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The phrase "a matter of logic" is correct and usable in written English.
It can be used when discussing reasoning, arguments, or situations that are based on logical principles or reasoning.
Example: "In this debate, it's essential to focus on the facts; it's really just a matter of logic."
Alternatives: "a question of reasoning" or "a matter of rationality".
Exact(46)
As a matter of logic, both things cannot be true.
It is, as Hermione might say, a matter of logic rather than wizardry.
As a matter of logic, this disparagement of childless leaders is ludicrous.
It makes no sense as a matter of logic or law".
There was nothing complex about the Go Forward Plan: it was just a matter of logic and common sense.
As a matter of logic and policy, there is no way to distinguish the game on which Cuomo has blown the whistle from the way Social Security works.
Similar(14)
As a matter of mathematical logic, no code can achieve all three.
As a matter of pure logic, it is hard to argue for anything else.
As a matter of legal logic, there is some similarity among Google, Ann Landers, Socrates and other providers of answers.
The majority's explanation was perfectly reasonable as a matter of legal logic: you have to be in custody to file a habeas petition, and Mr. Wilson was out.
In that case, if Monroe was at the scene, as she had confessed she was, then as a matter of simple logic she was guilty.
More suggestions(16)
a matter of rationality
a matter of mindset
a matter of reflection
a problem of logic
a matter of thinking
a matter of fact
a matter of attraction
a matter of altitude
a work of logic
a quagmire of logic
a science of logic
a matter of perspective
a sort of logic
a bedrock of logic
a department of logic
a matter of interpretation
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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