Impossibility in Belief Merging (Extended Abstract)

Impossibility in Belief Merging (Extended Abstract)

Amilcar Mata Diaz, Ramon Pino Perez

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence
Journal track. Pages 5632-5636. https://doi.org/10.24963/ijcai.2018/799

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 Perez. 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.
Keywords:
Knowledge Representation and Reasoning: Belief Change
Knowledge Representation and Reasoning: Information Fusion
Knowledge Representation and Reasoning: Knowledge Representation and Game Theory ; Social Choice