Question formal status of trees in H&GPSG (fwd)

[Martin Jansche]

On Thu, 26 Jun 2003, Andrew Carnie wrote:

> In early transformational grammars, trees were viewed as short hands for
> derivational history. That is a tree S
> 				      / \
> 				    NP   VP
>
> was viewed as statement of the operation of replacing S with NP and VP.

True, but that has nothing essential to do with transformational
grammars, as no transformations are involved necessarily.  It is a
property of, say, context-free grammars that you can view them a bit
more procedurally as a rewriting system (start with an S, rewrite it
into NP VP, then maybe rewrite the VP as something else, etc.), or
more declaratively as a particular kind of well-formedness constraints
on finite trees (in this case, a tree whose root bears the label S is
well formed if it has two children of which the first is labeled NP
and the second VP, etc.).  CFG rules impose "local" well-formedness
constraints, in the sense that you can check whether a tree is
well-formed by looking only at local subtrees (a node and its
children).  There can be, and have been, other kinds of
well-formedness constraints, e.g. surface filters (which look at the
terminal yield of the tree) or various command relations (which may
take aspects of the structure of the whole tree into account).
Still, in all cases only a *single* tree is involved:  no essential
use is made of derivations or transformations.  Other formal systems
that involve transformations can often be viewed as imposing
well-formedness constraints on a finite sequence of finite trees,
checking not only whether each individual tree in a sequence of trees
is well-formed, but possibly also imposing constraints that involve
multiple trees in the sequence, e.g. checking whether tree n+1 was
"derived" from tree n by some admissible transformation.

> Sometime later, (probably in late EST/early GB times when
> transformations stop operating over strings but over combinations
> of structurally related tree nodes), trees come to be viewed as
> manipulable objects, that is, they are themselves a linguistic
> structure rather than a retelling of derivational history,
> although they also serve that function.

I'm not sure whether this historical characterization is accurate.
As soon as you define structural relations on trees (going back to the
original command relation, then to c-command, etc.), the trees have a
different ontological status, beyond being a recording of rewrite
operations.  This is orthogonal to the question of whether trees can
be manipulated.  If they can be manipulated, this means that the
primary objects described by a syntactic theory are sequences of
trees.  If not, then just plain trees.  This is what distinguishes
most generative theories (most of them do not mention cross-tree
constraints) from transformational theories (which presumably do).

> In P&P and MP this becomes even more the case, where the sets
> created by merge are themselves the *only* syntactic objects.

I don't think I know what this means.

> So, could someone give me the short and dirty version of what GPSG
> and or HPSG think about the formal status of trees.

Of course I'm speaking only for myself, not for {G,H}PSG.

> I know they are representations of features, but I'm really trying
> to look for the deeper answer than that. Are they objects that can
> be manipulated or are they merely records of the relationships
> between the feature structures or is the whole question silly in
> the context of PSG assumptions.

As I understand it, what Classical GPSG (as in Gander, Krane, Pillock
& Sachs, 1985) and Classical HPSG (as in Pollard & Sag, 1994) are
about is describing well-formed syntactic objects.  For HPSG, the
primary objects are generalizations of trees (feature structures,
finite labeled directed acyclic graphs, etc.).  For present purposes,
it's safe to pretend they are trees.  HPSG has nothing to say about
how trees come into life -- trees just are.  But for each given tree,
you can ask what a specific syntactic description has to say about it,
which is really not all that much, namely just an indication of
whether it is well-formed or not.  So say you have built yourself a
tree which you think might represent a well-formed object of the P&S94
description of English.  You take that whole tree and check whether it
satisfies all the constraints given in the appendix to P&S94.  P&S
(1994, but I think their opinions are unchanged today) do not care how
that tree came into existence -- perhaps you generated it by a series
of transformations, but those are not reflected anywhere in the final
tree you have.  All they care about is whether your tree is a
well-formed specimen according to a set of constraints that's supposed
to describe well-formed syntactic objects of English.  The point is,
most HPSG theories are theories of what is, not theories of how things
came to be.

In other words, if you're looking at NP movement, it doesn't matter
whether the NP was generated in a specific position and then moved.
What all frameworks (including GB, GPSG, HPSG, etc.) agree on, in a
broad sense, is whether, say, a fronted NP and its trace are in an
admissible relationship, as described by a particular theory.  It's
only GB that cares about how an NP ended up in its surface position,
as it draws a distinction between an NP that was generated in a lower
position and moved upwards leaving behind a trace, or an NP that was
base-generated in its surface position while simultaneously generating
a trace in the appropriate place.  Not a whole lot hinges on the
distinction, except that there are constraints on movement.  If you
can express those constraints in terms of properties of the final
tree, you can eliminate movement altogether.  Abandoning specific
transformations in favor of the catch-all "Move alpha" was a first
step in that direction, but since there were constraints expressed in
terms of movement in GB, it never quite made it all the way to
completely eliminating movement.

But movement is the only place where you can talk metaphorically about
trees being manipulated.  (Of course it's still possible to also talk
about it declaratively, as I did above, in terms of sequences of
trees.)  Except for movement, which was arguably not central to GB,
when did GB have anything to say about tree manipulations?

- martin