A two-phase method for extracting explanatory arguments from Bayesian networks

On Relating Abstract and Structured Probabilistic Argumentation: A Case Study

“…In this section we summarise [10]'s method for explaining (forensic) Bayesian networks with argumentation. A Bayesian network is a graphical representation of a joint probability distribution.…”

“…Formally, it is a pair (G, P r) where G is a directed acyclic graph (V, E), with a finite set of variables V connected by edges E from V × V, and P r is a probability function which specifies for every variable V i the probability distribution P r(V i |parents(V i )) of its outcomes conditioned on its parents parents(V i ) in the graph. [10] assume that all variables are boolean.…”

“…Then ϕ ∈ ψ iff ϕ and ψ assign different values to the same variable. The basic idea is illustrated with Figures 1 and 2, displaying an example from [10]. The variable of interest in the BN is whether the suspect committed the Crime.…”

“…The problem will be studied in the context of a simple instantiation of the ASPIC + framework [8]. In particular, [10]'s recent proposal will be studied to explain forensic Bayesian networks in terms of ASPIC + -style structured argumentation frameworks (SAF s) with probabilistic argument strengths. Since SAF s are an instance of [1]'s abstract argumentation frameworks (AF s), Timmer's probabilistic SAF s are a suitable candidate for being related to abstract probabilistic frameworks.…”

“…Section 3 gives a conceptual analysis of the problem of defining probabilistic strengths of structured arguments. Section 4 summarises [10]'s structured model of probabilistic argumentation. Section 5 then formally investigates its relation with abstract probabilistic argumentation frameworks, while Section 6 draws some general conclusions on the relation between abstract and structured models of probabilistic argumentation.…”