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The phrase "given the premise" is correct and usable in written English.
It is typically used to introduce a statement or argument that is based on a previously stated or assumed premise. Example: Given the premise that all human beings have the right to equal treatment, it is unacceptable to discriminate based on race or gender.
Exact(24)
Just given the premise of "The Newsroom," do you think you risk running into some of the problems you faced with "Studio 60 on the Sunset Strip"?
Given the premise of the dying city, it's a sure bet that Lina and Doon will find at least a partial deliverance.
Mr. Rohde's characters love to hold forth — about man, God, the law and the state but oddly, given the premise, not so much about art.
Given the premise of his post, I was also struck by Chait's follow-up point: Nor do Lowry and Kristol offer a plausible story as to how a better bill will emerge.
Berry is hardly the first visionary rock musician to have behaved in unforgivable ways, and given the premise of the ceremony it is, after all, a Hall of Fame a wave of posthumous adulation was expected (and, depending on how you sift art from artist, deserved).
Given the premise that innovation thrives "when ideas can serendipitously connect and recombine with other ideas," Mr. Johnson writes, it is a strange fact "that a great deal of the past two centuries of legal and folk wisdom about innovation has pursued the exact opposite argument, building walls between ideas".
Similar(36)
Thus, given Barbara as axiomatic, and given the premises of the reducible syllogism, the contradictory of its conclusion is false, so the original conclusion is true.
That is, the KS argument shows that (given the premises) a spin 1 particle cannot possess all the properties at once which it displays in different measurement arrangements.
So given the premises of (10), adding 'every S is D' would lead to contradiction: every S is P, and not every S is P.
Given the premises, both of which are supported by plenty of evidence, the conclusion follows inexorably.
It is the ability to look upon leadership as a discipline, with a set of methods and tools that are adaptive and the best possible fit for achieving the results you are trying to reach, given the premises of your team and surroundings.
More suggestions(20)
investigated the premise
given the proposition
revived the premise
involved the premise
given the prerequisite
given the hypothesis
given the understanding
given the supposition
given the presumption
given the axiom
given the circumstance
given the idea
given the requirement
given the rationale
given the premises
given the starting point
given the prior
conceived the premise
hand the premise
given the presupposition
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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