If the question is formulated with negation to the verb, and it is answered with one word: да or нет, what is the rule of how to understand it:
- Imagine that the question is a logical expression (no matter does it have negation or not in it); answer да means that you think that the whole expression is true, answer нет means you think it is false.
- Take the verb of question without negation; answer да, if in your full answer (which would repeat the verb) you would not need to put negation to the verb; answer нет, if you would put negation to the verb in your full answer.
- There is no definite rule, in each particular case the meaning is clarified with intonation, or facial expression, or with additional questions/answers.
As far as I know, variant 1) used in Chinese and Japanese, variant 2) is used in English.
Here are the examples:
Parent asks his/her child: "Так ты не будешь есть?" --"Нет!" (said strongly).
Asking acquaintance: "Ты его не знаешь?" --"Да."