Dynamic Consequence and Public Announcement

Review of Symbolic Logic 6 (4):659-679 (2013)
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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.

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Ángel Nepomuceno Fernández
Universidad de Sevilla

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References found in this work

Defaults in update semantics.Frank Veltman - 1996 - Journal of Philosophical Logic 25 (3):221 - 261.
A logical analysis of some value concepts.Frederic Fitch - 1963 - Journal of Symbolic Logic 28 (2):135-142.
Dynamic logic for belief revision.Johan van Benthem - 2007 - Journal of Applied Non-Classical Logics 17 (2):129-155.

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