Group A:
This is so-called "Moon Cake." // The period is inside the double quatation marks
This is so-called "Moon Cake". // The period is outside the double quatation marks
I know the former is more standard-conforming in most publications; however, I think the latter is more intuitive and meaningful. Because the period is used to stop the whole sentence, rather than stop the phrase itself. I think the former is counter-intuitive, although the usage is standard-conforming.
Please consider another two sentences:
Group B:
She said: "I don't know."
She said: "I don't know".
It is obvious that the former is more meaningful than the latter, because the period is used to stop the whole sentence, and the double quatation marks are used as a quatation. This time, it is standard-conforming and intuitive.
What's your opinion?