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The phrase "knowledge based on" is correct and can be used in written English.
You can use this phrase when you are referring to knowledge that is derived from a particular source or experience. For example, "The student's knowledge of the subject was based on the research they conducted in the library."
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Science is knowledge based on hypothesis, experimentation and observation.
Children come into school with a wealth of prior mathematical knowledge based on their life at home.
Thus, Descartes's apparent knowledge based on authority is set aside, because even experts are sometimes wrong.
First, knowledge based on verbal testimony is inferential and therefore vitiated by all the defects of inference.
It is knowledge based on experience and on understanding of the patient that leads to the greatest therapeutic success.
But in a global economy based on knowledge, based on innovation, no development strategy can be based solely upon what comes out of the ground.
Sometimes there was concern over the existence of "cunning men and women" with inherited knowledge based on a cosmology incompatible with the new Protestantism.
Kuhn questioned the traditional conception of scientific progress as a gradual, cumulative acquisition of knowledge based on rationally chosen experimental frameworks.
For those that do, a priori knowledge is knowledge based on a priori justification.
A more general approach to common knowledge based on justified knowledge was offered in (Artemov 2006).
Presumably this will reveal the degree of certainty of the knowledge based on such ideas.
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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