怎么样理解not that we know of

句子: Well, not that we know of.（书本上翻译成：并不像大家所知道的那样）

请问老师：we know of若是定语从句，副词not难道可以修饰代词that吗？

可以的。这种否定叫做局部否定。比如：

I did it, but not for you. 我作了那件事，但不是为了你。

局部否定其实是省略了重复的句子成分。比如上句假如不省略则为：

I did it, but I didnt do it for you.

又如：

I like Tom, not you. = I like Tom, I dont like you.