Sjoerd T. Timmer

A structure-guided approach to capturing bayesian reasoning about legal evidence in argumentation

Over the last decades the rise of forensic sciences has led to an increase in the availability of statistical evidence. Reasoning about statistics and probabilities in a forensic science setting can be a precarious exercise, especially so when independencies between variables are involved. To facilitate the correct explanation of such evidence we investigate how argumentation models can help in the interpretation of statistical information. In this paper we focus on the connection between argumentation models and Bayesian belief networks, the latter being a common model to represent and reason with complex probabilistic information. We introduce the notion of a support graph as an intermediate structure between Bayesian networks and argumentation models. A support graph disentangles the complicating graphical properties of a Bayesian network and enhances its intuitive interpretation. Moreover, we show that this model can provide a suitable template for argumentative analysis. Especially in the context of legal reasoning, the correct treatment of statistical evidence is important.

Explaining Bayesian Networks Using Argumentation

Qualitative and quantitative systems to deal with uncertainty coexist. Bayesian networks are a well known tool in probabilistic reasoning. For non-statistical experts, however, Bayesian networks may be hard to interpret. Especially since the inner workings of Bayesian networks are complicated they may appear as black box models. Argumentation models, on the contrary, emphasise the derivation of results. However, they have notorious difficulty dealing with probabilities. In this paper we formalise a two-phase method to extract probabilistically supported arguments from a Bayesian network. First, from a BN we construct a support graph, and, second, given a set of observations we build arguments from that support graph. Such arguments can facilitate the correct interpretation and explanation of the evidence modelled in the Bayesian network.

Exact algorithms for Kayles

In the game of Kayles, two players select alternatingly a vertex from a given graph G, but may never choose a vertex that is adjacent or equal to an already chosen vertex. The last player that can select a vertex wins the game. In this paper, we give an exact algorithm to determine which player has a winning strategy in this game. To analyze the running time of the algorithm, we introduce the notion of a K-set: a nonempty set of vertices W ? V is a K-set in a graph G = ( V , E ) , if G W is connected and there exists an independent set X such that W = V - N X . The running time of the algorithm is bounded by a polynomial factor times the number of K-sets in G. We prove that the number of K-sets in a graph with n vertices is bounded by O ( 1.6052 n ) . A computer-generated case analysis improves this bound to O ( 1.6031 n ) K-sets, and thus we have an upper bound of O ( 1.6031 n ) on the running time of the algorithm for Kayles. We also show that the number of K-sets in a tree is bounded by n ? 3 n / 3 and thus Kayles can be solved on trees in O ( 1.4423 n ) time. We show that apart from a polynomial factor, the number of K-sets in a tree is sharp.As corollaries, we obtain that determining which player has a winning strategy in the games G avoid ( POS DNF 2 ) and G seek ( POSDNF 3 ) can also be determined in O ( 1.6031 n ) time. In G avoid ( POSDNF 2 ) , we have a positive formula F on n Boolean variables in Disjunctive Normal Form with two variables per clause. Initially, all variables are false, and players alternately set a variable from false to true; the first player that makes F true loses the game. The game G seek ( POSDNF 3 ) is similar, but now there are three variables per clause, and the first player that makes F true wins the game.

Demonstration of a structure-guided approach to capturing bayesian reasoning about legal evidence in argumentation

Reasoning about statistics and probabilities can, when not treated with cautiousness, lead to reasoning errors. Over the last decades the rise of forensic sciences has led to an increase in the availability of statistical evidence. To facilitate the correct explanation of such evidence we investigate how argumentation models can help in the interpretation of statistical information. Uncertainties are by forensic experts often expressed numerically, but lawyers, judges and other legal experts have notorious difficulty interpreting these results [3, 1, 2, 5]. In this demonstration of our main paper [6] we focus on the connection between formal models of argumentation and Bayesian belief networks (BNs). We use BNs because they are a well-known model to represent and reason with complex probabilistic information. We introduce the notion of a support graph as an intermediate structure between Bayesian networks and argumentation models. A support graph captures the inferences modelled in a Bayesian network but disentangles the complicating graphical properties of such models and instead emphasises its intuitive understanding. Moreover, we show that this intermediate model can function as a template to generate different arguments based on the data.

A Tool for the Generation of Arguments from Bayesian Networks

This demonstration shows how arguments, formalised in a well defined framework, can be automatically constructed from a given Bayesian network.