Let users search for posts that contain none of the tags they didn't select

I’m looking for a way to allow visitors to select a bunch of tags (or categories, whatever can be made to work), and then see only posts that do not have OTHER tags. Example: Webtender’s “in my bar” feature, where people check the ingredients they have on hand, and are then shown only recipes that can be made from those ingredients.

Or put another way, if my tags are bananas, oranges, apples, melons and apricots, someone checking bananas, melons and apricots would get only recipes that do NOT contain the oranges and apples tags. The user’s selection would act not as an inclusion filter but as a sort of reverse exclusion filter – excluding everything the user DIDN’T check.

It doesn’t have to be tags per se. The site hasn’t been built yet, so it can be built around whatever solution is found to work.