Relative to the set the arguments in Figure 11 (A , B , and
C ), argument C is necessarily IN, since no defeater
questions its status. Therefore, argument B is OUT (having a defeater,
namely A, which is IN). Consequently, argument A is IN, since it
has no defeater which is IN. This is the only assignment of IN and OUT
labels that is consistent with rules (1) and (2). Consequently, A
is justified, and so is its conclusion (John is liable), B is
overruled, and C is justified.
This example shows the connection between dialectics and
nonmonotonicity. By introducing new arguments into an argument framework
(typically, the set of the arguments proposed in a debate or
constructible from a given set of premises), the status of the
pre-existing arguments may change relative to that framework: arguments
that were justified can now be overruled and arguments that were
overruled can now be justified.
Rules (1) and (2) above fail to univocally determine the status of those
arguments in cases where we have an unresolved conflict (see Figure 13,
which depicts the divergent opinions of two experts).