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‘KNOWABLE’ AS ‘KNOWN AFTER AN ANNOUNCEMENT’

Published online by Cambridge University Press:  01 October 2008

PHILIPPE BALBIANI ,
ALEXANDRU BALTAG ,
HANS VAN DITMARSCH ,
ANDREAS HERZIG ,
TOMOHIRO HOSHI  and
TIAGO DE LIMA
PHILIPPE BALBIANI*
Affiliation:
IRIT, Université de Toulouse
ALEXANDRU BALTAG*
Affiliation:
Computer Science Laboratory, Oxford University
HANS VAN DITMARSCH*
Affiliation:
Department of Computer Science, University of Otago and IRIT, Université de Toulouse
ANDREAS HERZIG*
Affiliation:
IRIT, Université de Toulouse
TOMOHIRO HOSHI*
Affiliation:
Philosophy Department, Stanford University
TIAGO DE LIMA*
Affiliation:
Department of Technology Management, Eindhoven University of Technology
*
*CNRS INSTITUT DE RECHERCHE EN INFORMATIQUE DE TOULOUSE UNIVERSITÉ DE TOULOUSE 118 ROUTE DE NARBONNE 31062 TOULOUSE CEDEX 9 FRANCE E-mail:balbiani@irit.fr
†OXFORD UNIVERSITY COMPUTING LABORATORY WOLFSON BUILDING, PARKS ROAD OXFORD OX1 3QD UNITED KINGDOM E-mail:alexandru.baltag@comlab.ox.ac.uk
§DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF OTAGO PO BOX 56, DUNEDIN 9054, NEW ZEALAND
SCNRS INSTITUT DE RECHERCHE EN INFORMATIQUE DE TOULOUSE UNIVERSITÉ DE TOULOUSE 118 ROUTE DE NARBONNE 31062 TOULOUSE CEDEX 9 FRANCE E-mail:herzig@irit.fr
**PHILOSOPHY DEPARTMENT STANFORD UNIVERSITY STANFORD, CA 94305-2155, USA E-mail:thoshi@stanford.edu
‡DEPARTMENT OF INDUSTRIAL ENGINEERING AND INNOVATION SCIENCES EINDHOVEN UNIVERSITY OF TECHNOLOGY P.O. BOX 513 5600 MB EINDHOVEN THE NETHERLANDS E-mail:t.d.lima@tue.nl
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Abstract

Public announcement logic is an extension of multiagent epistemic logic with dynamic operators to model the informational consequences of announcements to the entire group of agents. We propose an extension of public announcement logic with a dynamic modal operator that expresses what is true after any announcement: ⋄φ expresses that there is a truthful announcement ψ after which φ is true. This logic gives a perspective on Fitch's knowability issues: For which formulas φ, does it hold that φ → ⋄Kφ? We give various semantic results and show completeness for a Hilbert-style axiomatization of this logic. There is a natural generalization to a logic for arbitrary events.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 1 , Issue 3 , October 2008 , pp. 305 - 334
Copyright
Copyright © Association for Symbolic Logic 2008

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