O que significa “claimed” in “It would be odd if they claimed proficiency in the language on the basis of being able to read it” ?

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claim is usually referring to ownership of something. In this context, it is about the person's ability to understand a language.

So the sentence is essentially saying:

It would be odd if he stated he is proficient in a language, just because of the fact that he can read the text.


In the sentence above ⬆️ "he is proficient", is the same as him claiming proficiency and "claimed proficiency" in your text.

He is just making an assertion of his ability of being fully versed in the language, similar to a native, just based on his reading comprehension of said language.