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Argument diagram extraction from evidential Bayesian networks

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Abstract

Bayesian networks (BN) and argumentation diagrams (AD) are two predominant approaches to legal evidential reasoning, that are often treated as alternatives to one another. This paper argues that they are, instead, complimentary and proposes the beginnings of a method to employ them in such a manner. The Bayesian approach tends to be used as a means to analyse the findings of forensic scientists. As such, it constitutes a means to perform evidential reasoning. The design of Bayesian networks that accurately and comprehensively represent the relationships between investigative hypotheses and evidence remains difficult and sometimes contentious, however. Argumentation diagrams are representations of reasoning, and are used as a means to scrutinise reasoning (among other applications). In evidential reasoning, they tend to be used to represent and scrutinise the way humans reason about evidence. This paper examines how argumentation diagrams can be used to scrutinise Bayesian evidential reasoning by developing a method to extract argument diagrams from BN.

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Notes

  1. For example, to derive P(c|a 1,a 2) from CPTs expressing P(A 1|C) and P(A 2|C), Bayes’ law is applied as follows:

    $$ P(c|a_1,a_2)=\frac{P(a_1|c)P(a_2|c)P(c)}{P(a_1|c)P(a_2|c)P(c)+P(a_1|\overline{c})P(a_2|\overline{c})P(\overline{c})} $$

    The values for P(a i |c) and \(P(a_i|\overline{c})\) are given by the CPTs for P(A i |C). However, the calculation of P(c) and \(P(\overline{c})\) relies on prior probabilities.

  2. In our algorithm, a path from V 1 to V 2 to V 3 via edges \(V_1 \rightarrow V_2\) and \(V_2 \rightarrow V_3\) is denoted \(V_1 \rightarrow V_2 \rightarrow V_3\).

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  1. Department of Informatics, King’s College London, Strand, London, WC2R 2LS, UK

    Jeroen Keppens

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  1. Jeroen Keppens
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Keppens, J. Argument diagram extraction from evidential Bayesian networks. Artif Intell Law 20, 109–143 (2012). https://doi.org/10.1007/s10506-012-9121-z

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