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I understood the question as a polite variant of "Вы знаете Ивана Петрова?". Similar to "Не знаете ли вы Ивана Петрова?".

Thus we have agreed about difference between polite and literal...

Of course, all these variants are possible, but in this case we are talking about the concrete context:

А: Вы не знаете Ивана Петрова?
Б: Да, я его знаю.

The answer sounds unnatural for...

It is not quite natural to use "да" in the Russian answer, to my thinking. Maybe others would not agree. Better using "нет". English and Russian answers of this kind differ; for the English language,...