Forgiveness, I find, is often more helpful to the person forgiving than to the people being forgiven. Holding a grudge (poor word choice, but I can't think of a better one) takes energy, it sours your mood and outlook. I have forgiven my abuser, and I'm glad I did. I'm not wasting my energy ruminating on him or his actions beyond involuntary memories. I don't wish him harm (like many of my loved ones do). I sincerely hope and pray that some day he'll become a better person. I don't care what he thinks. He doesn't even know I've forgiven him. Forgiving him has brought me a little more peace. I spend my energy learning to thrive despite my past and the scars it has left me with.
I don't mean to say I'm not afraid of him, or that the things he did don't still haunt me. I am, and they do. If I ever ran into him, I'd do whatever's necessary to get away as quickly as possible and then melt into a quivering mess once safe. Forgiving someone doesn't require forgetting their actions, and it definitely doesn't mean you're validating them. It means you're collecting up all the hatred and other malicious feelings you have toward a person over their actions, deciding that you won't let that weigh you down anymore, and casting it off. What that person chooses to do with your forgiveness is their own issue, and shouldn't matter.
Forgiveness doesn't mean repairing or rebuilding bridges you've burned, either. In the case of abuse, those bridges should be burned. If you want to go with this metaphor, forgiveness means you're not going to keep running back to where the bridge used to be and lighting another fire, just to be sure. A rather radical and forward thinking former pastor I once knew made a good point about burning bridges in one of the last sermons I ever heard him deliver. If the people on the other side of the bridges you burned really care about you, they'll get a boat. Forgiveness works like that. You get to forget about the bridge. Don't worry about it. Your abuser probably isn't going to get a boat and row because that's too much work to get to someone they obviously didn't cherish, and that's not your problem. Burn the bridge and let yourself walk away.
Forgiveness isn't something you can do just once, either. In the beginning, and possibly again in tough times, you have to do it again and again until you mean it. Eventually it becomes true, and you feel better for it.