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ARROW UPDATE LOGIC

Published online by Cambridge University Press:  13 October 2011

BARTELD KOOI  and
BRYAN RENNE
BARTELD KOOI*
Affiliation:
Faculty of Philosophy, University of Groningen
BRYAN RENNE*
Affiliation:
Faculty of Philosophy, University of Groningen
*
*FACULTY OF PHILOSOPHY, UNIVERSITY OF GRONINGEN, OUDE BOTERINGESTRAAT 52, 9712 GL GRONINGEN, THE NETHERLANDS. E-mail: b.p.Kooi@rug.nl
†FACULTY OF PHILOSOPHY, UNIVERSITY OF GRONINGEN, OUDE BOTERINGESTRAAT 52, 9712 GL GRONINGEN, THE NETHERLANDS. E-mail: bryan@renne.org
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Abstract

We present Arrow Update Logic, a theory of epistemic access elimination that can be used to reason about multi-agent belief change. While the belief-changing “arrow updates” of Arrow Update Logic can be transformed into equivalent belief-changing “action models” from the popular Dynamic Epistemic Logic approach, we prove that arrow updates are sometimes exponentially more succinct than action models. Further, since many examples of belief change are naturally thought of from Arrow Update Logic’s perspective of eliminating access to epistemic possibilities, Arrow Update Logic is a valuable addition to the repertoire of logics of information change. In addition to proving basic results about Arrow Update Logic, we introduce a new notion of common knowledge that generalizes both ordinary common knowledge and the “relativized” common knowledge familiar from the Dynamic Epistemic Logic literature.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 4 , Issue 4 , December 2011 , pp. 536 - 559
Copyright
Copyright © Association for Symbolic Logic 2011

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