New PA-proposal

[Jakob Nissen]

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).

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

[Pierre Abbat]

Changing "fi'u" like this breaks existing text. Also, "fi'u", in current
usage, is meaningful at the end of a number string; it denotes the golden
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 would
you denote transfinite ordinals?

> 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.

"pi'e" has two distinct uses: separating numbers which have only a vague
notion of relative significance, such as year, month, and day or parts of a
continued fraction, and separating digits in a base greater than 16. Hours,
minutes, and seconds can be interpreted either way, except when a time ends
in "pi'e nono pi'e xano" (a leap second). We may need to introduce a new
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
an IPv6 address, multiple copies of "no no no no" can be between them (if
there's any ambiguity in where to put the 0000 strings, the IPv6 address is
invalid).

> 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.

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

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

> 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.

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

Pierre

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

[djandus]

This seems really impressive and well-thought-out to me and deserves careful inspection.

I have to admit, from the start I was afraid that your demands for the grammar would make it far too complicated, but it actually seems rather intuitive. Just to make sure I understand things, I'm seeing that to make a string:

PA1 combine freely

PA2 exist individually

PA3 modify the string to the right

PA4 separate strings, modifying internally

PA5 are PA4 but with single usage

PA6 are specialized individual numbers

Just looking at that, the "pretty pretty simple simple" part of me wants to sort them primarily by basic grammatical usage. That is, combine PA2 and PA6 since they both have words that stand alone as number strings, and combine PA4 and PA5 since they both modify internally. The extra grammatical rules can be explained in subgroups. (e.g. refer to PA6 as PA2* or something) To clarify further, I feel that while it is certainly a valuable goal to make every grammatical PA construct be meaningful, it is also lofty and should be sacrificed when necessary for the sake of having a primary grammar that is clear and easy to understand. Additionally, the secondary rules are more particulars on interpretation or restrictions to provide a computer than a human. (As in, expressing that the words you call PA5 can only be used once is extremely simple to tack on as an extra subcondition, while it is more valuable for structure and grammar to group it with PA4)

To illustrate my point, I'll use notation entirely distinct from selma'o -- I'll use "#" for an unmodified number string, which can be composed of what you call PA1 (any combination), PA2, or PA6. I'll use "." for an internal modifier, and "-" for a left-hand modifier.

With this simple categorization, I'd like to ask for clarification on your more interesting grammar suggestions. You claim that right-grouping is necessary, but the example you provided seems (to me, correct me if I'm wrong) to illustrate left-grouping! That is, I'm getting the gist of your grammar suggestion to be that you can have any number of number strings automatically associated together. (Providing there is some way to tell them apart, implying in my mind that either another internal separator or number string terminator is desired.) That is:

# # # #

is parsed as having four number descriptions all describing the same amount. Additionally, I see you applying a primarily left-grouping methodology with PA3, saying that you can have any number of left-hand modifiers "prefixing" any string:

+++++# +++++#

would have two strings with five modifiers each, both of which are numerical descriptions of the same amount.

Additionally, I would describe the internal modifiers less as separating numerical strings, and more like joining strings together. (Though this is simply a matter of perspective.) Either way, that part says you can simply have

#.# #.#.#

Which would be two numerical descriptions, one composed of two substrings and the other composed of three.

This sort of grammar seems pretty simple, though implementing it certainly would require a few very critical editations to the current grammar. (I am certainly fond of fi'u for the golden ratio -- something that could easily be accommodated for in this grammar with the use of a special separator/marker/terminator of some kind.)

Before I close, I'd like to address your example of {li rau su'o pa} with how I see your grammar would be implemented. {rau}, being of your PA2, represents a full string (#). {su'o}, of your PA3, is a left-hand modifier (+). {pa} is, of course, PA1, and without any adjacent PA1 represents a full string (#). Thus, the structure is simply

# +#

with the two descriptions "enough" and "at least one" purported as equivalent descriptions of the same value. With this outlook, there is no issue of "left grouping" or "right grouping", as there are simply stacked left-hand modifiers that only modify the next string. One issue would be declaring that the internal modifiers are "close grouping", with {pi} and {pi'e} grouping before left-hand modifiers as expected. Otherwise, the grammar would be complete, intuitive, and often more so than the current, if your {li rau su'o pa} assessment is accurate. (I apparently don't know the current PA grammar well enough, as it simply seems silly to me to try to group {<rau su'o>}.)

