We now consider a second approach for the valuation step, called the global approach. Here, the key idea is that the value of must describe the subgraph whose root is . So, we want to memorise the length of each branch leading to in a tuple (for an attack branch, we have an odd integer, and for a defence branch, we have an even integer).
In this approach, the main constraint is that we must be able to identify the branches leading to the argument and to compute their lengths. This is very easy in the case of an acyclic graph. We therefore introduce first a global gradual valuation for acyclic graphs. Then, in the next sections, we extend our proposition to the case of graphs with cycles, and we study the properties of this global gradual valuation.