I voted yes. The personal aspect is a no brainer for me. I don't care if it's a bear, dog, bigfoot, or a tree shrew, if they're going to hurt me or my family/loved ones, including my dog(I hold him in higher reguard than most people)I'm going to try my best to put some large holes in them.
As for the property though, I think it depends. If it tries to get into my house, no doubt. If it's digging in my garbage, absolutely not. Then there are some grey areas in between. Like tearing up my truck or car. Not sure if I can just stand by and watch that. Then there is always making noise, yelling, and as a last option, a warning shot. I think trying to deter the bear should be the first line of defense and in every incident I've ever heard of it worked. Killing ANYTHING in self defense is always a last resort when all other options are exhausted.