Re: Training Aggressive Dog
There are few methods you can attempt to fix this situation. I think you should definitely at least talk to a professional about this problem. We can't see exactly how the dog is acting. A professional can come into your home and assess the situation in a way that we over the internet cannot.
Second, please try to understand that dogs behaving aggressively is just another way for them to communicate. Is it appropriate? Of course not. But he is telling you something. He is telling you he is upset, afriad, angry, or feeling territorial in the presence of visitors.
That said, please do not correct your dog for aggression problems. This includes hitting, kicking, yelling, leash jerks, "alpha rolls", or even a stern look. There are a variety or reasons for this. First off, aggression will do nothing to fix the dog's feelings about this situation. You are simply correcting the behavior, not changing the dog's negative feelings. For example - you yell, give a leash jerk, or bop a dog on the nose for growling. You may stop the dog from growling, but he's not feeling any less aggressive. He'll probably just stop growling and go to snapping or snarling next. You correct the snarling and snapping? Well next time he'll bite. This leads to the "biting without warning" thing. The dog was warning people before, but was corrected for communicating... so now he has to step up the behavior to hopefully get the result he's looking for.
Also, punishing a behavior that already has a negative connection is going to make the dog feel even more ill at ease. If the dog is corrected whenever visitors come over - he'll likely associate the visitors with the corrections, which will just compound his negative association with them. It's very possible and very common for dog's aggression problems to escalate when punishment or corrections is used in an attempt to curb the behavior. Instead of just growling when they come in the door, he could easily start getting upset when he hears them in the driveway, or escalate to snapping when they're in the house.
Not only that, but it's very likely your relationship with the dog will be damaged through the use of heavy aversives. A dog will easily start to distrust and dislike someone who often times talks to them sternly, gives them leash jerks, hits or kicks them, or yells at them.
Visitors in your home are obviously creating a fairly intense emotional response in your dog. You want him to associate the strangers with something other than fear, anger, or the desire to protect something. You want to pair the arrival of visitors with something he wants really, really, badly. It has to be something extremely desirable. Not just a biscuit, but hot dog slices or moist liver treats. Not just a toy, but an exciting session of his favorite game. Not only that, he has to ONLY recieve that desirable thing when visitors are around. He shouldn't be getting it at any other time.
You want to start this 'game' when the visitors are hopefully not producing an all out aggressive display in him. Start with someone just pulling into the driveway... produce the desirable object, and continue to give it to him until they leave. When they are gone, remove the toy or treat, and wait again until a new visitor arrives. After a few repeats, he will associate someone pulling into the driveway as play or treat time. Escalate it to someone walking up to the door. Then someone knocking. Then someone entering the house.
You want to always be giving the dog the treat, or game. It may sometimes feel like you are rewarding aggressive displays, but you really need to create the correlation of "visitors = the thing I desire most in the world." This positive correlation will eventually overwrite his negative association.
Manipulate the situation if you can. If the dog gets so upset by witnessing someone walk through the door that he's ignoring the thing he wants, start with rewarding the dog in a different room, as well as attempting to find a more desirable object. You may need to shop around for a treat or game that he really, really, wants. Slowly move the dog to where the visitors are actually entering the house.
If you can, start slow. With repeated visits from the same person. Then a new person. Eventually, when he seems alright with one person entering the house, try two people (preferably ones he's alright met before).
Eventually, when it's safe, you can have the visitors be the one's producing the desirable game or treat. This will create an even more positive association with the visitor.
If you want to, you can also try and REALLY reinforce non-behavior. Whenever he reacts calmly to a situation that would normally produce a reaction, praise him! It's sometimes hard for us to notice and praise a non-behavior, but once you get in the groove of doing so, you can really help shape the dog to behave the way you desire. (This works for any behavior problem, really).
On top of all of this, remember Border Collies are extremely intelligent and energetic dogs, as well as very sensitive. They pick up things very quickly. They also need some fairly intense physical exercise. Misbehavior is often exacerbated by lack of physical and mental stimulation. Make sure he is getting very intense, hard, physical exercise every day, and is getting routine training sessions. You could even create a job for him to do. A dog that is mentally and physically understimulated is much more likely to act out and behave inappropriately.
Good luck!