Am I correct in assuming that this means I like one dog but not the other?
No, you don't like both dogs.
I guess logically it would mean that you don't like at least one of the dogs (not(A and B) = (not A) or (not B)), but normally when someone says that it means they don't like either of the dogs.
It just mean that you like neither of the two dogs, pretty straightforward.
Thanks. So in that case "I don't like either of the dogs" is a more accurate translation.
Also "I dislike both dogs." (Still incorporates the word "both".)
Literally though your translation would have its Polish equivalent in the following sentence: "nie lubię żadnego z psów".
So, how would one say in Polish "I don't like both dogs (but I do like one of them)"?
You can't. You have to say that you like one or that you don't like the other.
What an interesting little lacuna. I imagine in a logic class, you would have to use some long construction, like "it is not true that I like both dogs."
Of course you can! "Nie lubię obu psów, tylko jednego z nich". It might sound a bit weird but is grammatically correct.
Except that you specifically mentioned that you like one of the dogs and I believe the point was to avoid doing so.
Must be why the translation I put was wrong "I do not like either of those dogs"
This should be correct. "I don't like both dogs" means "I don't like BOTH but I do like one of them" which is a super weird thing to say anyway, rather than "I like one dog but not the other."