  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.
