The Review of Symbolic Logic

Table of Contents - December 2011 - Volume 4, Issue 04  

Research Article

ARROW UPDATE LOGIC

BARTELD KOOIa1 c1 and BRYAN RENNEa1 c2

a1 Faculty of Philosophy, University of Groningen

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.

(Received August 02 2011)

Correspondence:

c1 FACULTY OF PHILOSOPHY, UNIVERSITY OF GRONINGEN, OUDE BOTERINGESTRAAT 52, 9712 GL GRONINGEN, THE NETHERLANDS. E-mail: b.p.Kooi@rug.nl

c2 FACULTY OF PHILOSOPHY, UNIVERSITY OF GRONINGEN, OUDE BOTERINGESTRAAT 52, 9712 GL GRONINGEN, THE NETHERLANDS. E-mail: bryan@renne.org