Is it always right to forgive someone? Is this not accepting what they have done?

If someone has seriously hurt you by an act of betrayal or any other act is not forgiving them accepting what thye did to you. What I mean is that if one forgives this person then it validates what they have done. One can say that yes this happened against my will, and therefore not forgive this person. Is it it alright to not forgive someone and to deny them the right to be forgiven. I have thought about this for a very long time. I now need some advice on what I should do.