How can I help a child who lives in a world where conventional logic cannot be used to resolve issues? Where unintended slights or mistakes are multiplied over time in her mind and forgiveness and forgetting seems to never come?
It will be important to understand how she sees the world. Is it that she does not understand conventional logic, or that her logic is very different? What is the reason she holds on to unintended slights or mistakes?
Once you have an understanding of how she sees the world, and can demonstrate that through words or behaviors, then you can help her to understand how others see the world—what more conventional understandings of things are. This is not to say they need to give up their way of understanding the world, but rather that it will be important for them to understand more conventional logic if they are to understand others, interact with them effectively, and resolve issues with others (including you!).
Many people hold on to slights and mistakes out of fear—fear of being hurt again. It will be helpful to let her know that this guarded—resentful?—stance is probably hurting her the most of all, and that she may become bitter if she continues to hold on to negative feelings toward others long-term. Forgiveness allows us to let go—not just for the other person, but also (and maybe primarily) for ourselves, so we do not have a bitter, negative heart.