Are you also responsible for the physical safety of all people on your property while they are on you property? If so, wouldn't they require you to be armed?
See various “public” shoot outs where patrons have been injured/killed by criminals and ask your self about your property rights again. Yes, such events are low probability events but then so are hurricanes, tornadoes, floods, and earth quakes. It is better to think things through to their end before it happens than to have regrets later.
not necessarily. There are other ways to protect business invitess and employees available. But I've got an idea - you administer your personal property the way you want to and let others do the same. See how easy that is.