I have had similar concurs. If caught in the act of killing your live stock or biting someone on your property, then I would say yes he's fair game. It's a stressful pain in the ass to deal with folks who don't care for their animals or restrain them. I would call your county animal control first, possible the police or Sherriff. Get it on reports.There is a neighbors dog that comes on our property growling and acting aggressive but doesn’t attack. It has approached me barking in my yard. Do I have the right to “eliminate” the dog on my property if it is barking and growling but doesn’t attack. I don’t want to wait till it bites one of my kids, thanks.
The better man in me says, don't punish the animal for the ignorance of the owner. If the county grabs the dog it will probably be put down if it shows any aggression.
To your point, I'm always armed when walking about on my property.