I think that if question B is accused of being a duplicate of question A, and there is at least one answer that is a valid answer to question A that would not be a valid answer to question B, then question B is not a duplicate of question A.
I think it is exactly the reverse. If there is at least one answer to B that would not answer A, then B cannot be a duplicate of A. The reason for this is as follows:
There are three goals involved in the process of closing a question as a duplicate:
- Duplicate content should not be reproduced in multiple places.
- The same question should not have different answers in different places.
- Every question (not every post) should have the possibility of receiving any valid answer.
I think Goal #3 is the most important, because it affects the very purpose of the site, while Goal #1 and Goal #2 are issues of convenience/interface.
Now let's see how these goals would play out in various cases:
Every valid answer to A is a valid answer to B, and every valid answer to B is a valid answer to A.
In such a case Question B is obviously a duplicate (or question A can be considered the duplicate, but that doesn't matter for the purposes of this discussion) because closing as a duplicate upholds all three goals.
There are valid answers to A that would not be valid answers to B, and there are valid answers to B that would not be valid answers to A.
B is not a duplicate, because closing B would violate Goal #3, as there will now be valid answers to B that can never be posted (since they are not valid answers to A). Even though leaving B open might allow some answers from A to be reproduced on B (violation of Goal #1), that needs to be sacrificed in order to uphold Goal #3.
There are valid answers to A that would not be valid answers to B, but all valid answers to B would be valid answers to A (the case quoted above).
In this case B is a duplicate, because leaving B open violates Goal #1 (some of the answers to A might get reproduced on B) while closing B still upholds Goal #3 (because any answer that could have been posted to B can still be posted to A).
All answers to A would be valid answers to B, but there are valid answers to B that would not be valid answers to A.
B is not a duplicate because closing B would prevent some answers to B from being posted at all (violation of Goal #3). Even though leaving B open might allow some answers from A to be reproduced on B (violation of Goal #1), this must be sacrificed in order to uphold Goal #3. (Though B should not be closed as a duplicate of A, A would actually be a duplicate of B in this case, because A in this case is simply the B from the previous case.)
Now let's apply this to the examples created by Isaac Moses and Double AA to see where the conclusions would differ and where they would agree (even if they agree for different reasons):
Isaac's First Example
A: May one eat rabbits?
B: May one eat rabbits on Tuesdays?
B is a duplicate because it falls under my third bullet. While some answers may address eating rabbits without addressing eating rabbits specifically on Tuesdays, no answer can address eating rabbits on Tuesdays without addressing eating rabbits. (Even though addressing only eating rabbits on Tuesdays would not be a complete answer to A, partial answers are still answers, particularly when they are supplementing a more comprehensive answer that just didn't address a specific exception.)
Conclusion: Agrees with Isaac.
Isaac's Second Example
C: May one eat rabbits as part of this medical diagnostic test that requires the consumption of rabbits?
This is still a duplicate because even though, as Isaac points out, it is more likely for this case to be an exception to a general rule, eating rabbits for a medical test is still an example of eating rabbits. While someone answering A would probably not be expected to address C, since the answer to C can still be posted to A it remains a duplicate. If the person who has question C is concerned that no one will think to post the answer to C as an answer to A, there are various methods of requesting such an answer (e.g. bounty, comment, chat, etc.) Alternatively, we can edit A to explicitly exclude C (e.g. "Can one eat rabbits barring medical exigencies?"), which would not invalidate the answers to A, and then C could be reopened as a separate question.
Conclusion: Disagrees with Isaac.
Isaac's Third Example
D: May one eat rabbits on Tuesdays? It says in Bava Maiseh 37j that all herbivores that chew their cuds are permitted for consumption on Tuesdays.
This is still a duplicate because an answer saying that Tuesdays are an exception because of Bava Maiseh 37j can still be posted as a partial answer to A. In this case, if the existing answers to A don't mention any exceptions, you can even post a comment to those answers pointing out that they are not entirely correct because Bava Maiseh 37j proves that there are exceptions.
Conclusion: Disagrees with Isaac.
Isaac's Fourth Example
J: Who were the primary mentors of the rabbis who attended the famous Seder in Bnei Brak?
K: Of the rabbis at the famous Seder in Bnei Brak, were any each other's primary mentor?
K is a duplicate of J because any answer specifying that one of the rabbis at the Seder was the primary mentor of another rabbi at the Seder, by definition tells us the primary mentor of one of the rabbis at the Seder. This falls under my third bullet. (See, however, this comment.)
Conclusion: agrees with Isaac.
Isaac's Fifth Example
P: Experience-based advice for keeping a sukka from being blown around by the wind, with criteria ...
Q: Experience-based advice for keeping a sukka from being blown around by the wind, with criteria ... on a boat!
This is again a duplicate, because even though Q might be specific enough that you wouldn't expect an answer to P to address it, any answer to Q can still be posted as a partial answer to P, so it once again falls under my third bullet.
Conclusion: Disagrees with Isaac.
Double AA's First Example
A: Is there an obligation to wear tefillin on Chol HaMoed?
B: Do tefillin apply on Chol HaMoed Sukkot?
B is a duplicate because any answer discussing the obligation of tefillin on Chol Hamoed Sukkot is necessarily discussing the obligation of tefillin on Chol Hamoed, even if incompletely (since it wouldn't address Chol Hamoed Pesach). Since any answer to B can be posted to A, this falls under my third bullet.
Note that if there truly is a difference in halacha between Chol Hamoed Sukkot and Chol Hamoed Pesach, a better option might be to edit A to specifically refer to Pesach and now have two separate questions. If someone would later come and ask C about Chol Hamoed in general C can be closed as a duplicate of A+B. But the existence of this option does not affect the duplicate status if the option is not utilized.
Conclusion: Agrees with Double AA.
Double AA's Second Example
A: What books of Tanakh start with a ש?
B: What books of Neviim start with a ש?
B is a duplicate because any book of Neviim is also a book of Tanakh. Thus, any answer to B can be posted as a partial answer to A, and this therefore falls under my third bullet.
As in the previous example, we again have the alternative option of editing A to limit it to only books of Torah and Ketuvim, and then leave both questions open. However, here it would be not quite as good of an option, because specifying precisely Torah and Ketuvim but not Neviim would be a bit odd.
Conclusion: Agrees with Double AA.
Double AA's Third Example
A: Should one repeat Shemoneh Esrei if he forgot to say Mashiv HaRuach?
B: Do Ashkenazim repeat the Amida if they forget the insertion of Mashiv...?
This is also a duplicate. Any answer that discusses whether Ashkenazim repeat Shemoneh Esrei addresses A (albeit incompletely). Since any answer to B can be posted as an answer to A, this also falls under my third bullet.
Here the option of editing A is even less desirable than in the previous example, because there might be a lot more than three possible subcategories, so a question specifying everyone except Ashkenazim would be even more odd.
Conclusion: Agrees with Double AA.
Double AA's Fourth Example
A: Is pig kosher?
B: May one consume ham?
Since ham is a part of pig, any answer discussing the kashrut of ham is necessarily discussing the kashrut of pig (albeit incompletely), so any answer to B can be posted to A, and therefore this is also a duplicate as it falls under my third bullet.
Conclusion: Agrees with Double AA.
Note that even though my conclusion agreed with Double AA in all four instances, I don't know that we are agreeing on the underlying rationale.