In such a case, which arguments are justified depends on where we start
from: if arguments two argument \(\mathcal{A}\) and \(\mathcal{B}\)
attack each other (and neither of them is OUT on other grounds), then if
we assume that \(\mathcal{A}\) is IN and \(\mathcal{B}\) will be OUT,
and if we assume that \(\mathcal{B}\) is IN, then \(\mathcal{A}\) will
be OUT. We can deal with this situation by considering all possible
assignments of IN and OUT labels to the arguments at stake, consistently
with rules (1) and (2) above: an argument is justified if it is IN
according to every assignment; it is overruled if it is OUT according
every assignment; it is defensible if it is IN according to some
assignment and OUT according to some other assignment (Pollock 2008). An
equivalent approach by which to assess the status of arguments consists
in constructing alternative extensions, namely, maximal sets of
consistent arguments: justified, defensible, and overruled arguments are
contained in all, some, or no extensions (Dung 1995).
Unresolved conflicts concerning legal and factual issues are addressed
in different ways in the adversarial context of legal disputes, where
the judge is assumed to know the applicable law, while the parties
should bring evidence on the facts of the case. If an unresolved
conflict between competing arguments concerns a legal issue (e.g., there
are arguments supporting alternative interpretations of the same source
of law), the decision-maker (the judge) should resolve the conflict by
assigning priority to one of the conflicting arguments. If the
unresolved conflict concerns a factual premise that is needed to
construct an argument, it will be assumed that the factual premises have
not been legally substantiated, i.e., the factual argument will be OUT.
The dialectical interaction between arguments and counterarguments is
reflected in the allocation of burdens of proof and, more generally, of
burdens of argumentation. The idea of the burden of proof applies to
many dialectical interaction, in context-dependent ways (see Walton
2008, 59), but it acquires a specific significance in the law (see
Sartor 1993, Prakken and Sartor 2009). In a legal case, the party that
is interested in establishing a legal outcome bears the burden of
presenting and substantiating an argument supporting that outcome. For
instance, in the example in Figure 13, plaintiff Mary must provide
argument A , establishing John’s liability for negligence. She
must substantiate the argument’s normative premises (the general rule of
civil liability) by referring to sources of law, and its factual premise
(John culpably damaged Mary) by bringing in appropriate evidence. This
argument will be sufficient for Mary to win the case if its premises are
accepted and no counterarguments defeating it are provided by John (at
least with regard to factual premises, since the judge may independently
bring in legal information).
Thus, Mary can be said to bear the burden of proving that John did
damage to her, since without establishing this fact she will not be able
to construct argument A , which supports the outcome she favours.
She does not bear the burden of proving that John was not incapable,
since to build argument A , she does not need to establish that
fact. On the contrary, John bears the burden of proving that he was
incapable, since without establishing this fact, he will not be able to
substantiate argument B , which could defeat Mary’s argument
A (switching A ’s status from IN to OUT, in the absence of
further interfering arguments).
In general, when a party \(\pi_{1}\) fails to construct a certain
legally acceptable argument \(\mathcal{A}\) supporting her side, we say
that, unless evidence is provided for premise \(P\), \(\pi_{1}\)has the
burden of proof regarding P. This does not mean that the
counterparty \(\pi_{2}\) has no interest in \(P\). It is true that
\(\pi_{1}\) will fail to build the argument based on \(P\) if
\(\pi_{1}\) fails to provide evidence for \(P\), even if
\(\pi_{2}\ \)remains inactive. However, if \(\pi_{1}\) provides
sufficient evidence for \(P\) (and the other premises of \(\mathcal{A}\)
have been established), then \(\pi_{2}\) must provide evidence against
\(\varphi\), or counterarguments against \(\mathcal{A}\), if he does not
want to lose on the basis of \(\mathcal{A}\) (on the logic of the burden
of proof, and for further refinements, including the distinction among
the burden of production, the burden of persuasion, tactical burden, and
standards of proof, see Prakken and Sartor 2009, on the connection
between defeasibility and proof, see also Sartor 1993, Duarte de Almeida
2012, Brewer 2011). Figure 13 below exemplifies the context of the
burden of proof. Let us assume that the plaintiff (the alleged victim)
has the burden of showing that his cancer was caused by smoke and that
the standard of preponderance of the evidence applies. Then, even if the
two arguments have equal weight, the plaintiff’s argument would be
strictly defeated by the defendant’s argument (to defeat the defendant’s
argument, the plaintiff’s argument must meet the required standard of
proof). Thus, in an adversarial legal context governed by the burden of
proof, the status assignment of Figure 12 (no justified arguments, two
defensible one) would be transformed into the assignment of Figure 13
(one justified and one overruled argument).