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)