The idea seems to offend against logic.

这个想法似乎违背逻辑。

We mustn't offend against their customs.

我们不能违反他们的风俗。

This would offend against the principle of fairness.

那会违反公正的原则。

Don't offend against the rules of operating the machine.

不要违反机器的操作规程。

You can offend me but you cannot offend against the law.

你可以冒犯我，但不能违背法律。