Group Conflict as Social Contradiction - Conflict and Multimodal Communication: Social Research and Machine Intelligence - page 47

are rational according to L A . Hence, in order to accept an aggregation procedure,
agents have to accept that only propositional attitudes that are rational wrt L A can
be submitted and that amounts to endorsing L A .
We can now define social attitudes ( SATT ) as propositional attitudes that are
ascribed to the social agentive group. Our definition does not entail that the social
attitude is ascribed to any of the individuals of the group, although the attitude of the
group may coincide with the attitude that is ascribed to some of its members. Since
a social agentive group is defined by an aggregation procedure at a time, we can
define the relation of dependence of the social agentive group on the aggregation
procedure and denote it by DEP.g;f;t/ . Moreover, we define the dependence of
the social agentive group on the set of individuals at a given time by DEP.g;N;t/ .
A social attitude is a propositional attitude ( a ) that is obtained by means of the
aggregation procedure f . By using the notation of Sect. 2.3 , a 2 f.A 1 ;:::;A n / ,
meaning that a belongs to the output of the aggregation procedure when given as
input the profile of individual attitudes A 1 ;:::;A n . An exhaustive ontological treat-
ment of a 2 f.A 1 ;:::;A n / entails, for example, that the individual propositional
attitudes A j are ascribed to individual j .
SATT.a/ !9x 9t.SAG.x/ ^ DEP.x;f;t/^ DEP.x;N;t/^ a 2 f.A 1 ;:::;A n //
(2.2)
Definition ( 2.2 ) means that a social attitude depends on the group and the aggre-
gation procedure that define the social agentive group at a given time. Thus,
we can now legitimate the ascription of a social attitude to the social agentive
group by slightly modifying our previous definition of ascription: ASC.x;y/ !
.AT T.x/^ IND.y//_.SATT.x/^ SAG.y// . Note that, by Definition ( 2.2 ), a social
attitude is necessarily ascribed to some social agentive group. This is motivated by
the fact that we want to exclude that taking, for example, the beliefs of a number
of randomly chosen individuals and aggregating them by majority is sufficient to
define a social attitude. A propositional attitude needs to be ascribed to an agent,
whereas an arbitrary number of individuals does not count in general as a single
agent.
We can finally introduce the notion of social contradiction in order to analyze
the paradoxical outcomes of SCT. Firstly, we introduce a relation for making the
notion of contradictory set of attitudes explicit in our ontology. We identify sets of
attitudes with conjunctions of formulas and we express that the formula a 1 ^^
a m is inconsistent with respect to the reasoning principles of L A by means of the
relation CTR.a 1 ^^a m ;L A / . According to our previous analysis, the notion of
contradiction has to depend on the reasoning system that is adopted.
For example, CTR.Pab ^ Pba;f irreflexivity, transitivity, completeness g/
holds, whereas CTR.Pab ^ Pba;f transitivity g/ does not. A social contradiction
is just an inconsistent set of social attitudes. This definition entails that there exists
a social agentive group who maintains those inconsistent attitudes.
We can now stress the difference between the notion of social agentive group
defined by means of SCT and other notions of groups that may be treated, for