HPSG and GPSG

[Detmar Meurers]

Hi Howard,

> I would be interested if anybody knows any references on this question. I had
> gathered from somewhere (and since assumed) that the HPSG framework has the
> power of indexed grammars, though actual HPSG grammars (seek to) avoid this
> infinite set of categories by restrictions on subcategorization etc.  But if
> this is not definitely the case then I would be grateful for  more precise
> information.

This got me wondering about the point where you mention that the
"HPSG framework has the power of indexed grammars", which strictly
speaking is not false but has a potentially misleading implicature.
Different from GPSG or TAG, the HPSG framework does not have a
restriction of its expressive power through the formalism as such -
it's turing machine equivalent and thus can license languages from
any formal language class. So there is a shift of perspective from
GPSG to HPSG in that the search for a formalism that's just powerful
enough to model natural language is replaced by the search for
signatures and theories which model the properties and
generalizations actually found in natural languages.

Regarding the issue of finite or infinite categories, this was key
for keeping GPSG context-free given that recursion is only expressed
through phrase structure rules relating categories as data
structures. But for HPSG, restricting the number of categories would
not result in context-freeness (or any other restriction) since it
is no longer the case that the recursive power of the formalism is
tied to a phrase structure component. The HPSG formalism includes
implicational constraints and, depending on the formalization you
chose, also a relational extension of the constraint language (e.g.
to express list concatenation with append, or express relational
generalizations across constraints/"rules", etc.). So limiting the
number of categories in HPSG to a finite set has no effect unless
one also eliminates all recursive data structures (lists, sets,
etc.) which type constraints and recursive relations can apply to.

As to why HPSG has sidelined the question of finding the formalism
with just the right expressive power, I think this is a natural
consequence under the perspective that the key issue in linguistics
is, at least as far as I see, to

  a) identify the linguistic properties which are necessary and
     sufficient to model in order to make the empirically warranted
     distinctions and to
  b) discover and encode the general ways in which these modeled
     properties relate and license an infinite set of sentences
     with finite means.

So in that sense the role of the formalism in HPSG is entirely
secondary - as far as I'm aware, we've just been thinking about the
formalism and what it formally means in order to be able to
scientifically verify that the linguistic proposals that we write
down do indeed express what we want to express - in line with the
following quote ;-)

    It is an open question whether full-scale formalization is a
    worthwhile endeavor at the moment ... My personal feeling is
    that the point has been reached where these further steps should
    be undertaken, that there is sufficient depth and complexity of
    argument so that formalization will not merely be a pointless
    technical exercise but may bring to light errors or gaps and
    hidden assumptions, and may yield new theoretical insights and
    suggest new empirical problems for investigation.

    Chomsky (1981, pp. 335-6)

Lieben Gruß,
Detmar

--
Detmar Meurers, Assistant Professor, Dept. of Linguistics, OSU
201a Oxley Hall, 1712 Neil Avenue, Columbus OH 43210-1298, USA
http://ling.osu.edu/~dm/                 GnuPG key on web page