<xoi> and fuzzy stuff

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

la xorxes cusku di'e
>> How about something like:
>>
>> ti pafi'uci xoi barda ka clani le cnano
>
>It should be:
>
>        ti pafi'uci xoi barda le ka clani kei le cnano
>        This is big in the property of being long compared to the normal.
>        (The truth of the statement being 1/3.)
>

use of ka and kei seems like overkill here. How would you translate my version?
>
>>  Here's what
>> I want to do: Suppose I am using a 3-granularity fuzzy scale. Suppose
>> speaker and listener sample a population and find the average height is 160
>> cm. Speaker & listener then agree that:
>>
>> 0/3 fuzzily tall is the triangle   {{0,1},{160,1},{175,0}}
>> 1/3 fuzzily tall is the triangle   {{160,0},{175,1},{190,0}}
>> 2/3 fuzzily tall is the triangle   {{175,0},{190,1},{205,0}}
>> 3/3 fuzzily tall is the "triangle" {{190,0},{205,1},{Infinity,1}}
>>
>> So it is the *apices* of the fuzzy sets, {160,175,190,205} which form an
>> interval scale. Note that the sets overlap, and that a person of any height
>> between apices is partially in two sets. This is typical fuzzy stuff.
>
>That's all very nice, but you are not using {xoi} like that.

Agreed. I have not yet given an example of how I want to use <xoi> to say
this. This is because I am still unsure of how to construct the X3 or
<standard> part of barda when using <xoi>. My failure to specify a method
for specifying the <standard> is intentional. Any suggestions?

>
>Suppose that John is 1.60m, Mary is 1.70m, and Harry is 2.10m
>
>According to the rules above, you would say that:
>
>"John is 0/3-tall" has truth value = 1.0
>"John is 1/3-tall" has truth value = 0.0
>"John is 2/3-tall" has truth value = 0.0
>"John is 3/3-tall" has truth value = 0.0
>
>"Mary is 0/3-tall" has truth value = 0.33
>"Mary is 1/3-tall" has truth value = 0.66
>"Mary is 2/3-tall" has truth value = 0.0
>"Mary is 3/3-tall" has truth value = 0.0
>
>"Harry is 0/3-tall" has truth value = 0.0
>"Harry is 1/3-tall" has truth value = 0.0
>"Harry is 2/3-tall" has truth value = 0.0
>"Harry is 3/3-tall" has truth value = 1.0
>
>You are confusing two numbers: The numbers that identify each of your
>fuzzy regions: 0/3, 1/3, 2/3, and 3/3, and the truth values of the
>"belongs to fuzzy set x" statements, given by the triangles.
>
You have correctly applied the idea to calculate the fuzzy truth values. I
agree that the fuzzy set ordinal and the fuzzy set truth-extent are
different and I am not confusing the two numbers, and have not given an
fully lojban example yet. That is where I am stuck. The idea is the
listener will compare the number just before <xoi> with the standard
specifed in X3 of barda, and figure out which fuzzy set X1 is in, *not*
what the truth value of inclusion in that specified fuzzy set is. I
entirely agree that the two referents are distinct.

>And proposed {xoi} for the truth values. You are using it for the names
>of tha fuzzy regions.
>
Yes, this is a possible way of looking at what I'm trying to do. But the
fuzzy sets are more than just names; the peaks of the fuzzy sets define an
interval scale, which *could* be used as numerical inputs to <xoi>, and
remain consistent with the spirit of <xoi>. I believe this would be better
than using the fuzzy truth values before <xoi>, as otherwise we force
speaker-listeners to explicitly do fuzzy math calculations, which as you've
pointed out very well is undesireable.

>> I have no objection to attempting to come up with a mutually agreeable
>> interval scale for the beauty of roses. I think it would be hard, but I see
>> no reason why it couldn't be done.
>
>It could be done, of course, but then we would be using the word "melbi"
>as jargon, not as people understand it.
>
>For example, scientists use the word "energy" in a very objective sense,
>for a quantity that can be measured in joules, calories, or what have you.
>That is jargon. When someone says "I have a lot of energy today" you can't
>seriously ask them "Oh yes, how many calories do you have today?", because
>they are using the word "energy" in a more subjective way, not as an
>objective measure word.
>
>There is no law against redefining "melbi" and giving it units according
>to some measurable quantity. That does not mean that beauty, as understood
>by speakers of the language, is a quantity that can be objectively
>measured. You would be measuring something else and using an already
>existing word for your new concept. That is not the same as measuring
>or giving a scale to the already existing concept of beuty, which by
>its very nature cannot be given a scale.

I think that your view is a legitimate one, and is a clearer statement of
the  same point that Peter was raising. However, there is  another way to
think about the different meanings of a word like energy, which I believe
has some advantages. I would prefer to separate the concept of definition
from the concept of scale. Actually, dictionaries seem to do this quite
well. Often dictionaries include multiple subdefinitions, which often
correspond to different scales. Some examples:

"I'm full of energy today!"   (nominal scale)
"I have less energy on Fridays than on Wednesdays." (ordinal scale)
"I expended 0.4 kilojoules of energy today." (ratio scale)

Certainly the last statement would qualify as what you refer to as jargon.

>
>> The fuzzy zone is distinct from the two non-fuzzy zones:
>> height < 1.6 meters, is entirely 0/3 tall and not at all 1/3 tall
>> height > 2.0 meters is entirely 3/3 tall and not at all 2/3 tall
>>
>> If 1.6 meters < height < 2.0 meters, you are in the fuzzy zone. The
>> granularity is three, which means that there are four fuzzy set apices, two
>> at the ends, and two evenly distributed within the interval 1.6 to 2.0. at
>> the 1/3 and 2/3 positions.
>>
>> la xorxes pafi'uci xoi barda ka clani le <mitryranji [1.6,2.0]>
>>
>> "xorxes is in the first of three equal-interval fuzzy sets within the fuzzy
>> zone that begins at 1.6 meters and ends at 2.0 meters."
>
>Which three fuzzy sets? There are only two: 1/3 and 2/3.

There are four sets: 0/3,1/3,2/3,3/3. There are two sets fully within the
fuzzy interval: 1/3, 2/3. There are three intervals.
>
>And how do you get that reading? I get: The statement "Jorge is big in
>longness by standard <mitryranji [1.6,2.0]>" has truth value 1/3.
>
>I happen to be 1.78m, which means that you are right that I'm in the
>range you call 1/3. But what I don't get is why that makes the truth
>value 1/3. Had I been 1.82 instead of 1.78, then the truth value
>of "Jorge is big in longness by standard <mitryranji [1.6,2.0]>" would
>have been 2/3?

The meaning of <xoi> is yet to be defined, and is in a nebulous unformed
but forming state at this point. I hope I have made clear what I want to
achieve. Any ideas how we can get there?

co'o mi'e. 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