What's the difference between the tags
Are they both needed?
And if they are, wouldn't it make more sense for them to both start with either
Well, [logic-theory] is hardly used at all and has no official description. It looks to me as if its actual uses break down as follows:
I think [logic-theory] could reasonably be done away with. Anyone want to object before I do it?
[EDITED to add:] OK, I did it. The [logic-theory] tag is gone. If anyone really wants to make puzzles for which it would have been appropriate, and can do so without getting them closed as "textbook mathematics problem rather than puzzle", and really wants a specific tag, then I suggest that [mathematical-logic] would be better.