Multiagent Systems

of. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 474/731
7. Modal Logic 1. Reasoning about Knowledge
Example 7.1 (Muddy children – Shoham’s version)
A group of n children enters the house after having played
in the mud outside. They are greeted by their father, who
notices that k of them have mud on their foreheads (no kid
can see whether she herself has a muddy forehead, but
they can see all other foreheads).
Can the kids determine by pure thinking wether they
have a muddy forehead?
The father announces: At least one of you has mud on
her forehead.
He also says If you know (can prove) that your forehead is
muddy, then raise your hands now.
Nothing happens. The father keeps repeating the
question.
After exactly k rounds, all the children with muddy
foreheads raise their hands.