, Volume 171, Issue 2, pp 321–355 | Cite as

On the dynamics of institutional agreements

  • Andreas Herzig
  • Tiago de LimaEmail author
  • Emiliano Lorini
Open Access


In this paper we investigate a logic for modelling individual and collective acceptances that is called acceptance logic. The logic has formulae of the form \({\rm A}_{G:x} \varphi\) reading ‘if the agents in the set of agents G identify themselves with institution x then they together accept that \({\varphi}\) ’. We extend acceptance logic by two kinds of dynamic modal operators. The first kind are public announcements of the form \({x!\psi}\), meaning that the agents learn that \({\psi}\) is the case in context x. Formulae of the form \({[x!\psi]\varphi}\) mean that \({\varphi}\) is the case after every possible occurrence of the event x!ψ. Semantically, public announcements diminish the space of possible worlds accepted by agents and sets of agents. The announcement of ψ in context x makes all \({\lnot\psi}\) -worlds inaccessible to the agents in such context. In this logic, if the set of accessible worlds of G in context x is empty, then the agents in G are not functioning as members of x, they do not identify themselves with x. In such a situation the agents in G may have the possibility to join x. To model this we introduce here a second kind of dynamic modal operator of acceptance shifting of the form \({G:x\uparrow\psi}\). The latter means that the agents in G shift (change) their acceptances in order to accept ψ in context x. Semantically, they make ψ-worlds accessible to G in the context x, which means that, after such operation, G is functioning as member of x (unless there are no ψ-worlds). We show that the resulting logic has a complete axiomatization in terms of reduction axioms for both dynamic operators. In the paper we also show how the logic of acceptance and its dynamic extension can be used to model some interesting aspects of judgement aggregation. In particular, we apply our logic of acceptance to a classical scenario in judgment aggregation, the so-called ‘doctrinal paradox’ or ‘discursive dilemma’ (Pettit, Philosophical Issues 11:268–299, 2001; Kornhauser and Sager, Yale Law Journal 96:82–117, 1986).


Acceptance logic Public announcement Belief revision Discursive dilemma Institutions 



Thanks are due to the three reviewers of the special issue, who have provided detailed and thorough comments and criticisms that helped to improve the paper.We also would like to thank Gabriella Pigozzi for her comments and for discussions during and after NorMAS. Andreas Herzig and Emiliano Lorini are supported by the project ForTrust “Social trust analysis and formalization” (ANR-06-SETI-006) that is funded by the French institution Agence Nationale de la Recherche. The contribution by Tiago de Lima is part of the project Moral Responsibility in R & D Networks, supported by the Netherlands Organisation for Scientific Research (NWO) under grant number 360-20-160.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution,and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2009

Authors and Affiliations

  • Andreas Herzig
    • 1
  • Tiago de Lima
    • 2
    Email author
  • Emiliano Lorini
    • 1
  1. 1.Université de Toulouse, CNRS, IRITToulouse Cedex 9France
  2. 2.Eindhoven University of TechnologyEindhovenThe Netherlands

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