[la klaku]

Pierre:

The change of {fi'u} *does* seem to break existing text, and that is
bad. I could find no other PA, though, which needed to take both the
previous and the following number string. I'm also curious as to how
many texts has a {fi'u}-fraction - perhaps they could be changed?
When alone, fi'u could easily be defined as the golden ratio, though
this slightly breaks the consistensy. Still, how often does one use
that?

I seem to have missed {ci'i} altogether. I'm initially sceptical as to
whether an Aleph cardinal should have its "own" cmavo, but if it's
placed in PA3, it can take the next number string. I don't know enough
about aleph cardinality to know if the construct {ci'i NUMBER} means
infinity for any NUMBER. If so, this could be the default value with
no string following.

Perhaps we need new cmavo for keeping order on number strings, but I'm
not sure we need one for the two uses of {pi'e}. They seem to work in
the same way, differing only in semantics? This is easily resolved by
context.

In my system, {pa pi'e pi so pi'e pi rau} is grammatical. It probably
means 1:9/10:enough. Using the clock as an example, this could mean
1:00:54+enough.

{pi} and {ra'u} make no sense when they are the only numbers in a
number string. This is a problem. I take my suggestion back that
{ji'i} should be grammatical on its own. I'd like to see that a number
string cannot contain only PA5.

Perhaps {pi pai} is nonsense - you might be right.

Djandus:
I, too, agree that selma'o should be based purely on function. So yes,
there is no reason not to combine PA2 and PA6. Let's call this
hypothetical PA for PA2* If we fuse PA2 and PA6, we need a word for
"end number string". Otherwise, I think we could do without, since you
could just end a number string by beginning a new one. After all, why
have two number strings of the same selma'o describing the same
number?

PA4 and PA5 cannot be combined though, since only 1 of each PA5 makes
sense in a number string. (this, by the way is also a problem! if {li
pi pa ji'i} is grammatical, why not {li pi pa pi}? Solution: Only one
of each PA5 is permitted. That's a violation of the definition of a
selma'o, right? Darn.) I wouldn't like to see extra grammatical rules
for subgroups inside one selma'o - then I'd rather see ten selma'o of
PA. (why not? It encompasses 40 cmavo or so)

Right. Every grammatical string should not necesarrily be meaningful,
but it'd be nice if it were so, even if the meaning it conveys is
contradicory or silly.

I see it as right-grouping, because {za'u su'o fi'u vo} (more than at
least one divided by four) is understood (za'u(su'o(fi'u vo))).
Futhermore, {pa re ci} is structured (semantically, not necessarily
grammatically)

Otherwise, I agree with you completely.

[Mark E. Shoulson]

The situation in PA seems to be sort of a cop-out: "Whatever, look, it's
a bag of words, let the higher level (semantics) sort it out." We could
have done the same with the grammar as a whole, probably, but what would
that have accomplished?

Thus klaku, from the proposal:

> 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.

So this defines {pai} and {te'o} in terms of their radix expansions. {pi
pai} is {pai}/10, and if we were working in another base, it would be
{pai}/B (for base B). I started writing this to say this is a terrible
idea, but there is some consistency to it: {pi re} is {re}/10, etc.
Whenever you move the {pi} around, you multiply/divide by the radix.
Now, this reasoning would also lead to {pai no} equalling 10π and so on,
where you would probably rightly say they can't join this way. (which
makes me start thinking of having cmavo defined purely in terms of
moving the radix point... You don't need one for moving it to the left,
because numbers can't be infinite to the left and we can say {pi no no
pai} and so on for moving it more places, but you'd need one for the
right... Yeah, we could speak in terms of explicitly exponentiating the
radix... OK, yeah, I know, I'm rambling and these aren't good ideas.
Just stuff that hit me when trying to say this was a bad idea and
discovering it might not be.)

> 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.)

