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The phrase "upon their interpretation" is correct and usable in written English.
It can be used when discussing how something is understood or perceived based on someone's viewpoint or analysis. Example: "The outcome of the project may vary significantly upon their interpretation of the data presented."
Exact(2)
However, these individuals generally did not take their medications in compliance with their prescriptions, but as they saw fit based upon their interpretation of their signs and symptoms.
Schneider et al. (2009) also found that reviewers scored information differently depending upon their interpretation of the questions asked in the evaluation scheme.
Similar(57)
Manufacturers identify the suspect components based upon their interpretations of the allegations contained in the claims and notices, according to Ms. Aldana, the agency spokeswoman.
In this way, K-8 students are behaving like scientists, practicing investigative iteration, and reflecting upon their interpretations.
None of the three reviewers requested additional experiments, but all three reviewers thought that it was essential for the authors to defend some of their conclusions and expand upon their interpretations of the data.
In order to reason for pattern or significant information underlying the graph, test takers tried to making inferences through drawing upon their personal interpretation and prior knowledge.
The measure was developed for the survey respondent to answer the items based upon their own interpretation of "race" and how they use it in clinical practice.
Many churches have somewhat different confessions of faith and/or catechisms that are based upon their own interpretation of the Christian creeds, Holy Ordinances, system of church organization, and other matters.
Without these dialogues we're in danger of living in a world where any single, sanctioned group may decide what we might write or read or say or think, based upon their own interpretations of an "us" and "them" society.
The Scriptures were adopted from Jewish tradition, but their interpretation was based upon the concepts of salvation that emerged around the figure of Jesus Christ.
For example, the beginning of the entry for 'anaphora' in the MacMillan Encyclopedia of Philosophy (Supplement) reads "The study of anaphora (from Greek, "carry back") is the study of the ways in which occurrences of certain expressions, particularly pronouns, depend for their interpretations upon the interpretations of occurrences of other expressions".
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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