fuzzy truth

["Steven M. Belknap" <sbelknap@UIC.EDU>]

I would still like to be able to say something like:

The food at Le Francais in Wheeling Illinois is 8ish on a 0 to 9 scale. It
is possible that there is some easy way to do this already in lojban,
although I haven't seen any posts that quite get at what I want to do. As
I've written before, I believe this issue of fuzziness is important because
it is closer to how most people actually think about the world. Often
people are forced into an Aristotlean straitjacket which does not
correspond to what they mean.

For example, using the legal setting:

"Did you or did you not see the defendant defenestrate the errant politician?"

Now, perhaps I saw some shadows which on a 0 to 7 scale I am 4ish certain
corresponded to the defendant and the errant politician, and suppose I saw
these shadows perform the alledged defenestration to certainty 3ish on a 0
to 4 scale. If I attempt to answer this question yes/no, I will be
dissatisfied with my answer. If I equivocate, I will be accused by the
obnoxious lawyer that I am equivocating, and he will attempt to force me
into a falsely dichotomous Aristotlean universe of reply. It would be nice
if fuzzy replies would elegantly, compactly allow for this sort of thing.
There have been several objections:

1. People don't think this way. This is the way computers handle fuzziness.

The use of numbers in my examples is not meant to imply exactness-these
numbers are fuzzy. One example I see in my medical practice is when I ask a
patient to describe the severity of pain.

"How bad does it hurt?"
"Well, doc, its about a 3 on a 1 to 10 scale."

My patient does not mean its *exactly* 3. He is using a fuzzy concept.
Several years ago we did a study where we evaluated the degree of euphoria
experienced by an addict after a cocaine injection. For this purpose we
used a visual analogue scale, in which the subject drew a dot on a fixed
line corresponding to the intensity of euphoria, where the leftmost
position corresponded to "not at all" and the right most corresponded to
"Most euphoric possible." Despite the obvious subjectiveness of this,
addicts mapped out a sequence of points over time describing a smooth curve
that could be modeled with a pharmacokinetic/pharmacodynamic model based on
cocaine concentration in the blood and acute tolerance, which resulted
eventually in a publication to this effect. We showed that the degree of
euphoria wears off faster than the cardiac effects, which may explain why
addicts redose with cocaine before they recover completely and thus
inadvertently kill themselves.

People *do* think this way, or perhaps more accurately, people *can* think
this way.

2. We can handle this with a sequence of je' things, as suggested by xorxes:
je'ucai
je'u(sai)
je'uru'e
je'ucu'i
je'unairu'e
je'unai(sai)
je'unaicai

There are two problems with these types of schemes:

First, the granularity is fixed. If I want to use a 3 point fuzzy scale
(yes, maybe, no) for reasons of being purposely less precise than a 5 point
fuzzy scale, (yes, probably, maybe, possibly, no) then I can't get across
the intentional choice of greater granularity of my reply with the je'
schemes.

Second, there is no specification of ordinality. I think ordinality is
quite useful, as it seems important in expressing fuzziness. Je'uru'e and
the other je' things are not obviously distributed in an even way along the
truth scale.

3. You can actually say what you mean in lojban quite exactly by stating
the whole thing in mathematical terms.

I want to include ordinality, fuzziness, and granularity in my fuzzy
statements. Expressing all three concepts with the lojban constructs I know
is longwinded, unwieldy, and probably incomprehensible. I doubt that such
constructions would be used very often. Because lojban is based on the
predicate calculus, logic, and careful attention to semantics, I think
lojban is potentially vulnerable to this problem of one speaker forcing
false dichotomies on other speakers, and that a rich fuzzy logic mechanism
is required. I remember discussing this with lojbab when I visited him
several months ago, and I came away from our discussion convinced that this
would not require any sort of major or even minor change in the language.
Maybe using inexact numbers would be a start:

li piso'u to li piro

The closest gismu for fuzzy would seem to be <kerfa>

x1 is a/the hair/| [body-part] of x2 at body location x3

Although <kerfa> seems to be referring to animals (or perhaps the leftover
pizza in the back of my refrigerator), couldn't it also be used for the
idea of fuzzy sets or fuzzy logic?

<X1> <kerfa> <fuzzy numerator> <fuzzy denominator>

This would mean a change in the 3 position, as body location is not
analogous to body location. Perhaps there could be a better 2 position as
well.

If this is unsatisfactory, how about a lujvo or le'avla for fuzzy?

la stivn


Steven M. Belknap, M.D.
Assistant Professor of Clinical Pharmacology and Medicine
University of Illinois College of Medicine at Peoria

email: sbelknap@uic.edu
Voice: 309/671-3403
Fax:   309/671-8413