Re: TECH: fuzzy logic

[Logical Language Group <lojbab@ACCESS.DIGEX.NET>]

>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.

You have presented the strongest case for And's proposal yet, though not
to my mind convincing.

If you want to attach numbers to a scale, then je'a is +1 and to'e is -1
with na'e a  non-specific negative, and no'e a fuzzy near-0 value.  We
do not have a non-specific positive in na'e, though na'ena'e would serve.
(not ungood = mildly good, is an example in English translation).

BUT na'e is not solely used for scales on brivla, so we have to be careful
about adding to the set of scalar variables.  Otherwise we will get something
or another that will use And's proposal and have to be interepreted
isiomatically just as you fear as the case for NAhE xi quantifier.  So you
buy nothing.


Thus it can be seen 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.

is not strictoly an accurate statement. NAhE has more function than as a
converter from true/false selbri into scalar selbri, since it works on
non selbri.

But this alos points to a flaw.  because the result of NAhE is a scalar selbri
WHICH IS ALSO A TRUE/FALSE selbri, and your statement provides an implication
that the result of NAhe is NOT a true/false dichotomy, but a fuzzy one in
some general sense. It is, as you describe it, scalar, which is not the same
as "fuzzy".

I don't think that NAhE necessarily has any truth functional import at all,
though in some cases you might label that it is so by mal-idiomatic usage.
In other words, it changes the meaning of a selbri, and thus perhaps its
truth value, just as tanru modifiaction changes the meaning of a selbri.
Unlike tanru, which are complete open ended, NAhE modified the meaning of
theselbri (or selbri unit, BTW) along a scale, though the nature of that
scale is contextual (and hence again by your standard mal-idiomatic).
As such, one can see that NAhe is also supplemented by the tanru modifiers
"milxe" and "mutce" and "traji" when used in a selbri context, and these
then correspond to the subdivisions of scalar positives.    Mingling tanru
formulations with the scalar negation formulations has NOT been an issue
because I have always viewed NAhE as a tanru operator in a selbri.  It
is as described above somewhat loose in meaning, and the grammar of NAhE
is functionally similar to that of any other tanru modifier.  The main reason
that NAhE has been lexicalized as a cmavo is that natural languages do so
and commingle na'e with na in usage.  In addition, by giving it a distinct
grammar, we remove NAhE itself from being modified by other tanru elements.
It is thus a  degenerate tanru component.

>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.

More than that, it is a change in the definition, from strogly positive
(to'eto'e) to anywhere along the positive axis (na'ena'e).  Actually I
think it strong to label je'a as "to'eto'e", it is strongly positive
on the scale but I am not sure I would insist that it be extreme.  Hmm but then
I am not sure that I insist that to'e be at the extreme either.  In other
words "je'a xamgu" is not intended to bethe best thing in the universe,
nor "to'e xamgu" the worst, but neither would they cover "mildly good" and
"mildly bad" either.

>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.

Jorge has used combinations like na'ena'e etc for other points on the scale,
I think.

>Goran has
>raised the question, what do the rest of the NAhE_xiny mean.

That is a problem with any solution.  What does it mean to have a truth value
greater than 1, or a negative truth value, or an immaginary one, or a
matrix in the subscript?  But that same question can be raised with And's
solution - what would xVV-minus-five mean, or xVV-three-pi-i.  The MeX
grammar makes it easy to generate nonsense.

>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.


That is fine for mathematics, but Lojban is not limited to mathematical
usages, and indeed one should not assume a mathematical definition to any
Lojban usage outside the MEX subgrammar (not sure you can always do so within
 MEX either, of course, but it is more likely there %^)
Subscript as a general orthographic convention merely denotes some kind of
susidiary modification, written small and somewhat below-following on the line.
Lojban probably doesn;t even insist that they be subscripted as opposed to
superscripted.  I can envision footnotes being labelled with subscripts,
though that would clash with all the other conventions for use of subscripts,
so people would probably use something else.

>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.

That is probably true, but I am wary.  I think that je'a melbi is a totally
new selbri, distinct in meaning from melbi, though the meaning is derived
from that of melbi.  So the logical implication "da je'a melbi" ->
"da melbi" is not one I want to insist upon, because je'a deals with natural
semantics and not some kind of mathematical semantics.

