logic in prolog language

Question

I have a question in prolog here is the code:

sound(time1).
sound(time2).

sun(time3).

relax(X):-
    not(sound(X)),
    !,
    sun(X).
relax(_):-
    sun(_).

now I an running - relax(T). I get true when I run relax(F) I get true also. Why does it happen?

and one more question, why relax(time4). also gets false? I think I am missing something. thanks a lot!

Answer 1

The fact that relax(T) and relax(F) both give the same result, is normal: uppercase identifiers are variables. So the two queries are semantically the same: you query with an ungrounded variable.

Now why do we get true.? If you query relax(T), Prolog will first call the first clause of relax(X).

The first clause has a body that starts with not(sound(X)). So we actually query not(sound(T)). Not is satisfied by the negation as finite failure principle: Prolog will aim to "prove" sound(T), and if that fails (it cannot find a way to satisfy that query).

So now Prolog queries sound(T), and this query is satisfied: indeed, sound(time1) satisfies this query, since Prolog reasons that now T = time1. As a result not(sound(T)) is false, and thus Prolog backtracks.

Now Prolog will try the next clause: relax(_) :- sun(_). The _ is a "wildcard" or "don't care" variable. Furthermore if you use multiple _s in the same clause, those are not related. So you basically say: everything is relax/1, given there is at least one sun/1. So now Prolog will query for a sun(_). This query succeeds: sun(time3) is a valid candidate, since _ = time3. So that means that relax(_) succeeds. We did not alter the variable T (or F), so Prolog can only say that the query is true.

Now if we query relax(time4), that's a different story. Again Prolog will first try to satisfy the first clause of relax/1. This is again done by calling not(sound(time4)). But note that time4 is a constant. And in Prolog all constants are different: so time1 and time4 cannot unify.

So now Prolog first aims to unify sound(time1) (first clause for sound/1) with sound(time4), but since time1 and time4 are different, that fails. Next it aims to unify sound(time2) (second clause of sound/1) with sound(time4), but again no luck. Now there are no clauses of sound/1 anymore. So Prolog gives up and considers not(sound(time4)) to be true.

That means that Prolog will continu in the body of the first clause of relax/1. The next statement is a !, that is a "cut" in Prolog. It means that Prolog should, for this branching point - no longer consider the remaining clauses. So it will from now on, ignore the second clause of relax/1. Next it encounters sun(X). So now Prolog will call sun(time4) and aim to satisfy this. It will aim to unify with the first (and only) clause of sun/1: sun(time3). But as said before, time3 and time4 do not unify. So as a result, that fails. Since Prolog cannot take the second clause of relax/1 (due to the cut (!)), it thus has exhausted all the options, and decides that the query relax(time4) is false.