I can't explain such a statement by him on the basis of logic. He must have blown his top.

我从逻辑推理方面解释不了他讲的这番话，他想必是神经错乱了。

《新英汉大辞典》

This statement follows as a matter of logic: at world level, supply must equal demand.

这样的论断基于的逻辑是：在世界范围内，供给必须等于需求。

youdao

A statement failure occurs when there is a logic misstep in an application.

当应用程序中存在逻辑错误时，就会出现语句错误。

youdao

As a statement of logic, that's false.

从逻辑上讲这是不合理的

耶鲁公开课 - 博弈论课程节选

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