Re: fuzzy: use of <ni>, use of <jei>, need for <xoi>

[sbelknap@uic.edu (Steven M. Belknap)]

lojbab-

I am exploring the language for fuzzy operators, ideas, etc. The <fiuhi>
cmavo was a big step forward, hence the diminution of my vociferocity
regarding matters fuzzy. I hope fiuhi makes the cut for the baselined
grammer. There are a few unsettled issues:

1. From my recent post, what about fuzziness *between* semantic constructs?
>I do not see how <fiuhi> can describe fuzziness in the semantic space
>between two constructs; my previous example was paint which was a blend of
>red and yellow. Is there some slick way that I can say:
>
>"The paint is fuzzily 2 of 5, where 0/5 is red and 5/5 is yellow."
>
>Ideas?

2. How can cmavo be made fuzzy?

<da melbi 2/5 xoi be rozgu>

The <xoi> is being applied to the <be> here. This is ungrammatic, I think.
The idea is how can the degree of linkedness be modulated by a fuzzifier?
I'm not suggesting an upheaval here, I am just wondering if there is some
(not necessarily terse) construct which can do this.

3. The issue of the slash cmavo, <fihu>. If I use it to say "2 of 5" as
opposed to 2 divided by 5", it ought to be explicitly stated somewhere in
the refgrammer that the use of the slash cmavo is not restricted. The
definition I have is:

fi'u      PA3      fraction slash                            digit/number:
fraction slash; default "/n" => 1/n, "n/" => n/1, or "/" alone => golden
ratio

I want to avoid the situation where 3/6 is interpreted as "one-half"
instead of as "3 of 6" This would be wrong, as it would lose the
granularity.


>Before you can claim a cultural bias, you must provide a culture that
>actually has such an abstractor.  Fuzzy logic is an artifact that as far
>as I know is more recent than any natural language culture in origin and
>definition.  You have pointed out that there are words in language that
>can be interpreted best using fuzzy logic concepts, but I doubt if there is
>any culture that makes a clear linguistic distinction of the sort you
>seek.
>
>Lojban is not trying to be neutral among all imaginable cultures, just the
>ones that we actually know about %^).

I'm working on it! :-) I don't have any actual reference yet. I really need
to buy a copy of Macawley. I have identified some experts, but haven't read
their stuff, or gotten email back from them yet. I have opinions of native
Chinese speakers, most of whom agree that Mandarin is fuzzier than English.
Interestingly, all of them mentioned "politeness" as an aspect of fuzziness
in Chinese. If someone says:

<That ball is red>

in Mandarin, and you think its actually blue, you might say

<Yes, you are most perceptive to see the slight redness, but I wonder if
you think there might not be a bit of blueness as well.>

Apparently this is a nearly universal feature of conversation in Mandarin,
and some people who are fluent in English and Chinese find English
"impolite" for such "agreeing while disagreeing" conversation. I have
noticed that some Asians with whom I work agree with me in a way that I
know they to some extent disagree. Yin-Yang, Buddhist Wheels, Tao and all
that. Of course, there are other possible aspects about cultural
differences, wish to not offend etc., but fuzziness is apparently a common
way Mandarin speakers deal with differing perceptions, so "everybody can be
right, we're just talking about degrees here" can be invoked.


>BTW, I think I sent you pc's questions/comments on what he is looking for
>from you with regards to definition of what fuzzy logic stuff you want to
>see covered in the language.  Cowan is close to don with the refgrammar,
>and we are shortly going to be unwiling to consider documenting even
>semantic/conventional approaches to fuzzy logic, not to mention new cmavo and
>grammatical constructs.
>
>If you did not get this question, I can resend.

I got it, and I've been thinking about it. I addressed some of my concerns
in the three items above. Some other comments:

>
>Do find out what the fuzzys want.  Possibilities:
>a) fuzzy set theory: xhas property F to degree 0<=n<=1 (presumably a
>         _melipiny_ modifier on the predicate will do this within the present
>        system, though something fancier may be wanted)  Truth values are
>still
>        binary here.

Wouldn't <fiuhi> take care of this? Perhaps I am misunderstanding Cowan's
point.
There should also be a possibility theory formulation of fuzzy sets,
analagous to probability theory formulation of regular sets.

The more important issue is how the #fuzzy AND# and #fuzzy OR# operators
are defined. Perhaps this issue can be left alone for now and shoved into
the MEX, where a lot of stuff is just skeletally outlined, and obviously
will need to be fleshed out later.