I think this is likely a bad idea, and will lead to trouble. Might
prefer to just forbid more than one "number string" per number, or else
come up with... a better meaning for it. We already have (enough) ways
to indicate incidental relative clauses, etc. Maybe adjacent number
strings have explicit multiplication between them, like in ordinary math
notation (bad idea). Or maybe PA1 are really complete number strings,
and for number strings x and y, {x y} means "x times the radix, plus y."
That would yield a nice consistent meaning for how PA1 works as well as
a meaning for other adjacent number strings—albeit a fairly useless
meaning. Not a great solution either.

I'm not sure how happy I'd be with "messin' with th' established order
o' things," especially considering the usage breakage involved. But
that's another matter, and I could be convinced; I'm just looking at the
idea on its own.

~mark

[Jorge Llambías]

2011/11/17 Mark E. Shoulson <ma...@kli.org>:

> Thus klaku, from the proposal:

>> 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.)
>
> I think this is likely a bad idea, and will lead to trouble. Might prefer to
> just forbid more than one "number string" per number, or else come up
> with... a better meaning for it.

I proposed something similar here:
http://www.lojban.org/tiki/BPFK+Section%3A+Inexact+Numbers

Two adjacent simple quantifiers are interpreted, when possible, as if
joined with .e:

ro ci broda
all three brodas, all brodas and three brodas.

rau su'o mu broda
enough at least five brodas, enough brodas and at least five brodas.

su'o ci su'e bi broda
at least three at most eight brodas
at least three brodas and at most eight brodas
between three and eight brodas (inclusive)

Two adjacent simple quantifiers are interpreted, when joining them
with .e would give a contradiction, as if joined with .a:

me'i ci za'u ci broda
less than three more than three brodas
less than three brodas or more than three brodas
i.e. other than three brodas

mo'a du'e broda
too few too many brodas
too few brodas or too many brodas
the wrong number of brodas

mu'o mi'e xorxes

[Jorge Llambías]

On Thu, Nov 17, 2011 at 6:40 AM, Jakob Nissen <jakobny...@gmail.com> wrote:
>
> Klaku’s number proposal:
[...]

I had something similar here:
http://www.lojban.org/tiki/Internal+grammar+of+numbers
(you have to edit the page in order to see the grammar, the format got
messed up in one of the wiki moves).

[MorphemeAddict]

It seems that people are attempting to create a grammar for PA that produces all and ONLY those number strings that make sense. This is worthwhile, I think, but also unnecessary. We don't worry about which letters produce grammatical sentences, only which words. Also, given that Lojban's grammar treats all gismu equally and all members of a selma'o equally, there is strong precedent for not creating special grammar for PA.

 

stevo

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[la klaku]

MorphemeAddict:

We can't allow different PA to follow different grammar, that much is
true. We would need in total four grammatical classes (PA, DUhE, CEhI
and PIhE, for instance). PIhE should bind two strings together, so we
need a new in PIhE (let's call it {xi'e}, to make an analogy to
{pi'e}), which just binds two strings together without any meaning.
This is used to say, for instance {li du'a pi'i fi'u ro xi'e mu no}
(too many out of them all, which is fifty) to avoid confusion as to
what is equal to fifty - them all or the fraction (in this case, it's
them all).
So I agree. If we just make three classes, one can still say all kinds
of nonsense, but it least we know how to parse it correctly.

Xorxes (Jorge):

I agree to all of the definitions in your proposal, but have a few
things against the grammar:

1) How do we know which numbers are contradictory? Are "many" a
contradiction to "less than X"? This needs a ton of arbitrary rules. I
vote that two number strings should always be joined with .e. In cases
where .a is needed, use two numbers. By the way, this also ensures a
nice rule: One number, one value. Anyway, this is semantics, and
should not affect the decision in making the new grammar.

2) The exact gouping confuses me a bit. How do you know, in your above
50-too-many example, what 50 refers to? The fraction or them all? That
is why I propose the use of number strings to avoid confusion.

