Evaluation of argument strength in attack graphs: Foundations and semantics

Abstract An argumentation framework is a pair made of a graph and a semantics. The nodes and the edges of the graph represent respectively arguments and relations (e.g., attacks, supports) between arguments while the semantics evaluates the strength of each argument of the graph. This paper investigates gradual semantics dealing with weighted graphs, a family of graphs where each argument has an initial weight and may be attacked by other arguments. It contains four contributions. The first consists of laying the foundations of gradual semantics by proposing key principles on which evaluation of argument strength may be based. Foundations are important not only for a better understanding of the evaluation process in general, but also for clarifying the basic assumptions underlying semantics, for comparing different (families of) semantics, and for identifying families of semantics that have not been explored yet. The second contribution consists of providing a formal analysis and a comprehensive comparison of the semantics that have been defined in the literature for evaluating arguments in weighted graphs. As a third contribution, the paper proposes three novel semantics and shows which principles they satisfy. The last contribution is the implementation and empirical evaluation of the three novel semantics. We show that the three semantics are very efficient in that they compute the strengths of arguments in less than 20 iterations and in a very short time. This holds even for very large graphs, meaning that the three semantics scale very well.

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