METAGRAM -- Pt. 2 (and triggers too)

Time for some more METAGRAM (sounds like a vitamin). We're beginning to get
into some issues that I haven't thought through quite as well. Lots of room
to try to break (ahem... I mean 'debug') this system. This one's pretty
long, and by the end (point IV), I'm even discussing Triggers.


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(I) Extraneous words

First of all, you may have noticed that I use commas for "and":
I {needing{of (pen, paper)}}
"I need a pen and paper."

I didn't mention it, but you can also use the vertical bar (called a 'pipe'
by us UNIX programmers) for "or":
I {needing{of (pen | paper)}}
"I need a pen or paper."

Next, for words that don't seem to fall into my nice structure, especially
interjections, conjuctions, and direct addresses, I just enclose them in
angle brackets.

<because> we {needing{of milk}} I {going{to store}}

In that sentence, we could also put in a "therefore":

<because> we {needing{of milk}}
<therefore> I {going{to store}}

Or equivalently:

we {needing{of milk}} <so> I {going{to store}}

Here's another example with extraneous words that don't fit the structure:

<Mary> John {coming{to supper, during tonight}}
"Mary, John is coming to supper tonight."

I just realized, though, that what I _don't_ have yet, is a way to ask
questions or make imperatives:
*<Mary> you {coming{to supper}} <please>
which is literally translated into the incorrect declarative:
*"Mary, you are please coming to supper."
Okay, I could imagine some stuffy old maid saying something like that to
"politely order" someone to come to dinner! Hopefully, part of the solution
will come when I reach mood and conjugations (but not today).

Another form of extraneous words comes in the form of multi-word verbs (and
I don't mean auxileries!). I don't know what its called, but at least
English and German do this. Probably other languages too. For example, you
"look up" a word in the dictionary, you "shut up" when told to be quiet,
but machines are "shut down" when the're not needed. You "lock up" a house
for the night, but you "lock down" a nuclear power plant during a security
alert. These troublesome idioms don't translate very well if you try to
translate them directly, since the extra word can't really be seperated
from the main verb:

*locking {of house, upward}

There is nothing actually "up" about "locking up" a house. Instead, I just
create a sort of compound-word by splicing the two words together to form a
single semantic idea:

locking-up {of house}

This may not be the best way to go, but it works.


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(II) Restrictive Clauses

I think I'll move on to mentioning restrictive and non-restrictive clauses.
At first, I didn't think I was going to need these, but while attempting
various translations, I found they were definately neccessary. These can be
accomodated by a double application of rule 2 to the grammar:

N -> N {P1} -> (N {P2}) {P1}

The parenthesis above are not part of the grammar, but are just used to
show the order of precedence. The interpretation is that an N which fulfils
{P2} also meets {P1}, whereas the N that doesn't meet {P2} may or may not
meet {P1}. In other words, with logical semantics, {P2} -> {P1}.

Let me give some examples. These are adapted from E. Bach's article on noun
phrases in _Universals in Liguistic Theory_.

1) Eskimos who live in igloos have fun.
2) Eskimos, who live in igloos, have fun.

The first says that only the Eskimos that live in igloos have fun. In
logical semantics, "they live in igloos" -> "they have fun". No statement
is made about Eskimos that don't live in igloos. OTOH, the second example
says that, in general, Eskimos both live in igloos and have fun.

In my notation:

1') Eskimos  {living{in igloos}}  {having{fun}}
2') Eskimos  {living{in igloos}, having{fun}}

The first effectively means:
"Eskimos which are living in igloos -- they are having fun."
The second is more like:
"Eskimos are living in igloos and are having fun."

One way to think of this is that all {P} phrases are "selectors"
(restrictive clauses), except the rightmost one (a nonrestrictive clause),
which make a statement about the thing selected. Thus in (1') above,
{having{fun}} makes a statement about the Eskimos selected by {living{in
igloos}}, but in (2') above, {living{in igloos}, having{fun}} makes a
statement about Eskimos in general (since none are selected).

Theoretically, you could apply this several times:
N {P1} {P2} ... {PN}
but I don't know if there's any semantic difference between that and
N {P1, P2, ..., PN-1} {PN}

For example:
book {on shelf} {leather-bound} {biggest} {given{to me}}

which has the semantics of:
"Of all books, select only those on the shelf. Of those, select only those
which are leather-bound. Of those, select only the biggest. That book is
the one that is given to me."

But that seems to mean exactly the same as:
book {on shelf, leather-bound, biggest} {given{to me}}

which is:
"Select the biggest, leather-bound, shelved book. That is the one given to
me."

But I can't proove that in all instances this will always be the case. So
while I leave open the option for more than two predicates, I can't
currently think of any case where it would be semantically useful.


--------------------
(III) Quantification

If you're especially sharp, you may have noticed an ambiguity in the above
sentences about books.

book {on shelf}

Could mean "The book which is on the shelf (the one over there.)"
Or alternatively, it could mean
"A book which is on a shelf (_any_ shelf anywhere)."

