# On the dynamics of institutional agreements

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• Mathematics

## Abstract

Synthese (2009) 171:321–355 Knowledge, Rationality & Action 923–957 DOI 10.1007/s11229-009-9645-2 On the dynamics of institutional agreements Andreas Herzig · Tiago de Lima · Emiliano Lorini Received: 31 December 2008 / Accepted: 16 July 2009 / Published online: 13 August 2009 © The Author(s) 2009. This article is published with open access at Springerlink.com Abstract 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 AG:xϕ reading ‘if the agents in the set of agents G identify themselves with institution x then they together accept that ϕ’. We extend acceptance logic by two kinds of dynamic modal operators. The first kind are public announcements of the form x !ψ , meaning that the agents learn that ψ is the case in context x . Formulae of the form [x !ψ]ϕ mean that ϕ 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 ¬ψ-worlds inaccessi- ble 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↑ψ . 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

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