Group Conflict as Social Contradiction - Conflict and Multimodal Communication: Social Research and Machine Intelligence - page 40

Very simple agendas may trigger inconsistent outcomes, one example being the
agenda of the doctrinal paradox that we have presented in Sect. 2.2 fA;A ! B;B;
:A; :.A ! B/;:Bg . Technically, any agenda that contains a minimal inconsistent
set of cardinality greater than 2, such as fA;A ! B;:Bg , may trigger a paradox.
Thus, an agenda with respect to which the majority rule always returns consistent
outcomes is a very simple agenda that contains, for example, only unconnected pairs
of propositional atoms and their negations. Hence, paradoxical outcomes are very
likely to occur in any complex social decision.
The methodology of JA can be extended to treat many voting procedures and
characterize whether they may return inconsistent outcomes. Moreover, since the
notion of aggregation procedure is very abstract, one can in principle model
more complex procedures or norms, such as those that define decision making in
organizations and corporations.

2.4 Social Attitudes and Conflict as Contradiction

We have seen that JA provides a precise mathematical modeling of the relation-
ship between individual judgments and collective judgments. The relationship is
formalized by means of an aggregation procedure and several properties of such
aggregation can be discussed and analyzed. Moreover, it is possible to characterize
the situations that lead to inconsistent outcomes. In this section, we introduce
three notions that ground our ontological analysis of conflicts, that is, the notion
of propositional attitude , the notion of conflict as contradiction , and the notion of
social attitude .

2.4.1 Propositional Attitudes in JA

Propositional attitudes have been widely discussed in the philosophical literature
and, roughly speaking, they express a relationship between an agent i and a
propositional content p . For example, an agent can believe, judge, desire, prefer,
ought, . . . p , where p represents the content of the attitude. To our end, since the
point of view of this work is knowledge representation, propositional attitudes are
important as they allow for distinguishing a sharable propositional content of an
attitude from the agent to whom the attitude is ascribed. Thus, we view individual
propositional attitudes as sentences that are publicly expressed and communicated
to other agents. Moreover, by using propositional attitudes, we are assuming that
the matter of conflict between two agents can be in principle described by a third
person in a sharable way.
We can introduce a formal language to represent how agents can communicate
and reason about their attitudes, by building upon the rich logical tradition in the
representation of propositional attitudes. For example, beliefs can be represented in