>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.

Which is a problems with the scalars as well, because a value of "ny"
on melbi shopuld NOT mean "ugly" but no'e melbi, which is more like
"plain".  Some selbri scale between 0 and 1, and some scale between +1 and
-1.  And we have no theorit of semantics that even attempts to cover this.

>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.

The only way you can call xVV-zero something other than an idiom of this sort
is by drawing fine lines as to what constitutes an idiom.  xVV-zero and
xi-zero and no'e applied to melbi mean exactly the same thing about "da".

>Futrthermore, a subscript on je'a would normally be expected to
>describe some member of a set of je'as.

Only to someone stuck in a mathematical frame of mind.  But the analogy works.
je'a xi-value gives one of an infinite set of je'as that correspond to the
infinite scalar values that one might wish to assign along the 0-1 scalar
truth/applicability range.

>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

But if you insist on this then, any MEX use of "xi" must also be
"backcounting", which is NOT the way mathematicians use subscripts.
The grammar of XI is unambiguous  - the semantics of XI is, like most of
Lojban's semantics, not well defined.  All that you can associate with XI
semantics as a usiversal, is what can be inferred from the grammar - it
associates a quantifier with a grmmatical construct.  It is semantic
inference that determines what you are supposed to do with that number
applied to the construct - backcount (ri), switch contexts (tense/modals)
or perhaps what is proposed in this convention.

>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.

So we want a fuzzy value on idiomaticity??? %^)

There are lots of plausible meanings that one migtht come up with.  The
purpose of a convention is to select one such possibility as the norm.
There are many many many conventions embedded in Lojbanand have
historically been embedded in Loglan.  It has NOT been the case that JCB
has tried to make conventions apply universally - indeed he is rather more
uncontroleed than we are in the use of them.

To give one example that parallels in English, "xy" can mean the letter
X, usable in acronyms and spelling.  It can be used as a pro-sumti, in which
 case it is NOT standing for a sound.  It can also be used in Mex as a variable
name (not unlike a pro-sumti, but constrained by context to certain values)
or it can be used as a constant, such as in the subscript of another
MEX label.  These various usages certainly seem to be idioms, by your
definition, as is the one that makes "x" in mathematics more likely to be
a variable, but "n"" to be a constant.

>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.

Reading this makes me feel real weird.  There is this grammar change
proposal, which you are discussing the pros and cons of, and a countering
semantics convention proposal, which you have been mostly discussing the
cons of, yet you are not discussing any "grammar changes".  I feel that
I must call to your attention that to accept this discussion as a non-grammar-
change discussion is a convention, one I am willing to adopt since you have
been reasonable about introducing it, but without that disclaimer that you
just made, your message would be indistinguishable from any other posting
reagrding the grammar change proposal.

>Once again, I am not arguing against changing the grammar to express
>fuzzy logic

I never would have assumed you as being against a grammar change - rather
the opposite.

>I am arguing against the current policy of freezing the
>machine grammar

To be against freezing the machine grammar MEANS to be in favor of grammar
changes.  It goes against the unanimously voted wishes of the LLG voting
membership (which constitutes A form of permanent democratic committee as it
were) that the grammar of the language should be frozen.

>I am arguing for
>elegant solutions arrived at by prolonged discussion by the community
>and by committee.

So how do you express fuzzy logic prior to a committe decision?  If it needs
to be in the language in order for the language to be complete, then it needs
to be in the language on day 1.  If it does not need to be in the
language on day 1, it is a convenience and not a necessity.  Since we will
not know all of the potential necessities that science might discover
are endemic to human language, then committe deliberations will never end
and there wil never be a Loglan(/Lojban).

