## Lawrence S. Moss

Department of Mathematics

Indiana University

Bloomington

IN 47405 USA

lsm@cs.indiana.edu

http://www.math.indiana.edu/home/moss/home.html

### Abstract

This note discusses two semantics for a logic of group announcements and
verifies that the two have the appropriate relation.
The first semantics is the *hyperset semantics* of (Gerbrandy 1998,
Gerbrandy 1999) and (Gerbrandy and Groeneveld 1997).
The second is the *Kripke model semantics* of (Baltag, Moss and
Solecki 1998), where the relation between the two semantics was noted
(without proof).
A proof does appear in (Gerbrandy 1999).
The presentation here is more algebraic in that it uses *coalgebras* and
*final coalgebra maps* to give the semantics of (Gerbrandy 1998, Gerbrandy
1999, Gerbrandy and Groeneveld 1996) and the equivalence of the two semantics
is shown without bisimulation.

### Further Information

Dedicated to Johan van Benthem on his Fiftieth Birthday

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