Impossibility in Belief Merging


Abstract

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 Pérez. 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

  • Belief merging;
  • epistemic states;
  • Arrow’s impossibility theorem

Note to users:
Accepted manuscripts are Articles in Press that have been peer reviewed and accepted for publication by the Editorial Board of this publication. They have not yet been copy edited and/or formatted in the publication house style, and may not yet have the full ScienceDirect functionality, e.g., supplementary files may still need to be added, links to references may not resolve yet etc. The text could still change before final publication.

Although accepted manuscripts do not have all bibliographic details available yet, they can already be cited using the year of online publication and the DOI, as follows: author(s), article title, Publication (year), DOI. Please consult the journal’s reference style for the exact appearance of these elements, abbreviation of journal names and use of punctuation.

When the final article is assigned to volumes/issues of the Publication, the Article in Press version will be removed and the final version will appear in the associated published volumes/issues of the Publication. The date the article was first made available online will be carried over.

Author : Amílcar Mata Díaz, Ramón Pino Pérez

from ScienceDirect Publication: Artificial Intelligence http://ift.tt/2ttHwhW

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s