Re: TECH: fuzzy logic

[Gerald Koenig <jlk@NETCOM.COM>]

Lojbab:
>
>je'a xi pimu broda
>truly-sub-.5 broda is the dictionary translation of that Lojban.

djer:  There's more to it than that. NAhE such as je'a are operator
cmavo which convert a true/false binary selbri into a scalar selbri and
assign an ordered position on a scale defined by the selbri. The order
is je'a>no'e>na'e>to'e.  I use the word "scale" in the dictionary
sense:  "a system of grouping or classifying in a series of steps or
degrees according to a standard of relative size, amount, rank, etc: A
wage _scale_."

And has made the point that je'a has to mean "is to some degree .." if
we are to use it as suggested. And that is a new idiomatic definition
of je'a. At present we can only use the ranges (or are they points,
thus not fuzzy?) defined by je'a, no'e, na'e and to'e.  Goran has
raised the question, what do the rest of the NAhE_xiny mean.

Subscripts are used in mathematics to indicate particular members of a
class, such as the points on a line which may be designated X1, X2, X3,
etc.  The "X" part of the symbols asserts that X_n is indeed a member of
the line-set.  The _n designates a particular member.

Now when we consider je'a, which asserts that some predicate has
(scalar) truth, i.e. "da je'a melbi" ,[there exists something x which
is (truly,scalar) beautiful], we expect that da will always be in the
class, melbi.  However, when we consider the subscripted je'a---
je'a_xiny, and we let the variable ny approach 0, we find that we have
moved to the other end of the scale, and now we are talking about
something ugly.  A subscript value has converted something beautiful
into something ugly.  We don't expect this. We expect that da will
always be something beautiful, as asserted in the original sentence.
So we have created an idiom. Because an idiom creates a new meaning
different from what one would expect from the meaning of the component
words.

Futrthermore, a subscript on je'a would normally be expected to
describe some member of a set of je'as.  We have a similar case
documented in the grammar where back-counting sumti is accomplished
with "ru_xiny." Applying a similar convention to je'a means that
je'a_xiny refers to some previously used je'a in the sentence or
discourse.  Here is an example of such a usage:

i.le do du'u je'a jetnu ije
le mi du'u je'a jetnu ije
le je'axipa du le je'a xire

Your predications are (scalar fuzzy) true and
my predications are (scalar fuzzy) true and
the first scalar fuzziness is equal to the second scalar fuzziness.

My point is that the construct "je'a_xiny" has the above plausible
interpretation, John's proposal supplies another plausible
interpretation which I believe is more idiomatic, and requires more
explication to make any sense of. My interpretion is in no sense a
proposal and I am still on strike about discussing any grammar changes
in the absence of a permanent functioning democratic structure for
grammar change. I'm just talking about this particular issue as an
example of the problems that will arise with no change for 5 years.

Once again, I am not arguing against changing the grammar to express
fuzzy logic.  I am arguing against the current policy of freezing the
machine grammar and bringing in fuzzy logic through the back door of
idiom which I find indistinguishable from slang. I am arguing for
elegant solutions arrived at by prolonged discussion by the community
and by committee.

Here are some quotes from the ftp site for background to this
discussion:
__________________

"scalar negation ("na'e-word brivla"):

   "na" deals primarily with the truth or falsity of a bridi.  Lojban also
   supports a separate form of negation, called contrary or scalar negation.
   A scalar negation attaches tightly to the next brivla of the selbri, modi-
   fying the meaning of the word on some scale.  Scalar negation structures
   may appear anywhere where 'brivla' or 'selbri' is allowed.  Scalar negation
   words include "na'e" (other-than), "to'e" (absolute opposite-of), and
   "no'e" (neutral on the scale); "je'a" is a strong positive scale assertion,
   translating roughly as "certainly" or "indeed":

    |----------- POSITIVE ------------|------------ NEGATIVE -----------|
   je'a                              no'e             na'e             to'e

   Examples:
      mi [cu] melbi [vau]
      --      =====
      I am beautiful.

      mi [cu] na'e melbi [vau]
      --      ==========
      I am other-than beautiful.

      mi [cu] to'e melbi [vau]
      --      ==========
      I am ugly/opposite-of-beautiful.

      mi [cu] no'e melbi [vau]
      --      ==========
      I am plain/neutral on the beauty-ugliness scale.

      mi [cu] je'a melbi [vau]
      --      ==========
      I am indeed beautiful."
_____________

djer:
A dictionary translation of "je'a jetnu"  would be "certainly true" but in
a relative sense. It is not an absolute claim for truth as is seen in a
binary truth table. It just means that the truth value is between je'a
and no'e, and closer to je'a. Or does it mean that the truth value is
anywhere left of to'e? Or very close to je'a but not touching it?

Right there is a problem for this idiom because "mi je'a
xipinonononopa" melbi" would mean I was very close to no'e melbi, (or
is it to'e melbi as above?)  the next value on the scale, and I don't
think this is what the idiom is trying to say. But we can't know what
the idiom is supposed to say from the dictionary.

lojbab:

>
>But subscripts have no COMMON "literal meaning" in such a context - all
>we have is some suggestion of a 'different variety of je'a', since that is
>what subscripts usually mean in variable contexts..

