[lojban] New PA-proposal

[Jakob Nissen <jakobnybonissen@gmail.com>]

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’s number proposal:
The number system of Lojban simply doesn’t work. Due to historical
reason (I’ve been told), it was decided to let all numbers work the
same way in the grammar, make no distinction between the selma’o 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’e xo pi pi}) and
2) Strings of PA which makes sense are parsed wrongly, leading to
confusing results (like {li rau su’o pa}, which is parsed {li <rau
su’o> 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 “black hole”, 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’e}, 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’u}. 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’u} is changed: it can now only express 1/n.
In order to express a/n, use {a pi’i fi’u n}. They all should work
without having a number after them, in that case, the number should be
a default.
4)	The new PA4 should contain {pi’e and ki’o}, and can appear at any
time, in any number string, any amount of times. They sever the number
string, but {ki’o} allows two adjectent number strings to “fuse”
together again. When several PA4 are put together, the number string
{no no no} is assumed to be between them.
5)	The new PA5 should contain {ra’e, pi and ji’i}, and can appear once
in each number string. The grammar of {ji’i} is changed for this
purpose: the construct {ji’i ni’u/ma’u} no longer tell us whether
there have been “rounded up” or “rounded down”. Alone, it means works
as a number on it own, and tells us the other number strings are
approximate. For “typical number”, use {no’o}. For elliptical number,
I suggest the experimental cmavo {xo’e}. If no part of a string is
placed before {pi} or {ra’e}, the default is 0.
6)	The new PA6  should contain {pai, te’o and tu’o}. 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’o} defined?
a)	It’s not, sorry. It should be grammatical, though.
2)	How does PA6 work with PA5?
a)	{ji’i} works with all numbers. {pi te’o} is “0.271828…”, similar
with {pai}. {ra’e} is not defined with any number from PA6.
3)	What happens when you put several number strings next to each
other?
a)	All number strings then refer to the same number, describing it in
different ways. This means you can say something wrong. ({li pai su’o
vo} refers to “pi, which is more than 4”, for instance.)
4)	What is a number string?
a)	I propose it is defined as a construct where one or more PA-cmavo
interact internally. Thus {da’a pa no} is one number string, because
{pa} and {no} belongs to PA1 and can make number strings which each
other, and {da’a} belongs to PA3 and can make number string with any
number string to its right.
5)	How would you convey whether a number has been rounded down or up?
a)	I propose using {za’u} or {me’i} in an adjectant number string to
show that the number is smaller or greater than some unspecified
value, which is presumably then understood to be the exact number.
6)	How exactly should {xo} work?
a)	It should work like a PA1, but the response to it can be any PA or
mekso expression which is grammatical in the construct it is placed
in.
7)	How should number strings group in for instance {fi’u dau so’i}?
a)	Number strings should group from right to left. PA3 binds to any
number strings to the left of it, so the above should group {<fi’u
dau> so’i}.
8)	Objection! Right-grouping is a fundamental break in Lojban, which
uses left-grouping whenever it can!
a)	Well, even with the current rules, the meaning of numbers is
dependent on right-grouping, even though the grammar is left-grouped.
The meaning of {pa} in {pa ci}, for instance, can only be determined
by knowing how many digits are to the right of it. This is the nature
of numbers, not something peculiar in my proposed grammar (at least
unless we make it standard to write “backwards”, writing 42 as {re
vo}).
9)	Why the strange rules for {ki’o}? Why should it first separate
number strings, then fuse them together again?
a)	Firstly, I tried to make as few selma’o as possible, which is why
problem 1 and 2 still exist. Secondly, it makes sense, since in a
{ki’o}-construct, each of the number strings separated by {ki’o} are
given new value in the number string they are in. Therefore, it still
“seperates” number strings and assign them different functions. For
example in {li re no ki’o xa}, {re no} is assigned the value “20,000”
instead of “200” because of {ki’o}, while the {xa} is still “6”.
This grammar should allow one to express any number one wants, while
still being parsed the same way it is understood. The changes should
be easy to incorporate in the formal grammar, and change nothing in
earlier texts (since no one follows the current parsing rules anyway).

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I'd like to see people's objections and comments to this proposal.
mi'e la klaku

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