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The phrase "reasoning of" is correct and usable in written English.
It can be used to describe a form of logical analysis or to explain why something has occurred. For example, "Through reasoning of the facts presented in the case, the jury made their decision."
Exact(59)
Under the reasoning of Newman, no crime had been committed.
Employment lawyers accepted the clear reasoning of the judgment.
Sadly, the reasoning of Karen Matthews was all too obvious.
3. Construct viable arguments and critique the reasoning of others.
The reasoning of the Paris court was not immediately available.
The underlying reasoning of both parties is generally similar.
It is also appropriate to criticize the reasoning of judges in particular cases.
He went on to describe the reasoning of his more liberal colleagues as "pure applesauce".
Though Harding doesn't explore it, the reasoning of the ruling class seems to go like this.
Elsewhere, Tetlock has published an analysis of the political reasoning of Winston Churchill.
This is false reasoning of course, but it is the speciousness of writers.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com