根据事实的英文：
on facts

Wishful thinking belief based on wishes and not on facts
不根据事实而仅基于愿望的想法

We should ground our argument on facts
我们应该根据事实而立论。

I illustrated the function of the organization by facts
我根据事实来说明该机构的作用。

Expert witnesses are allowed to draw inferences from facts which the judge or jury is not competent to draw.
专家证人则被允许根据事实进行法官或者陪审团不能作出的推理。

They came to the conclusion that he hadn't run out of their city,putting two and two together.
根据事实推断,他们得出这样的结论,他还没有跑出这座城市。

This is a known fact.
这是众所周知的事实。

awake to the fact that
认识到￥的事实

acquittal in fact
依事实宣告无罪

These facts are relevant to the case.
这些事实和此案有关。

State the facts as they are.
如实地陈述事实。