ni/jei abstractions, fuzzy logic - response to many postings

[Logical Language Group <lojbab@access.digex.net>]

Various postings one general subject:
>If there is no clear meaning for ni, perhaps implementing a rich syntax
>for describing fuzzy sets with ni would be amusing and/or useful.
>Perhaps the capability exists but is simply unrecognized.

Some history will perhaps help.

JCB has three abstractors, corresponding to nu, ka, and ni.  They are
used two ways in TLI Loglan.  One way we would call a tanru usage.  In
this usage "nu carmi" would be an event of being bright, bringing to
mind a flashcube.  "ka carmi" having tanru scope and meaning
"brightness", the quality of being bright.  You can claim that something
is characterized by brightness, and you are ascribing a property and not
a quantity to it.  "ni carmi" would be "brightness" = "intensity".
These words are always defined in terms of English equivalents, so it
gets tough to figure out what they "mean" since they emphasize a
distinction English rarely makes.  Specifically, JCB never gave a place
structure for any of his abstractions.  He might use them in a tanru, or
put a "le" on the front implying that there is at least one place, but
he never discussed the semantics.

TLI Loglan also has a bridi form of abstractor, corresponding to "lenu"
and "leka", but in the TLI grammar, these are written as one word, and
the joined word flags a different grammar than the separated word "lenu
carmi" is not the same as "le (nu carmi)".  JCB gives examples for
"lenu" equivalent, and maybe for "leka" equivalent, but never for "leni"
equivalent, as far as I can recall.  Here, there is an "inside" place
structure i.e. that of carmi in "lenu carmi" or "leni carmi", but again
he doesn't suggest an outside place structure.

I am not sure if in TLI Loglan, you can put a be/bei on a lenu clause.
Probably not.

Back in truly ancient Lojban - indeed in 1989 when I was writing chapter
three of the first draft textbook, it became clear that the place
structure of these things was at issue.  This was also right about the
time we first had a complete YACC grammar for the language, and it
became quickly obvious that the grammatical distinction between "le nu
broda" and "lenu da broda" was artificial and complicated the grammar,
as well as opening up a hairy semantic mess regarding place structures
inside and outside, AND violating the audiovisual isomorphism of the
language, since in spoken Loglan/Lojban you might not be able to tell
the difference between "lenu" and "le nu".

So we rewrote the grammar to eliminate the distinction, and "nu broda"
in tanru needs the terminator "kei" within the tanru to give the
abstraction short scope.  But there was a dearth of real examples of
some of the abstractions.  Certain gismu seemed to go well with nu,
others with ka, and only a few had meaningful definitions with ni.  But
when we examined these cases, we found that there was a clear
correlation with English part-of-speech.  Noun and verb keywords tended
to go well with "nu" and "ka", adjectives, went well with "ka", and more
rarely with "nu" and "ni".  Adverbs, quite rare in the gismu list,
happen to go well with "ka" and "ni".  (Don't ask me to recreate the
examples - I have long forgotten them).  I therefore tend to associate
"ka" with characteristics, and "ni" with "degree".

But Lojban predicates are NOT categorized into these parts of speech,
and if the universality of the predicate is an assumption of the
language, then the difficulty in seeing a "nu" form of some
adjective/adverb, or a "ni" form of some noun, is an artifact of English
thinking.  There has to be a meaning of "leni nanmu" or "leni klama".
We may never really grasp that meaning until we can think solely in
predicates, but it must exist, by assumption.

jei was added separately, specifically to allow talking about truth,
falsity, and fuzzy logic.  It was always conceived of as a 0/1 scale,
and no one worried about whether or how it overlapped with ka or ni,
because it had a different purpose.

There ARE quantities that seem well suited for measurement on a 0/1
scale (ni nanmu?), and ni might or might not be essentially equivalent
to jei in such cases - or it might not.  There are other quantities,
like ni carmi, that seem like they are open-ended.  But I suspect that
we are just recreating the noun/adjective distinction again.

My solution was to put a scale place on the ni abstraction, so we can
decide in a specific context whether we want a 0/1 scale, an infinite
scale, or maybe a count scale, or something else entirely.  This begs
the question of what "ni" means, but so what?  "ni nanmu" might be a
count of the number of men, or it might be a degree of manliness of a
mass man (single or collective) which could range from 0 to 1,
especially if the mass contains some women, or a man with XXY
chromosome, etc.), or it might be an open-ended scale where a high "ni
nanmu" means some kind of oversexed stud.  In the later case "le jei
nanmu" probably is no different for that stud than it is for any normal
man with XY chromosome, appropriate genitalia, etc. i.e. 1

Now how you fill in that scale place is a "problem for the reader".
There is almost certainly a way - we have a predicate ckilu in the
language and other cases where we have to talk about scales (e.g.scalar
negation).

I think part of the problem with "ni" is that we are used to think of
measurement in terms of single quantities, and "ni" seems to make the
most sense in pure adjectives that have only one sumti.  We don't know
how to analytically quantify multi-place sumti.  Yet we do intuitively,
because good/better is generally a ni comparison.  We can't assign a
number to "goodness" (the quantity) except possibly in the cases where
x2 and x3 are held constant (e.g. goodness of fit for an approximation
of a mathematical curve), but we can compare two goodness quantities.

