Computing the grounded semantics in all the subgraphs of an argumentation framework: An empirical evaluation

Abstract

Given an argumentation framework AF = (Ar, R) - with Ar a finite set of arguments and R ⊆ Ar x Ar the attack relation identifying the graph G - we study how the grounded labelling of a generic argument a ∈ Ar varies in all the subgraphs of G. Since this is an intractable problem of above-polynomial complexity, we present two non-naïve algorithms to find the set of all the subgraphs where the grounded semantic assigns to argument a specific label l ∈ {in, out, undec}. We report the results of a series of empirical tests over graphs of increasing complexity. The value of researching the above problem is two-fold. First, knowing how an argument behaves in all the subgraphs represents strategic information for arguing agents. Second, the algorithms can be applied to the computation of the recently introduced probabilistic argumentation frameworks. © 2013 Springer-Verlag.