Prolog Negation

Question

I am trying to solve a simple query in Prolog that uses negation but I can't crack it. The query is "Find the categories that have never been sold".

The knowledge base is as follows:

category(stationery, 30, 200, 10, 2).
category(books, 10, 30, 3, 2).
category(consumables, 50, 300, 15, 3).

item(pen, stationery, 10, 150).
item(colgate_small, consumables, 20, 65).
item(colgate_medium, consumables, 45, 70).
item(colgate_big, consumables, 70, 34).
item(juice_small, consumables, 45, 23).
item(juice_medium, consumables, 60, 23).
item(juice_big, consumables, 80, 12).
item(book, stationery, 5, 65).
item(pencil, stationery, 7, 56).
item(newspaper, books, 50, 400).

sale(tom, 1/1/07, pen, 3).
sale(peter, 1/1/07, book, 85).
sale(peter, 1/1/07, juice_small,1).
sale(alice, 7/1/07, pen, 10).
sale(alice, 7/1/07, book, 5).
sale(patrick, 12/1/07, pen, 7).

Answer 1

Sam Segers answer is correct, though it will give you the list of categories not sold. If you don't want an aggregation but rather a predicate which will backtrack over all the categories which do not have any items sold you would write something like this:

not_sold(Cat):-
 category(Cat,_,_,_,_),  % Get one category at a time
 \+ (    % Applies negation
   item(Item, Cat,_,_),  % Check for items in this category
   sale(_,_,Item,_)      % Has the item been sold ?
 ).

This predicate, upon backtracking, will yield all the categories for which no items where sold.