AW: Increasing interest in the HPSG conference

[Carl Pollard]

Hi Ivan,

>
What I meant was, for
example, PHRASE STRUCTURE.  This doesn't exist on the view both you and I are
espousing. Hence notions like c-command or o-command aren't easibly definable,
right?
>>

I guess you would have to define them in the metalanguage as relations
on subterms of a normalized term. They would have no status in the
theory itself. This of course makes binding theory harder: what is the
local domain for Principle B, and what is it exactly that Principle B
constrains? Before you can settle that, you have to take a stand on what
pronouns are, syntactically: are they variables, as in PTQ, or are they
identity functions, as in our 1983 WCCFL paper and as in Polly Jacobson's
work? My guess is the latter is more promising, but there is no analysis
to back it up yet.

Dick Hudson was right, wasn't he, about HPSG being a nice framework
except for that PSG business ...

>
> Is what you mean by this that:
>
> (1) the theory contains identity constraints, period (feature
>     values are either atoms or functions),
> (2) there are no reentrant structures, and
> (3) trees can be constructed, if needed, but there are no constraints
>     in the theory that make reference directly to tree structures.
>
> FWIW, these are the assumptions embodied in the formal bits of the SWB
> textbook, which is GPSG-like in certain respects....
> >>
>
> What I mean is elaborated some in my earlier reply to Ash. In terms of your
> (1)-(3):
>
> (1) The theory is stated in a (higher-order) predicate logic, so the things
>     it talks about are indeed either constants or functions. And since
>     all the logical constants and quantifiers are definable in terms of
>     = and lambda, yes, all the assertions of the grammar are equalities if
>     you expand out all the definitions.
>
> (2) The closest thing to structures is the proof trees corresponding to
>     the terms that denote sentences. What is the analog of re-entrance
>     in a natural deduction proof? I suppose the closest thing is a lambda
>     that bind two occurrences of the same variable, e.g. parasitic gaps.
>
> (3) Right, the assertions of the grammar are ABOUT the syntactic entities
>     denoted by lambda terms, but THESE ASSERTIONS DO NOT TALK ABOUT THE
>     STRUCTURE OF THE TERM ITSELF, e.g. whether such-and-such a variable
>     occurrence whatever=commands such-and-such a subterm. The syntactic
>     structure of the terms themselves is irrelevant.
>
>
> So we seem to have some common ground, quite a bit in fact.

I agree. But I have to confess that I got clear on these concepts
(if in fact I am clear on them :-)) only after hearing your lectures
in Trondheim....
>>

When I look back at those lectures I have a hard time imagining them
clarifying anything to anybody. It took another three years to figure
out how to take the advice of all the people who told me to restate it
without mentioning category theory. The NASSLLI04 lectures only use
(relatively) simple math (the models are the same as in the
extensional fragment of Montague, augmented with lambda-definable
subtypes).

We've identified some commonalities between the views we've arrived at.
We still need to get clearer about what the diferences are and whether
they can be resolved.

Cheers,

Carl