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pycyn@a... wrote:
>
> Mike:
>
> <(1) While the formal syntax of the particular example you
> give indeed does not formally parallel the logical structure
> it is deemed to represent, nevertheless, the logical
> structure is clearly unambiguously established. Purely
> speculatively, could we not somehow re-analyze the syntax in
> order to reflect the logical structure? If so, would such
> a re-analysis satisfy your objection?>
>
> It should be noted that the claim that {ro nanmu cu prami lo ninmu}
is
> actually in perfectly good first-order logical form, even a
standard form,
> though in the semantic representation logical form (as far as we
know, this
> is a not-completely-resolved issue among semantic theorists).
Well, there is surely no doubt as to this expression's
logical meaning, but as I gather you must realize from
previous correspondences with And, there are some issues of
concern here. At this point, I feel it is highly debateable
whether the syntax represents the logical structure. Lo*an
sentences, like natlangs sentences, parse into trees with
a verb at the head node and NP's as separate subtrees.
Quantifiers are definitely subsumed by these NP-subtrees.
Which is to say, technically their scope can't be said to go
beyond the subtree of which they are a part, unless some
device such as an anaphor is introduced in the other branch.
In other words, the grouping and precedence of logic and
grammar simply don't line up. What is troublesome to me is
not working out some trivial example such as <ro nanmu cu
prami lo ninmu>, but rather what happens when we start trying
to represent much more complex expressions.
There are of course different ways of looking at it. We could
try to "get out of the box" that the whole concept of simple
trees puts us in and ask, what is so wrong with having cross-
branch connections and scope, based on linear word order?
Fair enough. The difficulty I see emerging from such a view
is working out rigorously and mechanistically the rules
governing such (for lack of a better word) multi-dimensional
structures. In order to maintain a minimal level of
naturalness, I would not be surprised if this were the way
to go. But I don't think we can so easily minimize the
complexity and difficulty involved. The feeling I almost
get is that we'd virtually have to pioneer our very own
theoretical semantics to make it rigorous.
> <In the example you give, the closest we come to capturing the
> logical structure using plain English as opposed to logicians'
> jargon is:
>
> - If something is a man, then it loves at least one woman.
>
> Or a bit briefer:
>
> - If it's a man, it's a woman-lover.>
>
> Or "Every man loves some woman or other." The other two are, of
course,
> going to get interpreted correctly, but are overtly wrong, one for
the wrong
> quantifier and scope, the other for lacking overt quantifiers
altogether.
These expressions were sloppy; the idea was to capture the real
logical structure using naturalistic language. In the first
sentence, the quantifier is implicit. One could also say
"if anything at all is a man, it loves some woman or other."
The second example also contains an implicit quantifier, as
long as we agree that the first <it> is not an anaphor. The
fact that these statements are sloppy rather illustrates the
insight that concerns me: namely that logical expressions are
at apparent odds with natural expressions to some extent.
> Even if you (or &) does not like the natural English or Lojban
forms, the
> rules for going to some preferred form -- at least of the usual
sorts (I am
> unclear what & has in mind as the final result) are clear and
mechanical. To
> be sure they can give rise to a variety of different forms, but
these are
> either provable equivalent or differ only in underlying
assumptions, which
> then have to be spelled out. (BTW the conditional form would
usually have to
> be deconditionalized for most natural-language cases. An arguable -
- and
> often argued -- point)
Well the idea of introducing the conditional construction was
simply to express the implicational operation which appears
in the logical expression. Besides clear quantifier scope,
this is the other thing that arguably is not reflected in
the simple predicate syntax.
At this point, please understand that I am only naming some
issues here on my mind. I too do not know how And handles
things in his conlang, though I vaguely gather it involves
employing quantifiers at the higher tree level as would be
demanded by straightforward logical representation. I would
be satisfied with *any* syntax that veriably assigns every
expression in the language one, and exactly one, equivalent
logical expression, and allows every possible logical
expression at least one linguistic expression. That seems
to me the minimal requirement for any true loglang.
> Quantifiers are not where the problem in Lo*an are, unless you
include -- as &
> does -- indirect question markers (and maybe direct ones) and
lambda
> variables in the list. Then the problem is just to mark scope --
or, more
> accurately, depth. The peripheral cases (no less important for
that, of
> course) need to be examined and some rules or devices (Lo*an is big
on
> subscripting -- yuck!) devised. The problem is not inherent, only
due to a
> lack of attention.
>
> The other problem is anaphora, for which Lo*an has Lord knows how
many
> devices, but countless insoluble cases, often because the devices
require a
> kind of syntactical awareness that is hard to achieve even with the
sentences
> written out in front of you, let alone on the fly in converation.
Yet even
> with all these devices there remain real-life cases that are
inaccessible:
> anaphora for a term reached by scaling one tree, swinging to
another branch,
> and scurrying back down that branch, for example. The only devices
to use in
> this case are fuzzy ones, not precise ones, and thus liable to
screw up
> syntactosemantic rules, however well they work in practice.
Lo*an are impressive accomplishments, IMO. As I said before,
it appeared to me that Lo*an were fully logical languages;
in fact I was quite ignorant that were any glitches at all
up until a couple days ago (which is probably why I never
considered comparing closely natlang syntax to predicate
logic; it was my intention to borrow what I needed from
Lo*an.) I suspect that overall, logicality is served well
by them, which is not the same as saying they are verifiably
rigorous.
So, it will be a fun challenge trying to put together
a language with both rigorous logicality and sufficient
naturalness to speak on the fly--or at least make the best
possible effort to create such a language.
Regards
--- Mike