Elegance is a convenience, not to mention a subjective value.  It is not
a necessity for the language.  There is no evidence that fuzzy logic
is a part of human language to any degree more than it is part of Loglan/Lojban
with or without the proposed convention.  The convention wouold give us MORE
 apparatus for discussing fuzzy logic than any natlang has to my knowledge,
and hence is not a necessity.  The xVV proposal would also give us more
capabilkity than any natlang has, and hence is not a necessity.
WE ARE *NOT* trying toIMPROVE upon human language,  We are trying to MODEL
it, to create something that is sufficient to handle all of its needs.  The
task we have set before us is already hard enough WITHOUT trying to do
better than a million years of evolution have done.  (Some might argue that
the addition of predicate logic to the lanaguage inherently makes the language
 impossible as a model of a human language, but that is a big part of what the
Loglan experiment is all about.)

>   "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.

You can see in this wording that NAhE changes the meaning of the selbri,
and is not a statement about the truth value.


>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?

I would use "indeed true" rather than "certainly true", but the differenceis
probably subtle.  In the case of jetnu, it is  almost certain that "je'a"
makes it an absolute claim of truth, or at least so strog of one that I
cannot conceive of a countere example.  It DOES NOT (barring adoption
of a XI convention or some other convention merely claim that the truth
value is between no'e and absolute truth (I am not sure what to make of a
recurive defintion that je'a means that the truth value is between no'e
and je'a - you are assuming one meaning of je'a - the official one, while
arguing that a deifnition exists that contradicts that one).  It definitely
 excludes anything "to the right of" no'e, so "to'e" is not part of the
 definition.
I'll stop here - I can't keep the recursive definition from tangling my mind.

>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.

Actually, I think that is what the idiom is trying to say. Because  no'e
is "xino" according to the convention, I think.  I also think it is xVV-no
according to And's proposal.

But I think I see what you are trying to say, and this is why your argument is
fairly strong against je'axi in particular, because  it becomes the case that
je'axi-value, where value is anything other than "1" is a claim that differs
from "je'a" by itself and contradicts it.  It thus seems like a violation
of metaphysical parsimony in Lojban in that the omission of a construct
does not allow the assumption of any value in the possible range.  Instead,
je'a ends up being a special case abrreviation of je'axi-value, and that is
not something we do very often in Lojban (though we do so in the case of
sexipa, I think, under current convention).

>But we can't know what
>the idiom is supposed to say from the dictionary.

The dictionary defines words (unless I put phrases in).  The interpretation
ofsets of words is always weakly idiomatic, and often strongly so, by
your definition.  What does "pano" mean, and how can you predict it
from the dictionary?  You need the standard convention of mathematics that
a 2 digit number means that youy multiply the first digit by the (unstated)
base and add the 2nd digit.  Then you need the standard convention that we
are using base 10 (or are we using base 2 - clearly it makes a difference -
and Lojban does NOT make it determinable in any exact sense).

But what about cixy - is that 3 times the base plus X.  No - standard
mathematics has NO qualms about swtiching conventions (idioms, as it were)
when it is convenient.

And MEX is a large subset of the Lojban grammar, and we are not trying to
reform or regularize what is said in MEX.  So thus an area of the languagee
that seems fairly important to you, by your invocation of mathematical
definitions of subscripts, is itself riddled by idioms.  Indeed the one
you cited is an idiom,becasue we do not know whether xyxipano should be
interpreted using base 3 or base 10 or some other base, making  it an idiom
that it is not identical in meaning to xyxici.

Do you see that this is the logical exptrapolation of your prejudice against
"idiom" - that among other things the entire edifice of mathematics becomes
unspeakable (as well as unspeakably idiomatic %^).

>>But subscripts have no COMMON "literal meaning" in such a context - all
>--More--
>>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.

I'm not sure.  In any event, if the set of points being subscripted is the
complete set of points along the continuum, then I think this interpretation
of subscript would fit your mathematical one.

>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 sentenc
>>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.

I havbe considerable evidence that JCB would not consider that our language
 sense in any way abides by the rules of logic %^)

By you reasoning, there can be NO phrases at all in the language.  Because
how can you predict what "roda" means from the dictionary definition and
the grammar.  You cannot from the latter - the grammar merely says that the
combined structure is legal and has the same grammar as KOhA by itself.
You can only make a prediction of meaning by observing the frequent patterns
pada reda cida, and assuming that the whole set works the same.  But then
you run into noda, and you find thatthe semantics that results is NOT the same,
and is NOT predictable from the pattern.  noda denies a value rather than
claims one or more.  That the idioms of logic are NOT inherently obvious
to human minds should be evident from the conditional in any language other
than Loglan/Lojban - no one other than someone trained in logic would devise
the truth consditions that logicians attroibute to the conditional.