>I'm suspicious of making {lo jei broda} a number at all.  People don't
>tend to quantify things precisely, so assigning a number makes me wary.
>And there's a lot more going on in natlang semantics; for instance, the
>truth of a statement is usually relative to some context.  Quite
>possibly the set of contexts that makes a statement true is enough to
>determine the "fuzziness".

In Lojban we have fuzzy numbers to go with fuzzy logic.  You should find
that lo jei broda can be anywhere from 0 to 1, such as piso'u, piso'a,
etc.  People have little trouble using these numbers in natlangs, and
even in using them in talking about truth (probably, not likely, not
especially, are all fuzzy values of truth)

>Hum.  The reason {lo ni gusni} is bounded on one end is a absolute
>minimum to the amount of brightness:  total darkness, while the absolute
>maximum is far beyond our experience.  (At a certain point the energy
>density of the photons would create a black hole, I believe.)  But this
>is particular to {gusni}.

Correct.  Other scales are effectively unbounded in both directions such
as melbi and xamgu.

Is {lo jei broda} equivalent to {lo ni lodu'u broda cu fatci}?  Would
{ka} be more appropriate?

Make that "jetnu" instead of "fatci", and you are closer, but there are
some distinctions because place structures don't quite match. jei has
the epistemology place of jetnu at the outer level, and does not need
the scale place of "ni".

>(Gismu queries here:  what's the relation of {carmi} and {denmi} to
>{mutce}?

Not much.

> Do they just have an indication of what kind of property is
>expected?  Why does {mutce} have a place for "in direction", while,
>e.g., {milxe} doesn't?  Doesn't the property (the x2 place) imply the
>direction?)

You need to see how the gismu are grouped semantically - this is
sometimes shown by the cross-references on the right, but they are not
all that systematic or clear about the relationship, i admit.

milxe, mutce, and traji are related, and deal with scales.  If you think
of one of those bidirectional scales, we have na'e'/no'e/to'e to
position on the scale.  For unidirectional scales, or close-ended
scales, milxe is akin to nutli and na'e, and is more or less neutral and
thus not towards any direction.  mutce is towards an extreme, and if
there is more than one extreme direction, you need to know which one.

carmi and denmi are contrasting in meaning - total amount vs.
concentration, and are particular kinds of scales, so you can have mutce
carmi and milxe carmi, mutce denmi, milxe denmi, etc.

>It would be useful if in lojban one could say:
>
>X is in the 2nd of 7 evenly spaced fuzzy sets along the truth vector
>birdish.  If such sets were not evenly spaced, there could be a facility
>for specifying the exact position of the 1.00 truth position of each
>fuzzy set.

Use jei and decimals in base 7.  Sounds like the truth value is .2 base 7
For irregular spacings, you need to define the scale, which sounds like an
ordered set of values.

>But the assigning of numbers is totally arbitrary, isn't it?  Why would
>an ostrich get a .652 instead of a .7513 in the bird scale?  Saying that
>it is .652true bird makes as much (or as little) sense as saying that it
>is .7513true bird.  There is nothing wrong with assigning to it that or
>any other number for a particular computer application, but it wouldn't
>make any sense to talk like that, especially because we would never
>reach an agreement on how much a bird an ostrich really is.  One thing
>is to say that an ostrich is more birdish than a bat, with which
>probably most people will agree, but a different thing is to actually
>assign them numbers.

Again, use the indefinite numbers, which allows for at least 7 sets
including endpoints, which could be added to by using multiple digits:

pino < piso'u < piso'uso'e < piso'o < piso'oso'e < piso'i < piso'e <
piso'a < piro

gives 9 sets from .0 to 1.0

>Why not:
>
>traji cipni
>mutce cipni
>milxe cipni
>tolmutce cipni
>na'e cipni

Some things wrong with this scale.  I'm not sure what the difference is
between milxe and tolmutce, for one.  And you are missing no'e cipni,
which should be somewhere above na'e cipni but not sure where (and no'e
mutce, which would be somewhere between mutce and tolmutce).


>Since we don't have much experience of such phenomena, I'm rather short
>of reliable intuitions on this.  But I think it might show that in
>principle the category Bird does have a defining feature, namely
>possession of bird genes, and therefore has gradient membership.

Genetics is not the defining characteristic of a prototype for most
people, though it might be for the scientificially-minded.  And even
then there is some question.  What are the relevant "bird genes"?  Is
"lo [dinosaur] cu cipni" true?

Is "lo [transsexual woman] cu ninmu" true?  Genetically a female
chimpanzee is about as much like a typical human female (no more than 3%
difference, I hear) as a transsexual (one completely different
chromosome out of 46 sounds like at least a 2% difference).

When you get to plants with diploids and the like, the variations in
numbers of genes and chromosomes in one "type" is so wide that it would
be hard to characterize "typical" genes.  Indeed this may be true with
birds, for all I know - there may be some bird closer in genetics to a
human than to some other extreme in the order of birds.

lojbab