While this could probably be determined from context (is there a bookshelf
in the room? What are we saying about the book on a shelf?), it is still
potentially ambiguous in some instances. What we need are quantifiers. I'm
not sure exactly how to do this but here's two ideas. First, we could treat
quatifiers as a special rule:

N -> [quantifier]N

For example:
[any]book  {on [that]shelf}
[any]book  {on [any]shelf}
[any]book  {on [no]shelf}
[that]book {on [that]shelf}
[that]book {on [any]shelf}
[that]book {on [no]shelf}

While this works, what makes more sense to me is to just make quantifiers
like adjectives and verbs. I.e. just another state:

P -> quantifier

Yes, I think this is how I'll do it (unless anyone knows a better way).
Also remember that the quantifiers can usually be ommitted if the context
makes things clear. Using this syntax effectively makes quantifiers into
restrictive clauses (which I called "selectors" above). This makes alot of
sense to me. I'm still not sure if I 100% like this system, though. I'll
need to work with it some more. In the mean time, here are some examples:

book {any} {on shelf{that}}
"The book which is any (book), is on the shelf which is that (shelf)."
"Any book is on that shelf."

book {every} {on shelf{none}}
"The book which is every (book) is on the shelf which is no (shelf)."
"Every book is on (something) which is not a shelf."

In the case of negations, they might be put onto prepositions:
book {every} {not-on shelf}
"Every book is not on a shelf."
Or better yet, onto states in general:
book {not-red}
book {not-falling}
I may come back to this point in later post.

Also, we could use quantifiers to ask some questions.

book {on shelf{which}}
"The book is on which shelf?"

who {coming{to dinner}}
"Who is comming to dinner?"

which could also be written:
person {which} {coming{to dinner}}
"Which person (='who') is coming to dinner?"

These quantifiers still can't ask the type of question I tried to ask in
section (I) though, i.e. questions about whether something is happening.


--------------------
(IV) Transformations
(or Case, voice, trigers(?), and subjectless sentences.)

We have seen that each phrase has a head followed by predicates of that
head. When translating English sentences, that head will probably be the
subject of the sentence. In active voice, this subject will typically be an
agent, while in passive voice, it will typically be the patient.

I {giving{of book}}
"I am giving the book."

book {given{by me}}
"The book is given by me."

We notice that when different roles are promoted to the head, the verb
changes its form (voice) and the former head is demoted to the verb's
predicate list. We also notice that the role of the nouns in this list is
always indicated by prepostions. So "by X" indicates X is an agent, "to/for
Y" means Y is the recipient/beneficient, and "of Z" means Z is the patient
(this is potentially confusing since 'of' is also frequently used for the
genetive case instead of the accusative, but this is a defect in the
English lexicon, not in my system!).

Lets see if we can generalize this concept to accomodate my impression of
trigger langugaes. (DISCLAIMER: I make no claim to know anything at all
about trigger langugaes except what I have heard on this list in the last
couple of days!). We'll adapt the example that's been floating around in
that debate for our purposes here.

"I killed a shark in the pool with a knife."
(Children, don't try this at home!)
Agent: I
Action: killing
Patient: shark
Location: pool
Instrument: knife

The standard English active-voice order is:
I {killing {of shark, in pool, with knife}}
"I kill a shark in the pool with a knife."

In English passive voice, we have:
shark {killed {by me, in pool, with knife}}
"The shark is killed by me in the pool with a knife."
(Would this be like a normal sentence in an ergative language?)

But we could also put the location or the instrument at the head. In this
case, I'll have to improvise with the verb-forms, since English doesn't
have these voices:

pool {killing-there {of shark, by me, with knife}}
"The pool is where there is a killing of the shark by me with a knife."

knife {killing-with-it {of shark, by me, in pool} }
"The knife is what is used used in a killing of a shark by me in the pool."


Note that these are all just simple transformations of the original
sentence, though.

Let's take this a step further and see if we can eliminate _all of these
nouns_ from the head. Since verbal gerunds can be used as nouns, we can
make the state "killing" a noun. (Cops, for example, might say "There was a
killing on the East Side."). If we then place this noun at the head of the
sentence, we get what might be considered a "subjectless" sentence in
English, but is merely a surface tranformation of the senteces above:

killing {of shark, by me, in pool, with knife}
"There is a killing of a shark by me in a pool with a knife."

Very odd indeed! In case you haven't guessed it yet, this is my concept of
a verb-centric METAGRAM, which seems to be very similar to the case frames
in Fillmore's work on case. It also seems to be similar to my impression of
what Lojban does (though I've admittedly only scanned a few sections of the
intro to Lojban).

I will make this observation though: this form is structuraly more simple,
since there are no recurssive predicates.

The point I'm making here is that METAGRAM is very flexible, and can
represent multiple types of surface sentence structures with just a few
very simple transformations (hence the "META-"). In fact, I would dare say
that we are beginning to get awefully close to the "deep-structure".
(DISCLAIMER: I am _not_ supporting this as an auxlang!)

However, making verbs to be able to function as nouns ("The killing of a
shark") as well as states ("the state of killing a shark") opens up a whole
new level of ambiguity (hmmm... open-up. There's one of those funny verbs
again!). I haven't solved this quite yet, but I hope to discuss it (and
maybe solve it) in my next posting, along with conjugations, negations, and
auxilary verbs. So far, things like tense, mood and aspect are the main
linguistic features we are lacking.


Thanks,
~Caleb

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