HPSG and GPSG

[Howard Anthony Gregory]

Many thanks to Detmar and Carl for their very helpful replies. I  should
perhaps explain that I am not really advocating CFG-based  ideas of
restricting the expessive power of the framework, merely checking that I
understand  correctly what is equivalent to what.  I agree with Detmar and
Carl's points,  along with the discussion  to  similar effect in P&S.


> 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.

I was assuming an HPSG that was tied to  phrase structure rules, as in the
presentation in (most of) SWB. In this case, I understand that the
relationship with indexed grammars holds (or  has been argued to hold). You
would still not get CFG's, as you point out, unless the other recursive data
structures were restricted to finite depth. (Is it the case that one would
have to eliminate them entirely?)

I guess the relationship between this and the HPSG formalism not tied to
phrase structure rules is analogous to that between DCG's and Colmerauer's
Metamorphosis Grammars. (From which you can take it that I am looking at these
issues partly from the point of view of implementing of HPSG grammars as
DCG's.)

Perhaps you could suggest where I could read up on the formal properties of
HPSG grammars whose treatments of word order are not tied to phrase structure
(Reape, Kathol etc).

> 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,
Howard

___________________________

H. A. O. Gregory
Seminar für Englische Philologie
Georg-August-Universität Göttingen
Käte-Hamburger-Weg 3
37073 Göttingen
Deutschland

E-mail: howard.gregory at phil.uni-goettingen.de
Web:    http://babe.engl.phil.uni-goettingen.de
             (http://www.gwdg.de/~hgregor1 - temporary)