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CONLANG  August 2012, Week 2

CONLANG August 2012, Week 2

Subject:

More Logic & Semantics

From:

Logan Kearsley <[log in to unmask]>

Reply-To:

Constructed Languages List <[log in to unmask]>

Date:

Wed, 8 Aug 2012 17:42:34 -0600

Content-Type:

text/plain

Parts/Attachments:

Parts/Attachments

text/plain (150 lines)

I've had a PDF about type-directed natural language syntax parsing
sitting on my desktop for quite a while, and finally got around to
reading it. I thought it would have something to do with coding
selectional features of predicates as types to do POS tagging and
binding disambiguation; turns out somebody just accidentally
reinvented Categorial Grammar to produce a syntax parser
(incidentally, they did it entirely in Haskell, which I found neat
because I've been contemplating the grammar of Haskell as I try to
figure out how to handle parentheses-less binding disambiguation in
Palno; also incidentally, that means that what I thought it was going
to be about is still a potential open area for new research). This
reminded me of my prior complaints about how introducing types into
Palno in order to allow unambiguous usage of higher-order predicates
would be horribly unwieldy, as I realized that the complex types of
lexemes in Categorial Grammar were exactly isomorphic to the complex
recursive function types that would be required for resolving binding
ambiguities with typed predicates in Palno.

My review of Categorial Grammar has made me more pessimistic about the
prospects of successfully implementing higher-order operations in a
human-usable language; there is no provision for parametric types in
Categorial Grammar, and clearly human brains can only handle explicit
selectional types of finite complexity, which means there must be a
fixed limit to the possible complexity of a type and thus a limit on
the number of types available in a language (which may correspond to
the creation of different lexical classes). And that means no
nth-order operators.
That's slightly disappointing, if true; in trying to create a
minimalist language with applicative semantics based on predicate
calculus, it's one thing to disallow something or to allow arbitrary
quantities of it, but quite another to have to specify "up to exactly
x fixed number". Of course, that being true depends on it actually
being a cognitive linguistic universal that humans can't handle
parametric types, which I think will be rather difficult to prove;
just because they happen not to be accounted for in Categorial Grammar
doesn't necessarily mean that they're impossible, and I have no idea
how to even start analyzing natural languages with that idea in mind.

In the meantime, I've been giving more thought to Palno's semantics
without higher order operators; much of my new thought can be
integrated into the interpretation of Palno's syntactic &
morphological structures without having to actually change those
structures, which is nice.

The only major morphological change that's needed is the introduction
of a bit of morphology to say "this is a logical predicate", i.e.,
asserts a truth value. Without that, we can interpret all predicates
as returning some sort of nominal- usually, the Davidsonian event
argument. Since Palno predicates are in fact, most of the time, no
longer interpreted as actual logical predicates after this change, I
am motivated to change the name of that particular lexical class; I am
not sure if it would be more useful to call them "operators" or
something like that as distinct from atoms, or to just group all Palno
open-class words into a single class of roots, some of which happen to
be 0-arity and return substantives and qualities and such.

Now I also recently re-read "Predicates and Pronominal Arguments in
Straits Salish" (Jelinek & Demers, 1994), since I've been toying with
doing a Salish-inspired language anyway, and I noticed a rather odd
claim:

"Pronominal arguments are a necessary but not a sufficient condition
for the lack of a noun/verb contrast; there are pronominal argument
languages that have nouns [...]. But for a language to lack a
noun/verb contrast, it must have only pronominal affixes and clitics
in A-positions (i.e. argument positions). Otherwise, if each root
heads its own clause, there would be an infinite regress in argument
structure."

with footnote:

"We thank an anonymous reviewer for raising the question of whether
there might be a language just like Straits Salish, except for having
DetPs in A-positions. In such a language, the predicates on which the
argumental DetP would be based would in turn have their own DetP
argument structure, and so on ad infinitum."

It seems to me they missed a rather obvious intermediate case; Salish
apparently only allow 1-depth trees, where a language that
*prohibited* pronominal arguments with no N/V distinction would
clearly have infinite trees, which is not practical for communication;
but one could still have a language with no nouns that allows *either*
subordinate clauses *or* pronominals as arguments, with pronominals
acting as terminals. I suspect that is what I shall end up doing if I
get around to my Salish-inspired language, but in the meantime, an
applicative language like Palno does nearly the same thing, with
0-arity roots serving as terminals; of course, one could argue that
their ability to serve as syntactic terminals is a good argument for
keeping a separate lexical class of atoms/nouns as distinct from
operators/verbs, but that could be circumvented by introducing
pronouns/variables as an explicit semantic class in Palno (which would
be a much bigger change than what I've contemplated so far), with
operators having arity of at least 1.

This gets me onto another topic which has long bugged me about Palno's
structure, which inspiration from Salish might actually help to fix.
Relative clauses in Palno have so far been handled either by an
internally-headed structure with morphology to indicate that an
internal argument is returned/projected rather than the usual value
for that predicate, or with a hacky adjunction-with-coreference thing.
The first option is now made to fit much better into the rest of the
language by my change in the interpretation of predicate/operator
applications (the predicate morphology could be seen as just one case
of a set of inflections that specify which argument of an operator to
use as the syntactic projection / return value), but is still a little
annoying because the syntactic structure does not exactly match my
conception of the final interpreted semantic structure, and the second
is just gross because there is no other occurrence of adjunction
anywhere in Palno's grammar. What would be very nice is to have some
way of encoding the logical proposition "x such that P1(x) & P2(x) &
P3(x) ...", etc., without having to introduce the capacity to bind
arbitrary variables in what is supposed to be a speakable language.
Salish languages *have* to do something like that in order to achieve
the implication of a nominal argument in a syntax that only allows
pronominal arguments by ensuring that the same referent is bound to
multiple argument positions in the main and subordinate-adjoined
clauses. They do this by having strict rules about what pronouns in
different clauses must or must not be coreferential with each other,
which sometimes disallow certain logically possible sentence types
(for which they have voice transformations to make up). Something
similar could be done with Palno, avoiding disallowed sentence types
by providing a sufficiently rich set of pronouns with agreement
features to handle the proper coindexing. A closed class of pronouns
would not be powerful enough to produce all of the logical semantic
structures that could be expressed in predicate calculus with
arbitrary variable binding, but should be able to nicely handle all of
the practical communicative needs of a human language. Without the
matrix/subordinate distinction available in Salish, a pronoun with no
agreement morphology could be seen as a variable binding which is then
referenced in a further series of conjoined clauses containing
agreeing pronouns until shadowed by another non-agreeing pronoun
indicating a new binding. Exactly what kind of agreement morphology to
use is something I shall have to think about.

That would somewhat complicate the grammar and make it no longer 100%
purely applicative, but the better structural match to semantics might
just be worth it.

With all of those changes implemented, Palno could still be used with
the purely applicative postfix grammar (still the simplest grammar for
any language that I know of), or slightly more complicated with
conjunctions and reduction of repeated arguments as it was before, or
at yet a third level with explicit coreferencing, which I expect to be
the most easily human-usable and still capable of fitting on a
postcard (for real, not like Esperanto is supposed to).

No, back to thinking about how to manage higher-order operators....

-l.

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December 1998, Week 5
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