>The expression (rosu'o) to mean ro with existential import is
>another idiom that gives me a sapir-whorf perfect 10 headache.

Why does this bother you and not "su'ore"?  If you think the latter is too
obvious, please explain "su'oro".  ALL numbers are conventions, and since
I have a 3rd and a 4th grader right now, this fact is brought home to me on
a daily homework basis %^)

>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.

If mathematics assumes a different convention than pure logic, which
assumes a different convention than common natural language, on what basis
do we decide.  In the past, we have simply tried to put all 3 conventions
into the language, putting the MEX version ONLY in the MEX grammar, and
trying to come up wit two distinct constructs for the logical andnaturalistic
semantics (e.g. ro da poi broda - which should have a logical convention
and ro broda - which should follow naturalistic ones even if they are
"illogical")

>With pc alone making the decision
>the tendency might be to tip to the logicians viewpoint.

No one has assumed that "loglan" meant "mathematical language".   Not a few
have assumed that it meant "logical language" in the sense that all
elements of the language had to abide by the supposedly unambiguous
conventions of logic - which pc has now made clear are not necessarily so
unambiguous or immutable.

The area where pc has the final say is specific to those areas of the language
that attempt to model predicate logic and tense logic, and we might extend
this to fuzzy logic if he were to claim such authority.  He is like me
"first among equals" in trying to interpret "gerku zdani".

> 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 langua
>>via such structures as XI+quantifier that when we do figure out what is neede
>>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.

Well, I have faith that the language can express ANYTHING without any change.
The only question is whether it can do so succinctly "enough" where the
latter is a very subjective decision.

I have no problems with stating abreast of current developements, but
this will be an individual thing (or perhaps a community-as-a-whole thing)
rather than a formal group thing, becasue among other things there is no
way a formal group can stay abreast of everything in all relvant fields.

Indeed one of the reasons I want/insist/demand that the language get out
of prescriptive committee deciding mode is that the people who do the
deciding and designing end up by that fact being cut offo from the community
if those  using the language naturally.  Even conducting these discussions in
Lojban would not remedythis, because the committee deliberations themselves
would have convention-determining import, and committee members spend too
much time thinking as language designed\rs and not language users.  And this
has afflicted Loglan/Lojban for far too long.

Fuzzy logic is a rapidly evolving very new field and I am quite sure that
what is understood about fuzzy logic in 10 years will be unrecognziable
today.  We cannot hit a rapidly movcing target, and that target will no
doubt like the rest of logic and matematics consist of idiomatic and
highly unnaturalistic  conventions that no one outside the fields could
hipe to understand.  I don't intend to try to do so.

Lest this seem a peculiar attitude, let me note that we are also not
trying to follwo the ever changing currents of linguistic theory.
The time since Loglan got started in 1954 has seen so many new linguistics
theories rise and fal, and the mainstream one of Chomsky has dipped and turned
and modified itself and its definitions like a roller coaster.  A language
that had attemtped to model any Chomskyan theory prior to 1980 or so would
be hopelessly obsilete now - NOT "evolvable", but obsolete as in throw it
out and start over again, because Chomsky has changed the basic
deifnitions that the idioms of linguistic theory are bulit out of, so that
the same statements mean something different and sometimes opposite from
what they once meant, at least the way people commonly understood what he used
 to say.

>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.

Not sure your implication.  Shouls we make OPrah and O.J into Lojban
operators because a lot of people seem to pay attention to them? %^)

Fuzzy logic is a new field.  So is chaos theory.  Do we have an advocate
for making sure that chaos mathematics is well represented in Lojban as well.
Do we rehabilitate the 4th tense because relativistic tense is so important
to a few areas of science?

We don't knwo what will be important, and trying to predict is a wasteof time.
No one has been even remotely accuirate in predictions in any field of
science over a period of more than a generation in the last century, and some
fields like computert science and AI and medicine have been unpredicatable
for even 5 ytears at a time.

lojbab