From cowan  Sat Mar  6 22:57:49 2010
Subject: Re: TECH: lambda and "ka" revisited
To: lojban@cuvmb.cc.columbia.edu (Lojban List)
From: cowan
Date: Wed, 8 Nov 1995 12:25:29 -0500 (EST)
In-Reply-To: <199511081620.LAA29093@locke.ccil.org> from "Chris Bogart" at Nov 8, 95 09:26:37 am
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la kris. ckaji le ka xe'u da cusku di'e kei

> >3)      le ka da de xe'u da gerku de
> 
> How would we use this in a sentence?  The property refers to two entities;
> would it be something like {lei re nanmu cu ckaji leka da de xe'u da pendo
> de}?  I think {lei} must be wrong here because there's only one entity
> (consisting of 2 men); but {le} would be wrong too, because it would be
> decomposable into {le pa nanmu cu ckaji leka da de xe'u da pendo de} and {le
> drata nanmu ...}.

I agree.  But you could use the shadowy "jo'u" (of JOI) which connects
two entities while leaving them two:

	la djan. jo'u la djim. ckaji le ka [xe'u da] bruna [xe'u de]
	John and-jointly Jim have-the-property-of brotherhood

> I don't know about lambda in logical theory but I know how it's used in
> Lisp.  The whole lambda expression, which tells you what it's arguments are
> then what their relationship should be, can be substituted wherever you
> would normally use a named function (i.e. brivla).

Beware!  This confuses general terms (brivla) with the abstract objects
(properties/attributes/relationships) which are based on them.  The
predicate "bruna" is true of something (or rather, ordered pairs of
somethings, namely the brothers of the world); the abstract object
"le ka bruna" is a theoretical construct representing the relationship
between the members of those pairs.  In -gua!spi, the relationship is
identified directly with the set of ordered pairs, but this fails in
general, because sets are equal iff their members are equal, which is
too strong (too weak?) an identity condition for attributes/relations.

Even in (Common) Lisp there is a difference between a mere piece of code
and a functional object based on the code.

> The analogy with Lisp
> would indicate that we could use it this way (brackets [] surround
> lambda-expressions for emphasis and clarification):
> 
>    pa nanmu cu [ka da de xe'u da pendo de kei] le drata nanmu
> 
> which would be equivalent to {pa nanmu cu pendo le drata nanmu} -- but it
> requires that {ka}'s places be defined by the {xe'u} clause.  This is a long
> way of saying the same thing, but it makes a nice formal way to define new
> lujvo:
> 
>    ca'e sezpendo cei [ka da xe'u da pendo da]
> 
> ...or pro-bridi
> 
>    mi do broda cei [ka da de xe'u da de zmadu leka gleki kei] .i do la alis.
> broda .i la alis. la djak. broda .i ...

I almost agree with you (modulo syntax of lambda), but what you say suggests
that there needs to be an explicit "anti-ka" operator that unwraps a property
and makes it a selbri.  (This is not "ckaji", because "ckaji" only tolerates
a one-place abstraction; this is a way of saying "x1, x2, x3 fit into the
property abstraction [whatever]").  I'll mull this over.

> Looking at things this way, then, {le [ka da de xe'u da pendo de]} would be
> identical in meaning to {le pendo}, and {le SE [ka da de xe'u da pendo de]}
> would mean {le SE pendo}, which strongly conflicts with my current
> understanding of how {leka} is used.

Not at all.  Again remember that a function considered as an object isn't
the same as the application of that function.  "le pendo" refers to something
which (in the speaker's estimation) returns T iff passed to the first argument
of the "pendo" recognizer.  "le ka pendo" is that recognizer itself.

> >We can't just have a new variable "xe'u" as a sumti by itself, because
> >the bound variable may need recycling:
> >
> >12)     do ckaji le ka ga xe'u da xirma gi lo xirma cu citka da
> >        You have-as-property the attribute-of
> >                either (you are-a-horse) or (some horse(s) eat you)
> >        You are either a horse or horse-fodder.
> 
> Don't we have the same problem with {ke'a}:
> 
>   la djan. poi ga ke'a xirma gi lo xirma cu citka ke'a
> [or would it be something like:]
>   la djan. poi ga ke'a goi da xirma gi lo xirma cu citka da

That works fine because "poi" is only ever attached to one sumti, so
we only need to be able to refer to that sumti, but potentially "ka"
objects can be 2-place or n-place (though the current language doesn't
seem to have any selbri that naturally demand other than 1-place (ka)
or 0-place (du'u) intensions), so multiple variables are potentially
needed.  Otherwise we could say "le ka xe'u bruna xe'u", where "xe'u"
would be a member of KOhA, and forget the "da" variables.  But that
won't work in general because the selfsame variable may need to appear
in multiple places in the bridi.

> PS how do {nu} and other abstractors fit into this picture?

"nu" and its subtypes are all 0-adic; they refer to specific events in
space-time that {fasnu}.  Likewise "si'o" and "li'i" are 0-adic, because
they refer to mental events that correspond to physical ones through the
perception of a named experiencer/thinker (the x2 of the abstractor).
"jei" is probably 0-adic also, and is related to "du'u", which is now
understood as a subtype of "ka" that is always 0-adic.

I still don't have a good understanding of "ni", and anyone who does is
urged to explain it to me; the discussion in the abstraction paper is
skating on thin ice.

-- 
John Cowan					cowan@ccil.org
		e'osai ko sarji la lojban.