ARG-ST as a head feature

[Carl Pollard]

Folks,

Adam quotes me:

>
 > Theories of coordination I am familiar with require some kind
 > operation on the head values of the coordinate daughters and some
 > other operation on the corresponding valence (SUBJ, COMPS, SPR)
 > feature values, which requires that for each valence feature the
 > corresponding value lists be of the same length and the operation be
 > taken componentwise. But this does not extend in an obvious way ARG-ST
 > if it can appear on phrases, since, e.g. in general two VPs phrases
 > can be coordinated whose head verbs have ARG-STs of different
 > lengths. This problem (but not the locality issue) is enough to make
 > me give up on the idea of ARG-ST going up head paths.
>>

and then goes on to say:

>
The presupposition in this discussion seems to be that head features of
coordinated phrases should be "the same".
>>

I do NOT presuppose this and was careful to say "some kind of
operation on the head values of the coordinate daughters", not that
the values had to be identical. With Roger Levy, I assume there is a
bounded distributive lattice K of elements that can be HEAD values,
with join = category neutralization (or indeterminacy, or
syncretization, whatever you want to call it) and meet being category
coordination.  These operations are distinct from logical conjunction
("unification") and logical disjunction. [For lattice theorists, the
lattice in question is constructed by taking P = the set of (possibly
underspecified) "basic" head values (i.e. not including values of
syncretic forms or of coordinations of unlikes)) and emdedding it into
K = Alex(Pow(P)), the Alexandroff topology of the powerset of P.]

Actually it IS possible to do coordination by "unification" (logical
conjunction) in this setting, but what this requires is to say that,
e.g. the head value of HIM is not accnoun but rather the logical
disjunction of all elements of the principal ideal of K generated by
accnoun. [For lattice theorists: conjunction is join in the Smyth
powerdomain Smyth(K).]

Adam goes on to say:

>
Of course, if ARG-ST were present on phrases, it wouldn't behave like
valence features in the sense that we wouldn't expect both coordinated
daughters to have the same ARG-ST.  But why would we want ARG-ST to behave
like valence features anyway?  ARG-ST has always had a rather different
ontological status than valence features.
>>

This is right. However, the question is: if ARG-ST propagates onto
phrases, then what should be the ARG-ST value of, e.g. a coordinate VP
whose coordinate daughters are headed by verbs with different ARG-ST
values? For valence features F \in {SUBJ, COMPS, SPR}, we can say: the
value of F on the mother is the componentwise neutralization of the
F-values of the coordinate daughters, which is only defined if the
F-values of all coordinate daughters are the same length.
Alternatively, if you insist on doing things unification-style, say
that "subcategorizing for accnoun" means the logical disjunction of
"subcategorizing for x" for all x in the principal filter of K
generated by accnoun.)

Here is something I think might work, using the following feature
geometry for categories (ignoring semantics, udc's, etc. for the
moment):

    |cat
    |     |head
    |     |MORPH  morph
    |HEAD |
    |     |ARG-ST freeze(string[cat]
    |
    |     |val
    |     |SUBJ  string[cat]
    |VAL  |SPR   string[cat]
    |     |COMPS string[cat]

The idea here is that possible values of MORPH (mnemonic for
"morphosyntactic features") would be members of K (the kinds of things
we usually think of as being possible values of HEAD, together with
things generated from them by coordination and neutralization).
freeze is an operation that takes a string of categories and turns it
into an atomic entity from the point of view of the operations of
coordination and neutralization. Technically what this means is that
we form the flat poset S of strings of categories and say that
possible values of ARG-ST are members of A = Alex(Pow(S)).

Finally, we define coordination [resp. neutralization] of two
categories by taking the meet [resp. join] (in K) of the MORPH values,
the meet [resp. join] (in A) of the ARG-ST values, and for each of the
valence features F, the componentwise neutralization
[resp. coordination] of the F-values. [Note: the dualization for the
valence features is analogous to the fact that slash in type-logical
grammar is a kind of (noncommutative linear) implication.]

The recursion in these definitions bottoms out in the lattices K and
A. The definition implies that the coordination and neutralization of
categories are possible only when the corresponding valence feature
values are the same length, but the ARG-ST values being neutralized
(or coordinated) are just "remembered". [For lattice theorists: they
are retrievable as the prime (for neutralization) or coprime (for
coordination) decompositions of the ARG-ST value on the syncretic
form/coordinate structure.]

If this is right, then we can treat ARG-ST as a head feature (in the
sense of propagating up the head path), but different from the usual
(morphosyntactic) head features in the sense that it is invisible to
the lattice operations used to compute the values of MORPH and VALENCE
features on coordinate structures and syncretic forms.

Carl

p.s. I didn't say what the members of P looked like. If you want you
can think of them as (not necessarily totally) well-typed abstract
feature structures of the kind that would normally be used as
(possibly underspecified) HEAD values, but the theory sketched above
in no way depends on modelling things as feature structures.