Equilibrium States in Numerical Argumentation Networks
This addresses a specific computational problem in formal argumentation theory, with incremental contributions to existing numerical methods.
The paper tackles the problem of finding argumentation network extensions compatible with initial argument values by proposing an iteration formula that converges to an extension, and investigates its properties and connections to other techniques.
Given an argumentation network with initial values to the arguments, we look for algorithms which can yield extensions compatible with such initial values. We find that the best way of tackling this problem is to offer an iteration formula that takes the initial values and the attack relation and iterates a sequence of intermediate values that eventually converges leading to an extension. The properties surrounding the application of the iteration formula and its connection with other numerical and non-numerical techniques proposed by others are thoroughly investigated in this paper.