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Take the question:
Did you not go to the store?
If I did not go to the store, should I then say yes? Or no?
If I did go to the the store, would my answer then have to be yes or no?
For me I would think that if I did you go to the store, then the answer to the question would be 'yes'.
GREAT QUESTION
If you are asked
Did you go to the store?
"Yes" means that you did go, and "No" means that you did not go.
If you are asked,
Didn't you go to the store?
the negative form of the question almost invariably implies doubt or criticism or both. Answers of a bare "yes" or bare "no" do not address that implication. The answer would normally emphasize the mere substance of the reponse with
Yes, I did
or
No, I didn't.
If no clarification is added, the usage of "yes" and "no" is the same as though the question were asked in the positive. To avoid potential social misunderstanding, however, ask questions in the positive and answer negative questions with a clarifying "I did" or "I didn't."
ADDITIONAL EDIT: In a comment below, reference is made to a response to a similar question. In that response, the point is made that rhetorical questions are frequently made in negative form.
Haven't I asked her a thousand times not to bang the door?
is not attempting to elcit information, but to elicit agreement and confirmation. Anything other than an emphatic answer is likely to be ill received.
To summarize, questions in negative form usually have a social dimension that is usually addressed by answering with extra emphasis.
Did you not go to the store?
Personally I dislike questions like this, for the exact reason you have discovered. I find it best to just sidestep the ambiguity and answer fully:
I went to the store.
or:
I did not go to the store.
Did you not go to the store?
If I did not go to the store, should I then say yes? Or no?
If you didn't go then it would be correct to say: No. I didn't.
If I did go to the store, would my answer then have to be yes or no?
If you did so then it would be correct to say: Yes. I did.
The question "Did you not go to the store?" contains assumption/suggestion that I went. So the answer should be "Yes, I did" if I went or "No, I didn't" if I did not go to the store. The same in the case of "You went to the store, didn't you?"
Did you go to the store?
is a standard enquiry, so of course "yes" and "no" have their usual meanings.
Did you not go to the store?
is asking for the same information, the difference is that there is an assumption that you did in fact go. For example, if it is Friday and you always go to the store on Fridays, but today you arrived home early, I might ask:
Did you not go to the store?
which really means
I expect that you went to the store. But you arrived home early, which is making me think you might not have gone. So, did you go to the store?
In this case, "yes" means you did go and "no" means you didn't - it's as if there was no "not" in there at all. But it can also depend on intonation. Generally, if you say it in a flat tone, it means as above.
Such a question is rarely ambiguous. But there might be a situation where you're really unsure about how to answer, in which case you might consider using "Yes, I did" or "No, I didn't" to clarify.
Did you go to the store?
This question is asking if you did go to the store. Therefore, 'yes' and 'no' are respectively answers of
[Yes,] I did go to the store
and
[No,] I didn't go to the store.
You answer 'yes' to indicate that the statement "you did go to the store" is true; 'no' indicates that this statement is false.
Since the question is now
Did you not go to the store?
you are now answering for the statement "you did not go to the store."
If this statement is true, then you answer yes.
However, as other answers have pointed out, a question phrased this way often displays or conveys a certain expectation, and sometimes isn't even meant as a question. This may be where the uncertainty in how to answer comes from.
Therefore, a full answer that addresses any ambiguity caused by expectations or implications would be
Yes, I did not go to the store.
or the negation,
No, I did go to the store.
(which you might consider as "I didn't not go to the store," which can be difficult to understand for some.)
For those unconvinced, consider how one would go about asking for the negation of a question if not in precisely this way - and if the trouble would be worth that interpretation.
"Did you not go to the store?" is a colloquial (possibly Irish) version of 'Didn't you go to the store?" It isn't a simple inquiry about a journey that can be parsed by counting up and cancelling out the double negatives. It's asking why there's no food on the table when the obvious solution would have been a trip to the store. 'Didn't you think of doing that (you idiot!)?'
Possible answers would include 'Sorry, I forgot!' or 'But it isn't MY job!'
