In this lecture, we will study how serialisability (see Lecture 2A) can be used to rank arguments.
We recommend the interested reader to read the full paper in the reading list.
Let us consider the argumentation framework displayed below.
We have a “feeling” that $c$ is better than $b$ or $a$.
But how do we formalize this intuition using serialisability?
We have seen in the previous lecture that we can reconstruct admissible sets by iteratively choosing initial sets.
<aside> ⚠️ DEFINITION
A serialisation sequence for $\mathcal{F} = (A,R)$ is a sequence $(S_1, \dots, S_n)$ with $S_1 \in IS(\mathcal{F})$ and for each $2 \leq i \leq n$, we have $S_i \in IS(\mathcal{F}^{S_1 \cup \dots \cup S_{i-1}})$.
To each admissible set of $\mathcal{F}$, there is at least one corresponding serialisation sequence.
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In our example with three arguments above, we can see that $\{a\}$ can only be selected after $\{c\}$.