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Multiagent belief revision

Author

Listed:
  • Antoine Billot

    (LEMMA - Laboratoire d'économie mathématique et de microéconomie appliquée - UP2 - Université Panthéon-Assas, PSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Jean-Christophe Vergnaud

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Bernard Walliser

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique)

Abstract

An original epistemic framework is proposed for the modeling of beliefs and messages within a multiagent belief setting. This framework enables public, private and secret messages as well, even when the latter contains errors. A revising rule—i.e. the product rule—is introduced in pure epistemic terms in order to be applied to all structures and message. Since any syntactic structure can be expressed through various semantic ones, an equivalence principle is given by use of the semantic notion of bisimilarity. Thereafter, a robustness result proves that, for a given prior structure, bisimilar messages yield bisimilar posterior structures (Theorem 1). In syntax, the beliefs revised thanks to the product rule are then shown to be unique (Theorem 2). Finally, an equivalence theorem is established between the product rule and the Belief-Message Inference axiom (Theorem 3).

Suggested Citation

  • Antoine Billot & Jean-Christophe Vergnaud & Bernard Walliser, 2015. "Multiagent belief revision," PSE-Ecole d'économie de Paris (Postprint) hal-01175921, HAL.
    • Handle: RePEc:hal:pseptp:hal-01175921
    DOI: 10.1016/j.jmateco.2015.05.004
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