Message-Id: <199603031447.JAA14257@locke.ccil.org>
Date:         Sun, 3 Mar 1996 14:06:58 +0000
Reply-To: ucleaar <ucleaar@UCL.AC.UK>
Sender: Lojban list <LOJBAN@CUVMB.BITNET>
From: ucleaar <ucleaar@UCL.AC.UK>
Subject:      Re: TECH: fuzzy: <xoi> vs. <fihuhi>
To: John Cowan <cowan@LOCKE.CCIL.ORG>
Content-Length: 5216

> 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 &.

{xoi} is effectively equivalent to John's {jaa xi}. {xio}, for fuzzy
set membership, would have been equivalent to {jea xi}, but I have
decided not to argue for this any longer, because NAhE is seeming a bit
messy and confusing and confounded and logically marginal and not wholly
to be approved of.

> 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>

John has corrected this to {jaa xi}, from the for him erroneous {jea xi}.
If John's proposal is adopted, then {jaa} can mean "is true to some
degree or other", with the actuall degree specified by the xi subscript,
and an absent xi subscript receiving default interpretation of "ro".

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

What place structure do you propose for them?

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

{ni ka} is already meaningful and grammatical - to the extent that {ni}
makes any sense, of course. It means "is the amount by which something
is the property of".

> >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.

I understand this. But a solution with a MOI saves only a very few more
syllables than a solution with a lujvo. Specifically, MOI saves (1) a
{li}, (2) the difference in length between the MOI and the lujvo, and
(3) sometimes a {ku} or {boi} at the end of the {li} sumti.

I agree with the principle that what we wish often to express should be
expressible with corresponding brevity. But it's very hard to get the
language to respect this principle unless it was actually designed with
an ongoing change process whereby forms with higher frequency than their
length warrants get given new shorter forms and forms with lower
frequency than their length warrants get given new longer forms and lose
their original short forms.

> >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.

We may need more than a lujvo here, but if so it's because we need more than
a selbri. The lujvo I have in mind would simply replace {pa fiui} by
{fuz zei fuz (be) li pa}, where {fuz zei fuz} is the lujvo.

> Logic is at the heart of lojban, and we need a fuzzifier cmavo to have a
> complete logic.

If you can tell me whereabouts the fuzzifier gets added to trad predicate
logic, then I can try to tell you whether there is an obvious actual or
potential solution within lojban. If the fuzzifier is a unary connective,
like NOT ("!"/"-"/"~"), then {jaa xi} now serves that function.

> 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.

You're right that cmavo in the selmao XOI take num expressions and yield
a NA, but cmavo in the selmao MOI take a num expression and yield a selbri.
I.e. MOI yields predicates.

> 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.

NA and selbri have different syntax and different semantics - the
difference is that between predicates and connectives.

As I said earlier, I think the best way to reach the light on this matter
is for you to forget lojban syntax for a moment and give us an
(approximate) idea of what your extended predicate logic looks like.

I'm not trying to have a go at you; I'm trying to descry what it is
that you crave.

In my (naive) "fuzzified" pred logic, NOT is replaced by something
equivalent to {xoi}/{jaa xi} - a fractional negator.

coo, mie and