Cheating Husbands

Josephine's Problem: In Josephine's Kingdom every woman has to take a logic exam before being allowed to marry. Every married woman knows about the fidelity of every man in the Kingdom except for her own husband, and etiquette demands that no woman should tell another about the fidelity of her husband. A gunshot fired in any house in the Kingdom will be heard in any other. Queen Josephine announced that unfaithful men had been discovered in the Kingdom, and that any woman knowing her husband to be unfaithful was required to shoot him at midnight following the day she discovered his infidelity. How did the wives manage this, if each day the queen announced whether or not all the cheating husbands were dead?