Re: object algebra

"Neo" <neo55592_at_hotmail.com> wrote in message news:4b45d3ad.0402282138.19372dd2_at_posting.google.com...
> > > Given EyeColor = {red, brown, NOT_APPLICABLE}. Given the table:
> > > Person EyeColor
> > > ------ --------------
> > > Mary NOT_APPLICABLE
> > > Bob NOT_APPLICABLE
> > >
> > > Then, Mary.EyeColor equals Bob.EyeColor leading an AI program to
> > > conclude that Mary and Bob have the same EyeColor.
> >
> > let color(X) be the color of an eye
> > let M be the set of Mary's eyes
> > let B be the set of Bob's eyes
> > for all m in M, for all b in B, color(m) = color(b)
> > Note that this works perfectly with having a N/A value in the
> > eye color domain. So this hypothetical AI program will not be confused.
>
> The robot would not be confused internally, but the validity of his
> conclusions about the "real" world could be incorrect or not quite
> correct (ie John and Mary have the same EyeColor).

No, they would be exactly right.

> If a human boy sees
> that John and Mary are missing their eyes, and we ask him if they have
> the same eyeColor, he should respond "They don't or can't have the
> same eyeColor because they are missing their eyes".

Human boys do not represent the pinnacle of logic as we know it. Anyway, that response shows the boy falls clearly (as do you) into the group of people who are not comfortable with nullary logic. Hence the second version of what it means to have all their eyes be the same color:

> > If, perchance, you are not comfortable with nullary logic, you might be
> > tempted to introduce additional clauses to the above:
>
> The problem with this approach is that it is difficult, if not
> impossible, for an AI-type program to know in advance if the
> "additional clauses" will apply to new set elements. Basically, it
> will have the assume the least specific existing relationship between
> the set and its elements.

Could you be more specific about this "problem" you perceive? Because the additional clauses are merely what's needed to have the answer come out the way you wanted the boy to answer.

Marshall Received on Sun Feb 29 2004 - 08:43:42 CET