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?
(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.
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.
Thank you Michael. Because I didn't register before posting this question it doesn't look like I can accept your answer; I'm sorry. You all have been very helpful.