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"on these grounds" is a correct and commonly used phrase in written English
It means 'based on these reasons' or 'for these reasons'. Example: The judge dismissed the case on these grounds, stating that there was not enough evidence to support the plaintiff's claim.
Exact(60)
On these grounds we predicted that PleC, directly or indirectly, regulates one of the newly identified buoyancy determinants.
On these grounds, it won - earnestly and doggedly, with immense profit in publicity.
On these grounds he should certainly be described as a historian.
On these grounds, Sātāra was annexed in 1848 and Jhānsi and Nāgpur in 1854.
On these grounds, any value above 0.5 was considered positive.
On these grounds, some perspectival variation became possible.
On these grounds, the EGM2008 data are used by this study.
On these grounds, [11C]Me@HAPTHI might improve clinical NET imaging.
On these grounds it is possible to formulate a general DEA model.
On these grounds, we shall not consider this possibility any further in this context.
On these grounds, the conclusion of the base case stage is supposed to follow.
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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