Message-Id: <m0jkHV0-0001ZOC@snark.thyrsus.com>
From: snark!cowan
Apparently-From: snark!cowan
Subject: Re: MEX comments
To: cbmvax!uunet!math.ucla.edu!jimc
Date: Mon, 3 Jun 91 11:05:59 EDT
In-Reply-To: <9105311612.AA23157@luna.math.ucla.edu>; from "math.ucla.edu!jimc" at May 31, 91 9:12 am
Status: RO

la djim. kartr. cusku di'e:
> John Cowan's MEX posting didn't get much comment recently.  I had very
> few nits to pick with it, except for one example (most likely a typo) 
> where something of the form "re ratcu" seemed to be interpreted as a
> sumti (should be "le re ratcu" (the two rats) or "re le ratcu" (two of
> the rats)).  I would say that it is quite serviceable for Lojban.

"re ratcu" is a good sumti, and means the same as "re lo ratcu" (now that
you know what "lo" means :-)).  Old Loglanists may remember this as the
"se sorme" concept ("ze mensi" in Lojban).

The syntax here is "quantifier [quantifier] selbri /KU#/ [relative-clauses]";
two quantifiers are used to handle things like "3 out of 5 dentists surveyed..."

> I will leave it to others to wrangle over RPN vs. infix notation, and
> whether it's tolerable to demand exactly two operands per operator
> (with fancy escape kludges).  Gua!spi uses the base grammar, with no
> special MEX syntax.  Because -gua!spi segregates phrase-grouping
> grammar from everything else, it can handle intermixed RPN, forward
> Polish, and infix, with any number of operands, with no markings and no
> parentheses.  Actually the mandatory phrase specifications imported
> from the grammar are equivalent to full explicit parenthesization. 

This solution works for -gua!spi, but requires too many cmavo to be tolerable
for Lojban.  Full-parenthesis was tried, and in fact there were two different
"(" cmavo (and corresponding ")" cmavo), one for "'(' apparent in symbolic
notation" and the other for "'(' added to keep parser happy".  It was ugh.

> There are a few points that I would like to see treated in more detail.
> First, what does "the number two" mean?

Numbers are primitive.  You are free to identify "li re" with "lo'i remei"
(the number two with the set of all pairs) a la Cantor, but the language
doesn't force this definition down your throat.  Remember that von Neumann
had a different definition of numbers, where 0 = {}, 1 = {{},{}}, 2 =
{{{}, {}}, {}}, etc.; this definition is just as satisfactory for 
foundations-of-mathematics work.

> Second, what is the most 
> convenient way to assert that the measure of something is given by some
> MEX?  In -gua!spi, all the math operators mean "x1 is in the
> equivalence class resulting from doing (math) on arguments x2...", so
> predication is trivial, and the answer as a number can be recovered
> with [the -gua!spi equivalent of] lo'i "set of referents fitting
> s-bridi".

This is the place structure imposed on operators by "nu'a".  You can do
MEX in -gua!spi style:

	lo'i vomei nu'a su'i lo'i remei lo'i remei
	the-set-of foursomes is-the-sum-of the-set-of twosomes and-the-set-of
		twosomes
	4 = 2 + 2

> Third, dimensioned quantities are common; how are they to be
> defined and expressed?  In -gua!spi: "x1 is in the equiv class of things
> which are x2 meters in size", a normal gismu.

Same here:  "x1 is x2 meters in length".

-- 
cowan@snark.thyrsus.com		...!uunet!cbmvax!snark!cowan
		e'osai ko sarji la lojban