Mark Shoulson:

It's totally a cop-out, and if I were in charge, I'd see many more
selma'o than now. I'm not, so perhaps we should keep it to a minimum

Thus my current suggestion:

selma'o PA: xo, all of current PA1 and PA2. Combines with each other
in the same string.

selma'o DUhE: du'e, mo'a, rau, ro, so'a, so'e, so'i, so'o, so'u, xo'e,
no'o, pai, te’o and tu’o. Constitute their own string.

selma'o CEhI: ce'i, ma'u, me'i, ni'u. za'u, da'a, su'e, su'o, ka'o and
fi’u. (and ci'i?): Takes the next string and convert in into a new
string. Right-grouping.

selma'o PIhE: pi'e, ki'o, xi'e (NEW), ji'i, pi and ra'e. Internal
modifier: Binds two strings together. Needs to be adjectent to a
string.

This sadly allows for totally crap numbers like {li ce'i pi pi xi'e
rau re no}, but at least a computer can parse it, and we should
understand it if it made sense (li <ce'i <pi pi xi'e rau>> re no)

I know I seem a bit pushy, but I'd like to see some product so the
discussion won't just go to into oblivion when the thread dies.

[And Rosta]

MorphemeAddict, On 18/11/2011 04:50:

> It seems that people are attempting to create a grammar for PA that
> produces all and ONLY those number strings that make sense.

A grammar for PA is a grammar only if it specifies what PA syntagms mean. That's what the job of a grammar is.

--And.

[Pierre Abbat]

On Friday 18 November 2011 08:20:50 la klaku wrote:
> Thus my current suggestion:
>
> selma'o PA: xo, all of current PA1 and PA2. Combines with each other
> in the same string.
>
> selma'o DUhE: du'e, mo'a, rau, ro, so'a, so'e, so'i, so'o, so'u, xo'e,
> no'o, pai, te’o and tu’o. Constitute their own string.
>
> selma'o CEhI: ce'i, ma'u, me'i, ni'u. za'u, da'a, su'e, su'o, ka'o and
> fi’u. (and ci'i?): Takes the next string and convert in into a new
> string. Right-grouping.

"fi'u" shouldn't be here, as it binds two strings together. Ditto "ka'o".
And "pa ka'o re ka'o ci ka'o vo" has a clear meaning (it's a quaternion),
but "pa fi'u re fi'u ci fi'u vo" does not.

> selma'o PIhE: pi'e, ki'o, xi'e (NEW), ji'i, pi and ra'e. Internal
> modifier: Binds two strings together. Needs to be adjectent to a
> string.

"pi" and "ra'e" can occur only once each, but "ki'o" can occur any number of
times. Also it might be useful to join numbers that contain "pi" with "pi'e".
What's "adjectent" mean?

Pierre
--
gau do li'i co'e kei do

[Jorge Llambías]

On Fri, Nov 18, 2011 at 1:50 AM, MorphemeAddict <lyt...@gmail.com> wrote:
> It seems that people are attempting to create a grammar for PA that produces
> all and ONLY those number strings that make sense. This is worthwhile, I
> think, but also unnecessary. We don't worry about which letters produce
> grammatical sentences, only which words.

Not the best analogy. PAs are words, and in any case letters have very
strict restrictions on how they can be combined to form words. In
fact, in Lojban there are two and only two letters that may be said to
belong to the same "letter-selma'o", i.e. such that they can always
occupy the same position in a phonologically valid word. All other
letters have their own individual grammars. (Exercise for the reader:
which letters are those?)

> Also, given that Lojban's grammar
> treats all gismu equally and all members of a selma'o equally, there is
> strong precedent for not creating special grammar for PA.

The grammar of PA would amount to splitting PA into several selma'o, of course.

[maikxlx]

2011/11/18 Jorge Llambías <jjlla...@gmail.com>:

> On Fri, Nov 18, 2011 at 1:50 AM, MorphemeAddict <lyt...@gmail.com> wrote:
>> It seems that people are attempting to create a grammar for PA that produces
>> all and ONLY those number strings that make sense. This is worthwhile, I
>> think, but also unnecessary. We don't worry about which letters produce
>> grammatical sentences, only which words.
>
> Not the best analogy. PAs are words, and in any case letters have very
> strict restrictions on how they can be combined to form words. In
> fact, in Lojban there are two and only two letters that may be said to
> belong to the same "letter-selma'o", i.e. such that they can always
> occupy the same position in a phonologically valid word. All other
> letters have their own individual grammars. (Exercise for the reader:
> which letters are those?)
>

You have a knack for summing things up. My guess is {e} and {o}, by the way.

