Legal Systems as Argumentation Bases

We have so far considered arguments and their interactions, i.e., conflicts giving rise to defeat relations. Let us now look at the set of premises that provide the ingredients for constructing a set of interacting arguments.
A set of such premises is not a consistent set of deductive axioms but is rather the sense of a repository of material to be used to build competing arguments and counterarguments (Sartor 1994). It is rather an argumentation basis, in the sense of a knowledge base (a set of premises) that can be used for constructing an argumentation framework (a set of interacting arguments). In Sartor (1994) I used the term argumentation framework (see also Stone Sweet 2002) to denote what I here call argumentation basis , to reserve the term argumentation framework to the set of arguments that are constructible from the argumentation basis (Baroni et al 2011).
Figure 17 (adapted from Baroni et al 2011) shows a process to determine the inferential semantics of an argumentation basis, namely, the set of all conclusions that are supported by that basis. First, we construct the maximal argumentation framework resulting from the argumentation basis, i.e., we build all arguments that can be obtained by using only the premises in the basis and to identify all defeat relations between such arguments. Then we determine what arguments and defeat links are IN or OUT (for all or some labellings), and consequently establish the status of each argument, i.e., whether the argument is justified, defensible or overruled relatively to the given argumentation basis. Finally, we identify the status of the conclusions: the conclusion of the justified or defeasible arguments being respectively justified or defensible relatively to the argumentation basis. A different (but equivalent) approach is described in Prakken and Sartor (1997), where the proof of a defeasible conclusion takes place in a game where the proponent of that conclusion has to build an argument (from the argument base) and defend it against all possible direct and indirect counterarguments an opponent my construct (from the same argument base)