Disclaimer: This is Xonix' solution. If you like it vote him up. But as it took me some head-scratching to figure out what was going on, I thought I might just as well offer my comments so others could benefit.
At first, here is his solution as a proper clause:
criminal(K):-
member(K,[a,b,c,d]),
(K\=a -> A=1;A=0),
(K=d -> B=1;B=0),
(K=b -> C=1;C=0),
(K\=d -> D=1;D=0),
A+B+C+D=:=1.
And it goes like this:
At first, he runs through the list of individuals (have to be lower case, so they're not variables). K
is instantiated to each of them in turn.
With each possible value of K
he runs through the rest of the clause. K
can be interpreted as the hypothesis who the criminal is. The next 4 lines are to provide bindings to each of the variables A, B, C and D. You can read them like this: Under the assumption that a
is not the criminal, a is truthful otherwise not. Under the assumption that d
is the criminal, b is truthful otherwise not. Asf. That is, the variables A, B, ... capture the truthfulness of the corrsponding individual, given a specific criminal.
As a known constraint is the fact that only one of them is truthful, the sum of their truth values must be 1. On backtracking, Prolog makes the next binding for K, and runs through it again. Turns out the constraint is only satisfied if a
is the criminal (and d
is telling the truth, if I'm not mistaken). Cute.