>   variant 1 allows modified predicates with different membership curves,
>        but these correspond to the usual adverbs of intensity "very,"
>"slightly --More--
>,"
>        "moderately," and so on, and we have all of those already.
>   the other variants of this seem to be the other positions on the
>        Guttman scale types and all of them seem to be handable with tanru
>or, p erhaps, BAI with numerals


Keep it simple in the default fuzzy grammer:

1. All fuzzy membership curves to be linear in the basic grammer.
2. The apices of the membership triangles have membership value equal to one.
3. The linear membership function of a given set drops to zero at the apex
of its two neighbors.
4. The default Guttman scale for <fiuhi> for utterances where X3 is
unspecified is an interval set, where 0/n is "not at all, to granularity N"
and n/n is "completely, to granularity N"
5. Granularity is explicitly specified. This needs careful thought. Perhaps
the fraction cmavo is not the best operator for talking about "3 of 7".
Perhaps another cmavo is needed for talking about sets. (Could the cardinal
operator, <mei> do this? It would make sense, but the X3 place would
collide with the brivla, no?)
   <0/6 fiuhi> does *not* reduce to <0 fiuhi>
   <3/6 fiuhi> does *not* reduce to <1/2 fiuhi>
   <6/6 fiuhi> does *not* reduce to <1 fiuhi>
This is important, because the speaker chooses the granularity he wants for
a reason.

<mi 1/1 fiuhi gleki kei lo kamkuspe be lojban>

"I am happy to fuzzy extent 1 of 1 regarding fuzziness in lojban"

is different in meaning from

<mi gleki lo kamkuspe be lojban>

"I am happy about fuzziness in lojban."

The fuzzy and the discrete formulations are different because in the former
I am using two fuzzy sets of happiness, the membership function of the 0/1
set tapers to 0 at 1/1 and the mebership function of the 1/1 set tapers to
0 at 0/1; I have then specified the 1/1 fuzzy set as the one I mean. In the
latter, I am using the default logic, which is presumably a discrete
two-valued logic. Actually, perhaps I am wrong about this: Is the default
logic for lojban a binary true/false logic, or is it an unspecified logic,
as in natural language? What does John Cowan think? What would JCB think?

If a speaker wants to use a non-linear membership function, or wants to
specify an apex membership less than zero, or wants to specify a
categorical/nominative fuzzy set, da must explicitly specify what da wants
in long-winded fashion. (Perhaps, in the latter case, through the gismu I
used in my recent post about the X3 place in <fiuhi> for Guttman scales)


>
>b) fuzzy truth values just require some things permitted in the places
>        where truth values go other than T and F, basically [0,1].  This gets
>        dealt with basically as does the corresponding issue for
>probabilities,
>        which is taken care of, isn't it?

No. Granularity means that "fractionals" used in the <fiuhi> do not reduce.
There is a sort of cardinality.


>   strictly this ought to lead to a whole lot of other connectives than
>        the usual ones, but I almost never see any of those other ones talked
>        about and they don't usually make much practical sense, so we'll
>cross
>        that bridge if someone suggests it seriously and demonstrates that
>they
>        know what they are about -- the issue never arose with
>        probabilities either.


Agreed. Leave unspecified for now. This gets complicated, and on some
issues there are several equally plausible implementations.
>
>c) fuzzy arithmetic (often mixed up with one or the other of the above --
>        as values or as measures)  As far as I can see, this just needs a
>piece
>        of mex, roughly on  a par with with the signs (- and, occasionally,
>+)
>        that says "fuzzy number"
>

Agreed. Fuzzy arithmetic ought to be in the mex, but this can be very
simply dealt with by adding a MEX cmavo of some sort, or perhaps by
specifying at the beginning of an utterance "we are using fuzzy numbers
here."


>--More--
>I'm sure there are some mixes of these and maybe some whole new levels of
>fuzziness that I have not kept track of, but I don't see much in the way
>of big changes here -- or of satisfying people who want big changes (We
>tamed the Juggernaut!) with practical and adequate solutions.

See the first three above. There was no Juggernaut; perhaps a more minor
Hindi deity than Krishna, though :-) But I am more optimistic now than I
was before that lojban will have the bare essentials of fuzziness, which is
all that is really necessary.

John may have addressed this: <fiuhi> seems analagous to &'s 1st fuzzy
operator <xoi>. What about his second operator <xiho> which maps to <jea xi
number>?

-Steven



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