Message-Id: <m0tJKsQ-0000ZUC@xiron.pc.helsinki.fi>
Date:         Sat, 25 Nov 1995 08:40:55 -0500
Reply-To:     Logical Language Group <lojbab@ACCESS.DIGEX.NET>
Sender:       Lojban list <LOJBAN@CUVMB.BITNET>
From:         Logical Language Group <lojbab@ACCESS.DIGEX.NET>
Subject:      fuzzylogic #2 tall
To:           Veijo Vilva <veion@XIRON.PC.HELSINKI.FI>
Content-Length: 6827
Lines: 119

>> While everyone might agree that "At six feet and three inches, John is
>> a tall man" is true, most would agree that "At seven feet and four
>> inches, Joe is a tall man" is *more* true.  Truth values near 1/2 (the
>> range is generally [0,1]) represent "I don't know" or "I'm not sure"
>> answers, with leanings toward one side or another.
>
>The dictionary definition of "tall" doesn't rely soley on measurement.
>It includes the idea of comparison:  Having greater than ordinary
>height.  You can't learn anything about tall by making a measurement,
>unless you then compare it to something.

I'm not sure all dictionaries agree, and current thinking seems to be
that most concepts are defined not with respect to something different
(i.e. not-tall, as you describe above), but rather against some ideal of
tallness.

In that sense Steve is right.  For any person A that everyone agrees IS
"tall", we can envision the possibility of someone B who is "more" tall.
It is not clear whether we would mark the statement "A is tall" as being
less than perfectly true MERELY because B exists.  Indeed, if this were
possible, that the statement "x1 is tall" could change truth values with
time though x1 did not change at all, simply by something else becoming
taller.

It is possible to define tallness as compared to something smaller.  But
I dare say that unless there is agreement as to what the reference is,
then it will be hard to get any consistency in values.  Is my 9 year-old
daughter tall?  She is 4'7 (140cm) - already fast approaching Nora's 5'2
(158cm) even though still a couple of years from puberty.  In some
contexts - against other 9 year olds - she is a bit taller than average,
but not exceptional.  When Nora is thinking of her in terms of her
imagining a grown Angela, Nora's relatively short height makes Angela
subjectively taller for her when other girls are NOT present as when
they are.  But when Angela wants to reach something on a high shelf,
suddenly she is "short".  Likewise, I am tall to Nora, and am above
average height.  But I don't tend to think of myself as tall at least
partially because I have stubby legs (if my legs were proportionate to
the rest of my body I would be 6'6 (2 meters).

Likewise baldness.  I am the antithesis of bald - my hairline hasn't
receded much at all.  My father on the other hand had a receding
hairline, but was in no way "bald" - a statement that he is bald is JUST
as false as it is for me, even though on Steven's scales he would be
more towards baldness than I would.  A good friend back in college,
however, though he still had hair all over his head, the impression was
largely due to his letting it grow long, and he was almost bald at 22.
At age 22 and around other people who are that age, I would definitely
call him "bald".  Around some people I know now that have clean-shaven
heads, he was far from bald.

Hills and mountains were another of Steven's examples.  Here in Virginia
there are "mountains" that are well less than a kilometer high.  In
California they would be hills, unless you started defining mountains in
terms of steepness of ascent rather than altitude.  The Eastern
mountains tend to have the steep cliffs of the higher California ranges
rather than the rolling nature of the California foothills.  Clearly
context will determine the truth value of X is a mountain as well.

Lojban, unlike English, incorporates the context in the words themselves
The Lojban word for "tall" has an implicit standard.  You can add a
standard place to "mountain", or a "to observer" to either.  These
places have MUCH more effect on truth value than "fuzziness" would
provide, and they largely make each observation of a truth value unique.

Even when you get past this, and talk about individual observations
under a standard context, my basic sense of fuzzy logic values, without
having any technical knowledge of the field, is that this granularity
and ordinality of Steven's is largely imposed by outsiders attempting to
quantify the unquantifiable.  There seems to me to be a BIG assumption -
that the scale of truith is linear.

When polltakers take a poll on a subject about which there is a wide
range of opinion, they often ask questions to determine not only "yes"
or "no" on a question, but strength of opinion.  So you get ranges like
"strongly agree", "mildly agree", "neutral", "mildly disagree",
"strongly disagree".  But poll results show that these categories are
NOT linearly divided.  On some issues, like abortion, you get strong
agreements and disagreements.  On other issues, you get pretty weak
reactions.  But I think that the consensus among researchers is that
people are prone, by their nature, to be biased towards either strong
opinions or moderate ones - the categories are NOT evenly divided on a
scale.  This matches much better with Lojban's fuzzy numbers so'V
than with integers.

Indeed, I suspect that if you asked the same question using integer
scales as with fuzzy scales, I'd bet that you would get different
results.

I have a sympathy with Steven's idea of multiple values of granularity,
at least partially from the cultural neutrality standpoint.  But I
suspect that pragmatically the 7 or 8 level granularity built into the
so'V scale is sufficient for most uses and vague enough to support
non-linear truth scales.  The je'u+CAI[+NAI] also gives a 7 level scale
though only 3 are really positive, and you also can use ju'o+ and .ia+
and .ie+ to express different varieties of "truth", also adding in lots
of subtle nuance through the use of other attitudinals (that very spicy
Thai curry I had the other day was excellent .iacai.oiro'osai).  These
might be a bit less amenable to computation than Steve's fuzzy logic
values, but the multidimensional scales possible are truly enormous.
And you can put attitudinals on virtually every word of a statement to
express the relevance/importance/certainty of that component of the
sentence to the total truth value.

And attitudinals have the simplest possible grammar - essentially none.

If this (and my other discussion on how to express things with ni) still
is not satisfactory to Steven, I can think of one solution that is
simple and inexpensive in terms of change.  For the price of one cmavo,
which can go into XI (subscript), you can cover all bases.

"xi'i vo pi'e ze" could be placed anywhere a free modifier is permitted
(almost as flexible as indicators, though with a few restrictions) and
could be used as a label of "degree of truth" for that component.  As my
example shows (4:7) you can express the ordinal and the granularity.
And if someone ever comes up with some other numbers they want to stick
on (correlation coefficient?), they can do that too, since as we have
been discussing, the grammar of PA is rather open-ended.

lojbab