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The phrase "there is a basis" is correct and usable in written English.
You can use it when you want to express that a certain statement or opinion is founded on a certain fact or set of facts. For example, "There is a basis for saying that the economy is improving, as unemployment rates have dropped in the last year."
Exact(60)
It must prove there is a basis for the appeal on a point of law.
Promotions will be fair and viewed that way, and even if they're not there is a basis for discussing that--for employees to air their grievances.
When for every input which must be classified there is a basis function Φ(‖x − y‖) the network will give a function, adaptive to every pattern.
Is there merit to the SMA? Assess whether there is a basis for the criticism.
"There is a basis for this movement.
I do believe that there is a basis for resolution.
"I don't think there is a basis for that".
2. There is a basis in international law for intervention.
If the guns can be silenced, there is a basis for renewed peace talks.
With legalisation there is a basis on which to start unpicking all of that.
There is a basis in folklore for the modern achievements in wave research.
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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