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epistemic modal logic (van Benthem 2011 ). Intentions can be modeled by using a
number of techniques in multiagent systems. Moreover, ought sentences are widely
studied in deontic logics. Preferences can be represented by means of a fragment
of first order logic: we introduce predicates Pab that represent the information
a is preferred to b .” The rationality constraints on preferences, i.e. transitivity,
reflexivity, and completeness, can be expressed by means of first order formulas
(Porello 2010 ).
Therefore, general propositional attitudes can be in principle taken into account
in the framework of JA (Dietrich and List 2009 ). We briefly sketch how. It is
enough to extend the logical language that is used to model individual attitudes.
For example, if we want to deal with beliefs, we extend the agenda ˚ that we have
introduced in the previous section, by adding individual belief operators in epistemic
modal logic B i A , standing for “The agent i believes that A .”
Let A be a type of propositional attitudes, we label L A the logical system for
representing the type of propositional attitudes A . That is, L A refers to the language
to represent propositional attitudes A and to the logical rules to reason about such
attitudes, e.g. an axiomatic system for that logic. Accordingly, we define an agenda
˚ A as a subset of the language of L A . In the previous section, we have defined
the possible sets of individual judgments by means of J.˚/ , namely we assumed
that individual judgment sets are consistent and complete with respect to (classical)
propositional logic. In the general case, it is possible to define judgment sets that are
rational with respect to different logical systems (Porello 2013 ). We define J A A /
as the set of possible sets of attitudes that satisfy the rationality constraints that are
specific to A . For instance, in case A are preferences, sets of preference attitudes
have to respect transitivity. In case A are beliefs, they should be consistent, in the
sense that an agent is not supposed to believe A and :A at the same time, therefore
we exclude sets containing both B i A and B i :A .
The general form of an aggregation procedure is a slight generalization of the
one introduced in the previous section. An aggregation procedure is a function
from profiles of individual attitudes to sets of collective attitudes: F W J.˚ A / n !
P A / . The notion of collective rationality again may change as we may add more
specific constraints on the type of attitudes at issue. For example, in preference
aggregation we add the constraints on preference orders. Since each one of
these extensions includes propositional logic, the impossibility theorem shall hold
for the larger fragment. Thus, it is at least in principle possible to extend the map of
consistent/inconsistent aggregation to richer languages.
2.4.2
Conflict as Contradiction
Once we represent agents' attitudes, we can introduce a general definition of the
notion of conflict. The notion of conflict that we define is placed at the level of the
representation of propositional attitudes.
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