Why is this prolog query both true and false?

Question

My SWI-Prolog knowledge base contains the following two facts:

f(a,b).
f(a,c).

Now if I pose the query

?- f(a,c).
true.

But

?- f(a,b).
true ;
false.

Why is f(a,b) both true and false? This also happens when there are three facts in the KB. If I append f(a,d). to the KB, then f(a,d) is true (only), but f(a,b) and f(a,c) are both true and false. What's going on, and what can I do so that Prolog answers (only) true to these queries?

Solution 1

(Note: this answer is somewhat of a guess)

Consider how Prolog determines whether f(a,c) is true or not. It checks the first rule, f(a,b), and doesn't find a match, but the second rule, f(a,c) matches. Therefore, f(a,c) is true. Furthermore, since there are no more rules for f, there is no point in allowing a backtrack to occur -- there are no other possible solutions.

Now consider f(a,b). Prolog will check the first rule, and find a match. Therefore, f(a,b) is true. However, not all rules have been exhausted. Therefore, Prolog will allow the search to continue (if you hit ;). When you do continue the search and backtrack, it will discover that the remaining rules, specifically f(a,c), do not match f(a,b). Therefore, the result is false.

Solution 2

Just in addition to Michael Williamson's answer. If you want to tell Prolog to stop looking for answers after the first successful hit, then use the cut (!):

?- f(a, b), !.
true.

?- f(a, c), !.
true.