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The phrase "a more refined formulation" is correct and usable in written English.
It can be used when discussing an improved or more sophisticated way of expressing an idea or concept.
Example: "After several revisions, we arrived at a more refined formulation of our hypothesis that better captures the essence of our research."
Alternatives: "a more polished version" or "a more sophisticated expression".
Exact(2)
After Raymi and another narrator describe the Al Qaeda victory, the second narrator offers a more refined formulation, noting that the seven soldiers' lives were spared: "If you don't support the mujahedeen, then at least don't stand against them".
(Given Davidson's openness to the possibility of strict indeterministic laws (4.1), a more refined formulation of the closure principle would read 'every physical event that has an explanation has a physical explanation'.
Similar(57)
They constitute a more refined expression of the underlying attack when compared to isolated alerts.
Banana Republic: a more refined Gap madhouse.
There's also a more refined camera.
Today it is home to a more refined set.
Post's own left her with a more refined impression.
Their mother, Nsoroma, had a more refined palate.
The '01 has also received a more refined engine.
The result of this makeover is a more refined, more competitive, yet still distinctive sport utility.
3. Mix up the fabrics, the weights — a rough-textured fabric with a more refined one.
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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