented without any contradiction or misalignment, and in a way that makes sense with respect to the competing argument narratives. This paper describes a novel approach to compare and ‘average’ Bayesian models of legal arguments that have been built independently and with no attempt to make them consistent (...) in terms of variables, causal assumptions or parameterization. The approach involves assessing whether competing models of legal arguments are explained or predict facts uncovered before or during the trial process. Those models that are more heavily disconfirmed by the facts are given lower weight, as model plausibility measures, in the Bayesian model comparison and averaging framework adopted. In this way a plurality of arguments is allowed yet a single judgement based on all arguments is possible and rational. (shrink)

(2013). Legal idioms: a framework for evidential reasoning. Argument & Computation: Vol. 4, Formal Models of Reasoning in Cognitive Psychology, pp. 46-63. doi: 10.1080/19462166.2012.682656.

Fenton et al. present a Bayesian‐network analysis of the case, using their previously developed set of building blocks (‘idioms’). They claim that these idioms, combined with their opportunity‐based method for estimating the prior probability of guilt, reduce the subjectivity of their analysis. Although their Bayesian model is less cognitively feasible than scenario‐ or argumentation‐based models, they claim that it does model the standard approach to legal proof, which is to continually revise beliefs under new evidence.

It is well known that Bayes’ theorem (with likelihood ratios) can be used to calculate the impact of evidence, such as a ‘match’ of some feature of a person. Typically the feature of interest is the DNA profile, but the method applies in principle to any feature of a person or object, including not just DNA, fingerprints, or footprints, but also more basic features such as skin colour, height, hair colour or even name. Notwithstanding concerns about the extensiveness of databases (...) of such features, a serious challenge to the use of Bayes in such legal contexts is that its standard formulaic representations are not readily understandable to non-statisticians. Attempts to get round this problem usually involve representations based around some variation of an event tree. While this approach works well in explaining the most trivial instance of Bayes’ theorem (involving a single hypothesis and a single piece of evidence) it does not scale up to realistic situations. In particular, even with a single piece of match evidence, if we wish to incorporate the possibility that there are potential errors (both false positives and false negatives) introduced at any stage in the investigative process, matters become very complex. As a result we have observed expert witnesses (in different areas of speciality) routinely ignore the possibility of errors when presenting their evidence. To counter this, we produce what we believe is the first full probabilistic solution of the simple case of generic match evidence incorporating both classes of testing errors. Unfortunately, the resultant event tree solution is too complex for intuitive comprehension. And, crucially, the event tree also fails to represent the causal information that underpins the argument. In contrast, we also present a simple-to-construct graphical Bayesian Network (BN) solution that automatically performs the calculations and may also be intuitively simpler to understand. Although there have been multiple previous applications of BNs for analysing forensic evidence—including very detailed models for the DNA matching problem, these models have not widely penetrated the expert witness community. Nor have they addressed the basic generic match problem incorporating the two types of testing error. Hence we believe our basic BN solution provides an important mechanism for convincing experts—and eventually the legal community—that it is possible to rigorously analyse and communicate the full impact of match evidence on a case, in the presence of possible errors. (shrink)

Sterols and the reductant nicotinamide adenine dinucleotide phosphate (NADPH), essential for eukaryotic life, arose because of, and as an adaptation to, rising levels of molecular oxygen (O2). Hence, the NADPH and O2‐intensive process of sterol biosynthesis is inextricably linked to redox status. In mammals, cholesterol biosynthesis is exquisitely regulated post‐translationally by multiple E3 ubiquitin ligases, with membrane associated Really Interesting New Gene (RING) C3HC4 finger 6 (MARCHF6) degrading at least six enzymes in the pathway. Intriguingly, all these MARCHF6‐dependent enzymes require (...) NADPH. Moreover, MARCHF6 is activated by NADPH, although what this means for control of cholesterol synthesis is unclear. Indeed, this presents a paradox for how NADPH regulates this vital pathway, since NADPH is a cofactor in cholesterol biosynthesis and yet, low levels of NADPH should spare cholesterol biosynthesis enzymes targeted by MARCHF6 by reducing its activity. We speculate MARCHF6 helps mammalian cells adapt to oxidative stress (signified by low NADPH levels) by reducing degradation of cholesterogenic enzymes, thereby maintaining synthesis of protective cholesterol. (shrink)

Modelling that exploits visual elements and information visualisation are important areas that have contributed immensely to understanding and the computerisation advancements in many domains and yet remain unexplored for the benefit of the law and legal practice. This paper investigates the challenge of modelling and expressing structures and processes in legislation and the law by using visual modelling and information visualisation (InfoVis) to assist accessibility of legal knowledge, practice and knowledge formalisation as a basis for legal AI. The paper uses (...) a subset of the well-defined Unified Modelling Language (UML) to visually express the structure and process of the legislation and the law to create visual flow diagrams called lawmaps, which form the basis of further formalisation. A lawmap development methodology is presented and evaluated by creating a set of lawmaps for the practice of conveyancing and the Landlords and Tenants Act 1954 of the United Kingdom. This paper is the first of a new breed of preliminary solutions capable of application across all aspects, from legislation to practice; and capable of accelerating development of legal AI. (shrink)

As is clear to any user of software, quality control of software has not reached the same levels of sophistication as it has with traditional manufacturing. In this paper we argue that this is because insufficient thought is being given to the methods of reasoning under uncertainty that are appropriate to this domain. We then describe how we have built a large-scale Bayesian network to overcome the difficulties that have so far been met in software quality control. This exploits a (...) number of recent advances in tool support for constructing large networks. We end the paper by describing how the network was validated and illustrate the range of reasoning styles that can be modelled with this tool. (shrink)