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From: Pierre Abbat <phma@phma.optus.nu>
To: lojban@googlegroups.com
Subject: Re: [lojban] New PA-proposal
Date: Thu, 17 Nov 2011 14:09:07 -0500
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On Thursday 17 November 2011 04:40:07 Jakob Nissen wrote:
> Firstly, I'd like to say that neither am I member of the BPFK or
> anything like that, nor do I have insight in the formal grammar of
> Lojban, since I know very little about programming or computer
> language.
> What I do know, though, are the goals and ambitions of the language,
> and to a large extend, what makes good Lojban good and bad Lojban bad.
> Recently, I went through the grammar of the PA-selma'o. and discovered
> to my horror how bad it is now. The day after, I began writing a
> proposal for a new PA-grammar, if not to change anything directly,
> then at least to begin a debate on how to improve this big and broken
> part of cmavo-space.
>
> Klaku=92s number proposal:
> The number system of Lojban simply doesn=92t work. Due to historical
> reason (I=92ve been told), it was decided to let all numbers work the
> same way in the grammar, make no distinction between the selma=92o of
> the different PA, and allow any string of PA to be grammatical.
> Furthermore, today, all numbers are grouped from left to right.
> This is not satisfactory. While it grammatically allows all thinkable
> number constructs, the grammar of the numbers do not in any way
> correspond to the way the numbers actually interact. This means that:
> 1) Strings of PA which make absolutely no sense are grammatical (like
> {li pai ra=92e xo pi pi}) and
> 2) Strings of PA which makes sense are parsed wrongly, leading to
> confusing results (like {li rau su=92o pa}, which is parsed {li <rau
> su=92o> pa}).
> This is bad. In short, the grammar of numbers might be internally
> consistent, but it does not relate to the language, and therefore
> seems like a =93black hole=94, where anything goes in the grammar.
>
> Proposed changes
> Therefore, I propose to rearrange the words in the different PA as
> follows in order to allow for at least a minimum of usable grammar in
> numbers:
> 1)	The new PA1 should contain {xo}, and all members of the current PA1
> and PA2. These constructs are mathematically exact digits, which can
> be combined to form number strings.
> 2)	The new PA2 should contain {du'e, mo'a, rau, ro, so'a, so'e, so'i.
> so'o, so'u and no'o (and {xo=92e}, in the number sense)}. These numbers
> are inexact or subjective, always are their own number string, but can
> appear before or after any number in order to give additional
> information about it.
> 3)	The new PA3 should contain {ce'i, ma'u, me'i, ni'u. za'u, da'a,
> su'e, su'o, ka'o and fi=92u}. These take the next number string or
> PA3+number string (with right-grouping rules) and modify it into a new
> number. The grammar of {fi=92u} is changed: it can now only express 1/n.
> In order to express a/n, use {a pi=92i fi=92u n}. They all should work
> without having a number after them, in that case, the number should be
> a default.

Changing "fi'u" like this breaks existing text. Also, "fi'u", in current=20
usage, is meaningful at the end of a number string; it denotes the golden=
=20
ratio. li fi'u vu'u fi'u fi'u du li pa.

"ce'i" followed by a cardinal number means a transfinite cardinal. How woul=
d=20
you denote transfinite ordinals?

> 4)	The new PA4 should contain {pi=92e and ki=92o}, and can appear at any
> time, in any number string, any amount of times. They sever the number
> string, but {ki=92o} allows two adjectent number strings to =93fuse=94
> together again. When several PA4 are put together, the number string
> {no no no} is assumed to be between them.

"pi'e" has two distinct uses: separating numbers which have only a vague=20
notion of relative significance, such as year, month, and day or parts of a=
=20
continued fraction, and separating digits in a base greater than 16. Hours,=
=20
minutes, and seconds can be interpreted either way, except when a time ends=
=20
in "pi'e nono pi'e xano" (a leap second). We may need to introduce a new=20
cmavo for one of these uses.

In base 16, "no no no no" should be assumed to be between two "ki'o". If it=
's=20
an IPv6 address, multiple copies of "no no no no" can be between them (if=
=20
there's any ambiguity in where to put the 0000 strings, the IPv6 address is=
=20
invalid).

> 5)	The new PA5 should contain {ra=92e, pi and ji=92i}, and can appear onc=
e
> in each number string. The grammar of {ji=92i} is changed for this
> purpose: the construct {ji=92i ni=92u/ma=92u} no longer tell us whether
> there have been =93rounded up=94 or =93rounded down=94. Alone, it means w=
orks
> as a number on it own, and tells us the other number strings are
> approximate. For =93typical number=94, use {no=92o}. For elliptical numbe=
r,
> I suggest the experimental cmavo {xo=92e}. If no part of a string is
> placed before {pi} or {ra=92e}, the default is 0.

There may be usages in which each section between two "pi'e" can have "pi" =
in=20
it. I don't know what they are though.

"ra'e" normally follows "pi", but when talking about p-adic numbers, "ra'e"=
=20
precedes "pi", and the sequence of digits preceding "ra'e" is repeated. How=
=20
would you interpret "pira'e" or "ra'epi" with no digits?

> 6)	The new PA6  should contain {pai, te=92o and tu=92o}. These are full
> numbers and can be modified by PA3 and PA4, but no other.
> Dealing with problems this gives us:
> 1)	How is PA6+{ki=92o} defined?
> a)	It=92s not, sorry. It should be grammatical, though.
> 2)	How does PA6 work with PA5?
> a)	{ji=92i} works with all numbers. {pi te=92o} is =930.271828=85=94, sim=
ilar
> with {pai}. {ra=92e} is not defined with any number from PA6.

I consider "pi te'o" and "pi pai" to be nonsense.

Pierre

--=20
Don't buy a French car in Holland. It may be a citroen.

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