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DYNAMIC CONSEQUENCE AND PUBLIC ANNOUNCEMENT

Published online by Cambridge University Press:  14 October 2013

ANDRÉS CORDÓN FRANCO ,
HANS VAN DITMARSCH  and
ANGEL NEPOMUCENO
ANDRÉS CORDÓN FRANCO*
Affiliation:
Universidad de Sevilla
HANS VAN DITMARSCH*
Affiliation:
LORIA, CNRS—Université de Lorraine
ANGEL NEPOMUCENO*
Affiliation:
Universidad de Sevilla
*
*DEPARTMENT OF COMPUTER SCIENCE AND ARTIFICIAL INTELLIGENCE UNIVERSIDAD DE SEVILLA, AV . REINA MERCEDES S/N 41012 SEVILLE, SPAIN E-mail: acordon@us.es
†LORIA, CNRS—UNIVERSITÉ DE LORRAINE BP 239, 54506 VANDOEUVRE-LÈS-NANCY, FRANCE E-mail: hans.van-ditmarsch@loria.fr
‡DEPARTMENT OF PHILOSOPHY AND LOGIC AND PHILOSOPHY OF SCIENCE UNIVERSIDAD DE SEVILLA, AV . CAMILO JOSÉ CELA S/N 41018 SEVILLE, SPAIN E-mail: nepomuce@us.es
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Abstract

In van Benthem (2008), van Benthem proposes a dynamic consequence relation defined as ${\psi _1}, \ldots ,{\psi _n}{ \models ^d}\phi \,{\rm{iff}}{ \models ^{pa}}[{\psi _1}] \ldots [{\psi _n}]\phi ,$ where the latter denotes consequence in public announcement logic, a dynamic epistemic logic. In this paper we investigate the structural properties of a conditional dynamic consequence relation $\models _{\rm{\Gamma }}^d$ extending van Benthem’s proposal. It takes into account a set of background conditions Γ, inspired by Makinson (2003) wherein Makinson calls this reasoning ‘modulo’ a set Γ. In the presence of common knowledge, conditional dynamic consequence is definable from (unconditional) dynamic consequence. An open question is whether dynamic consequence is compact. We further investigate a dynamic consequence relation for soft instead of hard announcements. Surprisingly, it shares many properties with (hard) dynamic consequence. Dynamic consequence relations provide a novel perspective on reasoning about protocols in multi-agent systems.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 6 , Issue 4 , December 2013 , pp. 659 - 679
Copyright
Copyright © Association for Symbolic Logic 2013 

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