>> Also, given that Lojban's grammar
>> treats all gismu equally and all members of a selma'o equally, there is
>> strong precedent for not creating special grammar for PA.
>
> The grammar of PA would amount to splitting PA into several selma'o, of course.
>
> mu'o mi'e xorxes
>

IMVHO we should be seeing proposals for fewer selma'o, not more.

[Craig Daniel]

On Fri, Nov 18, 2011 at 6:16 PM, maikxlx <mai...@gmail.com> wrote:
> 2011/11/18 Jorge Llambías <jjlla...@gmail.com>:
>> On Fri, Nov 18, 2011 at 1:50 AM, MorphemeAddict <lyt...@gmail.com> wrote:
>>> It seems that people are attempting to create a grammar for PA that produces
>>> all and ONLY those number strings that make sense. This is worthwhile, I
>>> think, but also unnecessary. We don't worry about which letters produce
>>> grammatical sentences, only which words.
>>
>> Not the best analogy. PAs are words, and in any case letters have very
>> strict restrictions on how they can be combined to form words. In
>> fact, in Lojban there are two and only two letters that may be said to
>> belong to the same "letter-selma'o", i.e. such that they can always
>> occupy the same position in a phonologically valid word. All other
>> letters have their own individual grammars. (Exercise for the reader:
>> which letters are those?)
>>
> You have a knack for summing things up.  My guess is {e} and {o}, by the way.

It's a clever challenge. I can't think of anything to make either e/o
or i/u the wrong answer, but I'm probably overlooking something.

[maikxlx]

On Fri, Nov 18, 2011 at 6:23 PM, Craig Daniel <craigb...@gmail.com> wrote:
>
> It's a clever challenge. I can't think of anything to make either e/o
> or i/u the wrong answer, but I'm probably overlooking something.

I figured it had to be a vowel because of voicing and gemination
constraints on the consonants.

{i} and {u} are barred because they can geminate and because they form
diphthongs but not the same ones.

{a e o}+{i} v. {a}+{u} bars {a}.

That leaves {e o}.

[Craig Daniel]

On Fri, Nov 18, 2011 at 6:34 PM, maikxlx <mai...@gmail.com> wrote:
> {i} and {u} are barred because they can geminate and because they form
> diphthongs but not the same ones.

Ah, right. Missed the lack of "eu" and "ou." Has to be e/o.

[djandus]

First of all, I’m extremely in favor of hierarchical selma’o. That is, there are very good reasons both for increasing the number of selma’o (increased grammatical clarity) and for decreasing the number of selma’o (less complicated grammar). I believe the only good solution at this point is to introduce a hierarchy, with subgrammars (lojbanized, paugerna). For instance, applied to this very thread, rather than make four completely new selma’o (PA DUhE CEhI PIhE) it seems we should make these be subclasses (lojbanized, pagselma’o) of an overarching group, say PA^ -- the idea being, PA^ represents any combination of the four pagselma’o which can be parsed on their own subgrammar without influencing any grammar dealing with PA^. So PA^ would be the thing to use when exemplifying sentence grammar with numbers in it (e.g. explaining xorlo) while PA, etc. would be used for explaining numerical grammar (e.g. THIS WHOLE THREAD). Even more succintly, PA^ would represent the abstract thing we have been referring to as the “number string”.

Secondly, I would like to more fully explain my issue with calling this right-grouping. What I mean to say is that we can define our pagselma’o in a simple way such that we get the exact (overall) behavior described at the beginning of the thread with a left-grouping system. (Or, even better in my opinion, any-grouping.) To explain that, here is a Google Doc with the full system as I see it. (Sorta-kinda like a “if this were becoming official, here’s a brief version of what I’d try to put in the CLL and/or jbovlaste”. This is another reason I really like the idea of hierarchical selma’o -- it is a more easily searchable structure for word classes.)