However they have been used, they have not been used or defined as an
operator to slice up a continuum. Je'a alone does not do this. Je'a is
merely a vague range on the continuum.  That is why the proposed usage
is idiomatic.  You have to know the idiom up front to get the meaning,
it could not be inferred from the atomic meaning of the words "je'a"
and "xiny" where xi means subscript and ny are numbers. Possible
exception would be the use of "puxipa" and "puxire" to refer to points
in the past, earlier or later, the usage was never clarified.  I
haven't seen "vaxire" used, but why not if this is the way we want to go
to identify points on a continuum?

djer:
>
>>I am trying to exclude idiomatic expressions
>>from lojban, especially in the quantifier area.
>
>>I don't see "ro" with or without existential import as meeting the
>>definition of an idiom.

lojbab>
>Well, since Lojban words are supposed to have exactly one literal definition
>and the two versions I have seen are contradictory as to requirig
>existence, then there will be instances where someone using "ro - but not
>existent" or rather assuming that meaning, will use ro such that the
>"literal meaning" is not preserved, and indeed the truth-value of the sentence
>is not preserved.

djer
I agree with this entirely.  What I am trying to say is simply that
whether the word "ro" is defined to have existential import or not is an
issue of definition of a single word, as opposed to strings of words
called idioms. When strings of words acquire special meanings not
understandable to language outsiders, that is an idiom.  Our innate
language sense fails to work on these things called idioms. They are not
logical.  The expression (rosu'o) to mean ro with existential import is
another idiom that gives me a sapir-whorf perfect 10 headache.

I haven't fully digested pc's posts on the subject and don't have a
position as to how the problem should be solved. I just felt that we
shouldn't ignore the position of mathematicians. It's another argument
for better language change process. With pc alone making the decision
the tendency might be to tip to the logicians viewpoint. Although if one
man has to make the decision, he's the best pe'i.

>
>>I believe that in the
>>quantifier area words should not differ from their literal meaning,
>
>So what is the literal meaning of "ro"?  That is one argument.
>
>In the case of je'a xi pimu, the quantifier ".5" has the meaning ".5", and
>I don;t see any implication that it is any other meaning.

It is not only a quantifier.  It is a kind of name.
It could easily have another meaning such as the one in my example
above. The question is, .5 of what, or what is the number naming or
measuring.

>
>Indeed, one might argue that use of quantifier subscripts in regular math
>e.g. xsub1 xub2 violates the literal meaning of quantifiers far more, since
>there is no requirement in mathematics that the ordinal properties of the
>integers are important or even apply to such subscripts - the numbers are
>merely used to show that the two x's are different.

djer:
yes, just a set of names, not a quantifier.


lojbab:
>
>All this is NOT to say that I am particularly fond of the xi-quantifier
>version of fuzzy logic.  Indeed, I suspect I dislike it and am not sure
>what it solves (surely not the whole problem of fuzzy logic) that warrants us
 defining the convention at this point.  I think that the needs of fuzzy logic
>in terms of Lojban expression is a problem that need not be solved now - we
>need only to have confidence that there is enough power in the current language
>via such structures as XI+quantifier that when we do figure out what is needed,
>we can do so with no grammar changes and perhaps even no additional cmavo

djer:
Well, this is where we differ. I think we should stay abreast of current
developments, and that it probably will require some grammar change. I
agree that we should have faith that the language can express a great
deal without any change.

lojbab:
>(there may be Zipfean arguments are a cmavo to shorten an unwieldy compound
 structure, but that means that we need to see the structure being used or
 useful.
>I remain unconvinced that there will be sufficient use of fuzzy logic in Lojban
>to warraant anything shorter than the 15 syllable expressions that Steven fears
>even though I personally am sure that the language won't require 15 syllables
 to express what is needed.
>
>>For example, (if I remember this right,
>>and I don't think I do), "qu'est ce que c'est un horloge"  means in
>>french, "what is a clock?' but if you try to translate it word for word
>>--More--
>>it is doesn't compute.
>
>Meaning that it is ungrammatical, or that it means something different from
>what you expect such as "raining cats and dogs" which is what I think of as
>an idiom, or "the paint ran" (on what limbs?) or "do your hair"?
>
>lojbab

>

djer:
It is grammatical in the French language. It not something different
from what you would expect, it just doesn't make sense at all unless
perceived as a whole. The meanings of the individual words do not
combine to form a meaningful expression. Therefore, you have to learn
the whole expression as a single entity. In our case of "je'a xiny" we
have to define the _pair_ of words with a meaning that cannot be
deduced from their usual individual meanings. As I outlined with my
example, there is more than one thing "je'a xiny" can denote, some
of them are close to the atomic meaning of the words, some are not. Far
better to define a new cmavo with a single meaning that to mess around
with these ambiguous compounds. At least if you think fuzzy logic is
important. I noticed at the UCLA bookstore that there were too many
people hanging out around the section on fuzzy logic for me to get
a look at the offerings.

 djer