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The phrase "a process of reasoning" is correct and usable in written English.
It can be used when discussing logical thinking, problem-solving, or the steps taken to arrive at a conclusion.
Example: "The scientist described the process of reasoning that led to her groundbreaking discovery."
Alternatives: "a method of deduction" or "a line of thought".
Exact(17)
Seyla Benhabib thus complains that "public reason in Rawls's theory is best viewed not as a process of reasoning among citizens, but more as a regulative principle, imposing certain standards upon how individuals, institutions, and agencies ought to reason about public matters.
It involves a process of reasoning.
Since seventh grade, he had been taking the "constructivist" or "inquiry" program, so named because it emphasizes pupils' constructing their own knowledge through a process of reasoning.
"That means that if you think you have identified the right rule, or the best possible solution through a process of reasoning, don't pretend that there will be a single right answer," he added.
Simulation tools can support a process of reasoning about the implications of uncertainties for the outcome of management policies in a specific river basin management context.
It will also be entitled to feel baffled by an opinion which, while recognizing the continuing authority of Gerende, undertakes to bypass that decision by a process of reasoning that defies analysis.
Similar(43)
Graduates of our professional program can identify human and environmental problems, can independently and collaboratively search for and create resources to develop solutions, and through a process of clinical reasoning based on evidence based practice determine and implement optimal intervention strategies.
Crenshaw (1990) [2] argues that because terrorist behaviour cannot be labelled as pathological or irrational due to the lack of empirical evidence to support such notions, it must therefore be considered a choice which is made following a process of logical reasoning.
Our results call for a redefinition of CI, in order to take into account the GPs' extended health-promoting role, and acknowledge that inaction or delayed action follows a process of clinical reasoning that takes into account the patients' preferences, and that is appropriate most of the time.
To draw a conclusion, we also need a logical process of reasoning.
In addition, Darwin anticipated current interest in implicit reasoning with his comment "The savage would certainly neither know nor care by what law the desired movements were effected; yet his act would be guided by a rude process of reasoning, as surely as would a philosopher in his longest chain of deductions" (Darwin 1974, 75).
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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