Trees

[Carl Pollard]

Hi Ash,

>
I have to confess that I don't really understand why a tree has to be
either a structural representation or a derivational history. Why can't it
be both? If you look at a proof in substructural logic or proof theory,
it's a derivational history if anything is. However, it can also
profitably be viewed as a representation. Can't we view trees this way
too?
>>

I agree the right way to think of syntactic derivations is as proofs,
though I don't think it is essential that the logic be substructural:
if you take Curry's advice (as Dowty, Reape, Kathol etc. did) to
separate purely combinatorial aspects of syntax ("tectogrammatical" structure)
from how syntactic entities "surface" ("phonegrammatical" structure) then
you can just use ordinary (intuitionistic) propositional logic for the
derivations.

But that point of view is inconsistent with treating the tree as a structural
representation. Why? It is because proofs are in one-to-one ("Curry-Howard")
correspondence with terms of a typed lambda calculus (TLC), and what
is significant is not the proof itself but rather its equivalence class,
where two proofs are considered equivalent if the corresponding terms are
equivalent in the usual sense of TLC term equivalence.

But this means that the gross geometric properties of the trees themselves
are synatctically irrelevant because they are not invariant under
equivalence. This explains, for example, why such questions as whether
syntactic structures are flat or binary branching are never comclusively
answered. If you do the derivation with the uncurried form of the verb
you get a flat structure, if you do it with the curried form you get a
binary-branching structure. But the two structures are still (in one-to-one
correspondence with) TLC terms, and in any model the terms denote the same
sentence.

This view also explains why it never gets settled whether, in BIG DOGS
BARK, the right way to get from the common noun phrase (CNP) BIG DOGS
to the NP (or DP) BOG DOGS is by a nonbranching rule or by a null
determiner. On the suggested view, there is absolutely no difference
between these two things, they are just two different ways of
informally describing a (TLC term that denotes) a function from CNP's
to NP's. Reifying the derivations as trees-qu-structural representation
creates an artifactual difference between the two.

So the problem lies not with PS94 elaborating tree-structural representations
into feature-structure ones, but was already present in the frameworks
(such as GPSG and GB) that used trees as structural representations.
THe HPSG feature-structure representations added insult to injury, however,
by creating even more distinctions-without-a-difference (e.g., in

  Pictures of Kim are more fun to look at than reports about Kim

are the two tokens of KIM identical or not?; or in

  To err is human

what is the case of the SUBJ of TO ERR? From the perspective I am suggesting,
this latter question is like asking whether the argument of the successor
function is even or odd.

Carl