Lastly, in order to not have to make this apparent in the Google Doc, I’d like to directly address the “separating strings” issue. There are two reasons we’d need a word to separating number strings: to separate the instances of the base PA class, or to allow a more complicated paugerna.

(I'm keeping the following text here so that you can see my old thoughts. I'm suddenly of a very different opinion on this issue. That is, I feel we don't need a new word to serve this purpose, as the word .e is supposed to be able to serve this purpose just fine. The only reason we'd need a different separate would be for a tanru-like semantics, but what on Earth would that mean?)

For the former, that is to say {pa no so} means 109, but saying 10,9 would require a separating word. Interestingly, this does not have any usefulness except for saying “1000,1thousand” as {panonono xi’e paki’o} or “half, .5” as {fi’o re xi’e pi mu}, where {xi’e} is the theoretical separator. So, it would have, at best, a didactic purpose, and therefore would be better expressed as an equality or some other bridi. Thus, this usage is... lame.
For the latter, we have very legitimate usage options. Once we can separate strings, this means we can also separate CEhI and PIhE (modifiers) from strings -- allowing us to give the modifying words different definitions for default arguments (or even have default behavior of a different paugerna). This I am strongly in favor of. It does make it a little false to say, then, that “fi’u” is of pagselma’o PIhE, since it would be parsed as CEhI without a preceding value, but I think this is the best way of doing it. (As someone else said above, we can tell a computer how to parse it without much difficulty, and I think it’s pretty intuitive anyway.)
(If your confused by me saying the versatile grammar requires a separator, then realize I have an understood requirement of PA^ (number strings) in that they must have a grammar that makes uniform sense, defined in the Google Doc. For example, I demand that if {fi’u} is parseable as a PA^, then there must be a way to use it in any other scenario that could take a PA^, which would often require a separator of some kind.)

(end of text I don't actually agree with)

Oh! And I just remembered, a long time ago there was a thread about mekso being relatively useless, and blah blah blah. I don't know what came of that, but if it were to be removed in any way, I would suggest merging some of the operators into PIhE, particularly things like {gei} and {ju'u}. However, sometimes mekso applications can be very not intuitive and maybe would be modified (I hope!) to be more consistently straightforward if they were to join these classes. For instance, I like the idea that these PA^, have no modifiers that do PA^1 <modifier> PA^2 PA^3, but instead work like {ka'o}, repeating the operator for each instance. If something else needed to be conveyed, I expect {vei...ve'o} could be implemented to help out.

mu'o mi'e djos

[la klaku]

djandus:

Your idea of heirarchial grammar is *brilliant*. We can keep the
current grammar satisfied, and still have something official (maybe
sometime even implemented in some machine?) that we can point to when
someone throws an impossible PA in a sentence. At the very least we
can unambigiously point out why {li pi pi pi pi} is nalsmudra.

I'm not all too satisfied with the specifics of your proposed PA^,
though. For instance, {pi ro} should be grammatical(*), while {pi pai}
should not. (I've changed my mind there). Also, we {pi}, {ra'e} and
{ji'i} should have different gunselma'o-grammar, as {pi ji'i mu}
should be grammatical, but not {pi pi mu}. You actually wrote that
these should only appear one in your definitions, but this is not how
selma'o are defined - they are always interchangable. Presumably also
so with gunselma'o.

*Actually, this could be easily defined to be ungrammatical. The
trouble is - it's used all over the place as it is now.

But this means we must make a lot of gunselma'o in PA alone? Well yes,
but since they're not (as of now) in the official grammar, there
should be as many rules as there are already semantic rules for
interpreting them "correctly".

The idea of taking some of the useless mekso cmavo and use it in our
PA^-grammar is brilliant, but I think we have a snowball's chance in
hell of getting the BPFK's approval for that one. (Though perhaps not?
It is, after all, Robin Lee Powell who is one of the most prominent
critics of mekso math)

There are also a few other minor issues: Does {ce'i}, which i've never
seen in print really deserve to be unique in that it takes the
previous PA^ instead of the following? Ofc we also would need to make
sure the gunma'o grammar of PA is consistent and unambigious. I'll
shortly mail you your document back with some editing, :)

mi'e la klaku

[djandus]

Okay, klaku and I have hammered out a lot of changes, and have a few big things. Here's the document link again, for convenience. Note that I added the capability for you all to post comments on the document. Please use it! It works a lot better than typing in the mailing list "Now when you said..."

