#15 exists_not problems

[Michael Kifer]

The way exists_not is defined leads to counterintuitive results, unfortunately.
for instance, suppose we have

neg(rrr(a)).
rrr(c).
ddd(b).
ddd(a).

Then (I am using Terry's Prolog program for exists_not):

| ?- exists_not([],rrr(c)).

no
| ?- exists_not([],rrr(b)).

yes

| ?- exists_not([],rrr(a)).

yes

But:

| ?- exists_not([X],rrr(X)).

X = a;

X = _h165 undefined;

Two things are wrong here:

1. the general call does not return all its true instances
2. The second answer, X = _h165 undefined, is hard to interpret logically.
   When combined with other things during inference, it yields all kinds of
   weird results from the users standpoint. For instance:

| ?- exists_not([X],rrr(X)), ddd(X).

X = a;

X = b undefined;

X = a undefined;

Here b is unexpected, but worst of all is that we get X=a twice with different truth values.

I am sure these problems are going to show up in the ATCO theories once we test them on examples with vars in them. In fact, they already showed up in a smaller way, which was the subject of my last week's email to Terry and I later mentioned it to Benjamin.