Coalitions of Arguments: An Approach with Constraint Programming

The aggregation of generic items into coalitions leads to the creation of sets of homogenous entities. In this paper we accomplish this for an input set of arguments, and the result is a partition according to distinct lines of thought, i.e., groups of “coherent” ideas. We extend Dung’s Argumentation Framework (AF) in order to deal with coalitions of arguments. The initial set of arguments is partitioned into not-intersected subsets. All the found coalitions show the same property inherited by Dung, e.g., all the coalitions in the partition are admissible (or conflict-free, complete, stable): they are generated according to Dung’s principles. Each of these coalitions can be assigned to a different agent. We use Soft Constraint Programming as a formal approach to model and solve such partitions in weighted AFs: semiring algebraic structures can be used to model different optimization criteria for the obtained coalitions. Moreover, we implement and solve the presented problem with JaCoP, a Java constraint solver, and we test the code over a small-world network. This work was carried out during the tenure of the ERCIM “Alain Bensoussan” Fellowship Programme, which is supported by the Marie Curie Co-funding of Regional, National and International Programmes (COFUND) of the European Commission. Research partially supported by MIUR PRIN 2010-2011 2010FP79LR project “Logical Methods of Information Management”, by the European Integrated Project 257414 ASCENS, and by COST Action IC0801 Corresponding author 1002 S. Bistarelli, and F. Santini / Coalitions of Arguments: An Approach with Constraint Programming