First of all, if anyone is confused on the purpose of the hierarchy, please speak up.

Some general points:

• We have changed the selma'o notation from denoting gumselma'o to denoting pagselma'o. For clarity, this uses an underscore rather than a caret. This both makes the notation more consistent when it changes as well as makes sure that PA always refers to the same words it does now.
  
• Additionally, for clarity, I've suggested a set of lujvo to describe the gumselma'o. Tell me if any of them suck or break any rules.
• The hierarchy is now relatively hammered out. It now looks like this:

PA:

• PA_
• PA__: (no, pa, re, ci, vo, mu, xa, ze, bi, so, dau, fei, gai, jau, rei/xei, vai), xo
• DUhE: du'e, mo'a, rau, ro, so'a, so'e, so'i, so'o, so'u, no'o [xo'e]
• PAI: pai, te'o, tu'o
• PIhE
• PI: pi, ki'o, ra'e, ji'i
• FIhU: fi'u, ka'o
• PIhE_: pi'e
• CEhI: ce'i, ma'u, me'i, ni'u. za'u, da'a, su'e, su'o, ci’i

One of the funniest things about this is that CEhI is the name of the preceding modifier gumselma'o when it's the least certain one to be in that class. Dealing with that first, I think that whatever we do, we should not define {ce'i} as it is officially -- that is, that {pa no pi re ce'i} is "10.2%". The only reason to make "percent" a succeeding modifier (for which we would need a new pagselma'o) is cultural: we're used to saying "ten percent". This is a terrible reason when PA could have so much order with just three pagselma'o. However, I do have a suggestion if people do not like ce'i as a preceding modifier. We can make it an internal modifier that serves the same function as {pi}, except that it asserts the {pi} position to be two digits to the left. In this way, {pa no ce'i} would still be "10%", but "10.2%" would instead be expressed as {pa no ce'i re}. Note that this version saves a syllable, since {ce'i} would take the place of {pi}. In the event of this conversion I suggest CEhI be renamed to DAhA, since it and {ci'i} are the only words in the class that don't come in symmetric pairs.

Another important discussion point addresses the parsing of PA__ strings. (e.g. {pa no pi re}, i.e. strings composed only of PA__ and PI} Rather than apply a bunch of restrictions to where PI valsi are allowed, (e.g. "{pi} can only be used once in a PA__ string") we say that each PI has to assert a new {pi} position, be it taken from the left string, the right string, or it's own (as in {pi} itself). This is illustrated in the second of three examples at the end of the Google Doc. (On a tangent, how is "second of three examples" supposed to be expressed in Lojban? The simplest thing I can come up with is {lo remoi be lo cimei ku mupli}) The only question left regarding how to parse PA__ strings then becomes whether to use left-grouping or right-grouping to evaluate PI. Right now, everything is as if we use left-grouping. (so that the rightmost {pi} or {ra'e} always "wins") However, I've discovered that this can make parsing something like {pa ji'i re pi no xa} awkward, as left-grouping dictates {<pa [pi] ji'i re [pi]> pi <no xa [pi]>}, which comes out to saying only the digit {re} is uncertain. We can either arbitrarily define some confusing order of operations, or simply use right-grouping. As klaku pointed out way-long-time-ago, PA__ are already semantically interpreted with right-grouping, so it wouldn't be too farfetched to apply PI to PA__ with right-grouping. It would, in fact, make a lot of sense. Note that this wouldn't change how the other PIhE or CEhI are evaluated -- they would still parse the same way, left-to-right, without any explicit grouping needed, just waiting for PA to be parsed for input.

If I missed any of the big changes or issues, I'm sure you all will find them.

[And Rosta]

djandus, On 21/11/2011 00:32:
> First of all, I�m extremely in favor of hierarchical selma�o.

