I'm still not sure I understand what we're trying to produce. Something like "a collection of four words, such that any subset of three has something in common not shared by the fourth" ?

Along the lines of

"red, orange, bell, conquerer"
-- conquerer is not a kind of pepper
-- bell is not the appellation of a figure in Middle Ages European history (Eric the Red, William of Orange, William the Conquerer)
-- orange is not... (but red, bell, and conquerer are - racehorces, maybe?)
-- red is not ...

(Wits and time fail me at this moment.)

Is that what we're looking for?