The Linear Algebra of Abstract Argumentation

In Abstract Argumentation, the task of modeling and analyzing semantics is a hot problem. An alternative representation of computational models of argument, based on the matrix theory, is proposed, in order to obtain a deeper understanding of extension-based semantics and of ranking semantics too. In this paper, we start from the concept of matrix representation of an argumentation graph and develop a general strategy to model both extension-based semantics and ranking-based ones, and both classical and new ones, in terms of matrix operations. This line of research is strongly based on linear algebra to evaluate arguments. Such procedures confirm the ability to evaluate arguments and open to new perspectives in the field of ranking semantics.