Impossibility in Belief Merging
  With the aim of studying social properties of belief merging and having a
better understanding of impossibility, we extend in three ways the framework of
logic-based merging introduced by Konieczny and Pino P\'erez. First, at the
level of representation of the information, we pass from belief bases to
complex epistemic states. Second, the profiles are represented as functions of
finite societies to the set of epistemic states (a sort of vectors) and not as
multisets of epistemic states. Third, we extend the set of rational postulates
in order to consider the epistemic versions of the classical postulates of
Social Choice Theory: Standard Domain, Pareto Property, Independence of
Irrelevant Alternatives and Absence of Dictator. These epistemic versions of
social postulates are given, essentially, in terms of the finite propositional
logic. We state some representation theorems for these operators. These
extensions and representation theorems allow us to establish an epistemic and
very general version of Arrow's Impossibility Theorem. One of the interesting
features of our result, is that it holds for different representations of
epistemic states; for instance conditionals, Ordinal Conditional functions and,
of course, total preorders.
