Graduality in interaction-based valuations

We consider two different valuation methods for taking into account the quality of attackers and defenders of an argument in order to define the value of an argument using only the interaction between arguments13:

The main difference between these two approaches is illustrated by the following example:


In the local approach, $B$ has two direct attackers ($C_2$ and $C_1$) whereas $B'$ has only one ($C'$). Thus $B'$ is better than $B$ (since $B'$ suffers one attack whereas $B$ suffers two attacks).

In the global approach, two branches (one of attack and one of defence) lead to $B$ whereas only one branch of attack leads to $B'$. Thus $B$ is better than $B'$ (since it has at least one defence whereas $B'$ has none). In this case, $C_1$ loses its negative status of attacker, since it is in fact ``carrying a defence'' for $B$.

Marie-Christine Lagasquie 2005-02-04