Nowadays, but not when Loglan was begun, hierarchical taxonomic categories are the mainstream way of doing things in grammatical analysis. (Google keywords: inheritance hierarchy, lexicalism|lexicalist, construction grammar.) If the job of defining Lojban syntax were handed over to linguisticians, hierarchical selma'o wd deffo be used.

--And.

[Jorge Llambías]

On Tue, Nov 22, 2011 at 4:26 PM, djandus <jan...@gmail.com> wrote:
> PIhE
>
> PI: pi, ki'o, ra'e, ji'i
> FIhU: fi'u, ka'o
> PIhE_: pi'e
>
> CEhI: ce'i, ma'u, me'i, ni'u. za'u, da'a, su'e, su'o, ci’i

I consider "ji'i" one of the "preceding modifiers".

http://www.lojban.org/tiki/BPFK+Section%3A+Inexact+Numbers

There are several long discussions about this somewhere.

[djandus]

I consider "ji'i" one of the "preceding modifiers".

This system doesn't parse any differently from how you'd expect for {ji'i xa pi xa}, as in the linked example you gave, but simply allows for constructs like {pa ji'i xa} for "16, with 6 being uncertain" -- clearly intended for simplifying significant figures and error analysis. This is the behavior I grabbed straight from the cll. The "rounded" semantics is implied, but not the "rounded up/down" semantics. (Which I'm perfectly fine with.) What I'm not fine with is that {ji'i PAI} makes logical sense, and sometimes {ji'i DUhE}, but these are currently disallowed since they would put {ji'i} in a separate pagselma'o. I wrote a possible work-around in the google doc definition, but I don't particularly like it. Given, it's basically the same sort of thing I did with {pi DUhE}...

I've been trying to match the current system as much as possible, primarily disliking {ce'i}. I didn't know there were previous thread expressing dislike with {ji'i} -- personally, I'd like to see both interpretations able to coexist.

[Pierre Abbat]

On Tuesday 22 November 2011 14:26:51 djandus wrote:
> The *only* reason to make "percent" a succeeding modifier (for

> which we would need a new pagselma'o) is cultural: we're used to saying
> "ten percent".

The Turks say "yüzde on" and write "%10".

Btw, "pagselma'o" and "nacvla" are misspelled; they both need "y" between the
voiced consonant and the voiceless one.

[djandus]

> The *only* reason to make "percent" a succeeding modifier (for
> which we would need a new pagselma'o) is cultural: we're used to saying
> "ten percent".

The Turks say "yüzde on" and write "%10".

The more I've been thinking about using {ce'i} instead of {pi} to indicate percentages, ({pa no ce'i re} for 10.2%,) the more I like it. It's clean and efficient, and consistent with all integer percentages in previous usage.

 

Btw, "pagselma'o" and "nacvla" are misspelled; they both need "y" between the
voiced consonant and the voiceless one.

Thanks! I remember finding a lujvo-making thing online that checked all of that stuff for me before, but I somehow lost it... Anyway, it's an easy find-and-replace, once I get around to it >< (Thanksgiving kept me busy!) Is it okay to use {pauselma'o} and {na'uvla} instead, or is it taboo to avoid the "y" buffering? (I'm not really fond of the sound of {pagy}, though {nacy} is a little nicer...)

As I mentioned, I got pretty delayed over the break -- I'm going to be going over the grammar pretty rigorously over the coming times!

mu'o mi'e djandus

[Pierre Abbat]

On Monday 28 November 2011 15:59:28 djandus wrote:
> Thanks! I remember finding a lujvo-making thing online that checked all of
> that stuff for me before, but I somehow lost it... Anyway, it's an easy
> find-and-replace, once I get around to it >< (Thanksgiving kept me busy!)
> Is it okay to use {pauselma'o} and {na'uvla} instead, or is it taboo to
> avoid the "y" buffering? (I'm not really fond of the sound of {pagy},
> though {nacy} is a little nicer...)

"pauselma'o" falls apart, but "na'uvla" is OK. You can say "paurselma'o".

Pierre
--
sei do'anai mi'a djuno puze'e noroi nalselganse srera