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The phrase "a process of deduction" is correct and usable in written English.
It can be used when discussing reasoning, logic, or methods of arriving at conclusions based on available information or evidence.
Example: "The detective employed a process of deduction to solve the mystery, piecing together clues from the crime scene."
Alternatives: "a method of reasoning" or "a deductive approach".
Exact(5)
The Times claims that its reporter Patrick Foster identified Horton "by a process of deduction and detective work, mainly using information on the internet".
The movie's funniest scenes - and everyone plays dead straight - concern the detective work of Professor Hilbert, as by a process of deduction and elimination he seeks to discover what kind of book Crick is in (a tragedy or a comedy), and how this walking fiction might intervene to control his own life or death.
The judgement whether a phrase is wellformed, under this view, is the outcome of a process of deduction.
Stumpf rejects both accounts and seeks to show, in the second part of his thesis, that axioms and mathematical propositions are analytic a priori; they are not acquired through experience but are the result of a process of deduction from concepts.
They understood their coded language woven into their belts through a process of deduction.
Similar(55)
The first is that traditional theories of reasoning, like mental logic or mental models, are rooted on formal logic and the idea that reasoning is a process of deductions are true.
They then manipulate the model by a process of logical deduction, arriving eventually at some prediction or implication that is of general significance.
The metamodern author, in other words, generates hypertext primarily if not exclusively via a wholly internalized process of deduction, winnowing down opposing message-values until only one or an interrelated group of actionable values remains.
The denouement is hardly likely, but Rouletabille's process of deduction is a delight, as is his bombastic dismissal of any dissenting points of view.
Significant recent court cases, including L'Aquila, are framed by process of deduction within a generalised legal infrastructure in order to identify the root causes of the apparent status quo of risk governance.
Induction is the inverse process of deduction, but it is a much more complicated mode of reasoning.
More suggestions(18)
a process of retention
a process of inference
a process of cost
a process of incorporation
a process of adjustment
a process of law
a collection of deduction
a process of transforming
a half of deduction
a process of learning
a set of deduction
a process of fact-finding
a genius of deduction
a process of growth
a process of reconstruction
a process of emergence
a process of elimination
a process of genrefication
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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