"Logic" often refers to a lot of things that aren't formal deductive logic, and almost every puzzle uses something that could be called "logic". Because of this, logic-puzzle gets tagged for a uselessly wide range of questions. I think that logic-puzzle is a bad tag name, and doesn't adequately describe what type of puzzles we actually want in it.
For the puzzles that involve formal logical deduction, we should use a tag name that indicates more obviously what the tag is (and isn't) for. I would suggest deductive-logic, although I'm not entirely sure that it wouldn't have the same problem. (Compare logic-grid, which is for a very specific type of puzzle but has been tagged for quite a few puzzles that just involve logic and grids.) Hopefully a better tag description could help here, maybe something like "A puzzle that involves combining information from given statements using formal logic to prove a conclusion."
We should also address the issue of logic-puzzle being used as a catch-all tag. A tag is supposed to group together similar questions, and if it's being used for everything, it doesn't fulfill that purpose. One option could be to get rid of it entirely. Alternatively, we could keep it with a broad definition, although it's hard to articulate what that definition actually would be. Using the inductive/deductive reasoning distinction, a first approximation might just be puzzles that don't qualify as riddle, cryptograms, pattern, lateral-thinking, enigmatic-puzzle, or situation. Looking at the current list of questions tagged with logic-puzzle, I think the ones that seem most out of place either belong in one of those categories (where they should be retagged) or are entirely off-topic for the site.