# From Hypersets to Kripke Models in Logics of Announcements

## 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