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Since the axioms of pure quantificational logic are valid and the rules of inference preserve validity, all theorems of pure quantificational logic are valid.
While these concerns are valid, they leave open the possibility that modifications to the design of the run-in might be able to preserve validity, even if patient selection is based on the results of the run-in.
In general, the rule that if ⊢A→B then ⊢A→(∃x B does not preserve validity if we allow that Fx may be made true at a world by an individual that does not exist there.
Moreover, this multidimensional measurement model preserved its validity 3 months after the hospitalization.
Therefore, in brief, our decision to include only primary diagnosis decreases our power, but preserved our validity.
The robustness of the results also preserves the validity of the NPA approach against the possibility of HYPs and network models evolving slightly due to the constantly improving understanding of the biological processes they describe.
Furthermore, economists must ensure new privacy models preserve the validity of public data for economic research.
When writers lay their hands on money, they feel they must conceal it to preserve their validity.
Finally, the new reality demands that we preserve the validity of the trans-Atlantic partnership in the 21st century.
Population diversity in the PLCO trial is necessary to preserve scientific validity and generalizability of trial results.
The announcements are significant in part because they indicate that the chip industry may find a way to preserve the validity of Moore's Law.
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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