A Matrix Approach for Weighted Argumentation Frameworks: a Preliminary Report
This work addresses computational challenges in formal argumentation for AI researchers, but it appears incremental as it builds on existing weighted frameworks.
The authors tackled the problem of computing semantics in weighted argumentation frameworks by representing them as non-binary matrices and characterizing extensions through matrix sub-blocks, resulting in algorithms for incrementally building w-grounded and w-preferred extensions from w-admissible ones.
The assignment of weights to attacks in a classical Argumentation Framework allows to compute semantics by taking into account the different importance of each argument. We represent a Weighted Argumentation Framework by a non-binary matrix, and we characterize the basic extensions (such as w-admissible, w- stable, w-complete) by analysing sub-blocks of this matrix. Also, we show how to reduce the matrix into another one of smaller size, that is equivalent to the original one for the determination of extensions. Furthermore, we provide two algorithms that allow to build incrementally w-grounded and w-preferred extensions starting from a w-admissible extension.