TECH: fuzzy: <xoi> vs. <fihuhi>

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

&:
>Steven appears to be getting excited about {fiui} as a way to do what
>he's been wanting to.

lojbab asked me to explore existing ways to fuzz in lojban, and I am making
a good-faith effort to do this. Besides trying <fihuhi>, (which is an
existing part of lojban in the sense that addition of this cmavo would not
affect the YACC grammer very much), my efforts have included:

1. Exploring the <xoi> and <xio> proposal made by &.

2. Working with the <jeha xi> subscripted formalism suggested by John Cowan
as an alternative to <xoi>. I don't like it, as it is idiomatic under the
current definition of <jeha>

3. coining <kamkuspe> and <kamkantu> for "fuzzy" and "continuous" as
applied to logic and sets.

4. Making a (possibly foolish) suggestion that <nika> might be one way of
making a fuzzy property abstractor.

5. Surveying experts in linguistics who have studied the issue of fuzziness
in non-Western languages.

6. Trying to correct various misunderstandings about fuzzy sets.

>It may well do what he wants, but if so then even
>without {fiui} there have existed ways to do {fiui}'s work. {fiui} is
>in MOI. Every MOI can be translated into a suitable lujvo with an extra
>{li} sumti.

This is understood. I have never said it was *impossible* to invoke
fuzziness in lojban. I have instead asserted that it is rather difficult
and cumbersome to do so. There are two issues: complexity and generality. I
argue that fuzziness should be both very simple to express, and that fuzzy
operators ought to also be very general.

Zipf reported that word frequencies were inversely proportional to number
of syllables. Sapir and Whorf (and before them von Herder and von Humboldt)
hypothesized that speakers of different languages will view the world in
different ways due to the differing structures of their respective
languages. If these observations/hypotheses are correct, then the use of
fuzziness will be impeded if the fuzzy operators are long and complex; the
use of fuzziness may also be impeded if the fuzzy operators are not
generalizable.

Why should we worry about whether fuzzy logic is easily expressed in
lojban? The reason was given by lojbab in his recent post:

>Only in the firm insistance on inclusion of the apparatus of logic does Lojban
>strongly deviate from metaphysical parsimony, because that is the supposed
>basis of the Sapir-Whorf test.  Thus we in theory have a middle ground on all
>issues except one in which we have an extreme ground, and thus we presume that
>strong deviations from norms can be attributed to the extreme logical
>metaphysics.  I myself don't really buy this, but it is an assumption of the
>project, and even I don't feel at liberty to change fundamental design
>assumptions and goals; besides, it serves as a useful basis for making
>decisions - when in doubt, split the difference and be "neutral".

lojban is a logical language. Fuzzy logic is an important generalization of
fuzzy logic. Failure to include operators which would allow elegant,
general means of expressing fuzzy logic would be a serious flaw, making the
language less attractive to potential speakers and possibly culturally
biased. I believe that natlangs may obscure cognitive distortions and
logical fallacies. One type of cognitive distortion, the false dichotomy,
may be clarified through the use of fuzzy logic. Certainly if lojban were
helpful in treating mental disorders, that would be of interest to
Sapir-Whorf testers. I am more optimistic than lojbab about the possibility
of using lojban to test Sapir-Whorf. I have already thought of some
experiments using automatic English->lojban->English translation by which
this could be done. (In months rather than centuries!)

>So, if {fiui} does the trick then there was no need for
>Steven to agitate for it: the resources - i.e. a lujvo scarcely more
>verbose than {fiui} - already existed (potentially) to do the job.

I fail to see how a lujvo alone gives us a general and elegant fuzzifier.
Are you talking about something like lojbab's <sei li {quantifier} ninjetnu
[se'u]>? As you pointed out, this is a metalinguistic construct, has the
wrong semantics, and does not work in subordinate bridi. We need more than
a lujvo here. Logic is at the heart of lojban, and we need a fuzzifier
cmavo to have a complete logic. lojbab claims that lojban isn't very good
at second order predicate logic, thus denying that *all* logical things
must be easily expressible in lojban. I consider this a false analogy.
Fuzzy logic is a lot more basic than second order predicate logic.

My enthusiasm for <fihuhi> was engendered by my apparently mistaken
impression that <fihuhi> did everything <xoi> did. Selmaho of the class MOI
take numerical expressions and yield ordinals. Selmaho of the class XOI
take numerical expressions and yield a NA. What is the implication of this
difference? (Apparently I am misunderstanding something rather major here.)
Is <fihuhi> less general than <xoi>? (For example, will <fihuhi> work in
subordinate selbri>)? Can <fihuhi be applied to bridi linked by <biho>? I
plead ignorance.

cohomihe la kamkuspe 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