ARG-ST as a head feature

[Carl Pollard]

Hi Martin,

You excerpted the tail end of my long message and then commented
on it as follows:

>
> 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.]

It seems to me that you've just invented Categorial Grammar -- you get
uniform operations on feature structures and the required
contravariance/duality for valence features.  How does this differ
from CG with extensions in the style of Bayer and Johnson (which
admittedly contains unnecessary machinery) or, better, Doerre and
Manandhar?
>>

This is the difference from Bayer: the coordination/neutralization
lattice is IN ADDITION TO the conjunction/disjunction lattice. The two
lattices have very different structures: the former is Alex(Pow(P))
(where the subsumption order on P is ignored) and the latter is
Smyth(P) where the subsumption order on P is retained. For instance,
in the former lattice, the primes and coprimes are the same elements;
but not so in the latter.

This differs from Bayer/Johnson because they CONFLATE
conjunction/disjunction with neutralization/coordination, with the
undesirable consequences noted by Heylen. (Roughly, you can't describe
a man with a dissociated personality, where one of the personalities
is a vegetarian optometrist and the other is a coke-snorting
gunrunner: the gunrunner gets turned into a vegetarian. In case the
metaphor is too opaque, being a vegetarian optometrist is conjunction;
being schizophrenic is neutralization.) By the way, I did not invent
the coordination/neutralization lattice; Roger Levy did.  (But I think
he got the idea of treating coordination and neutralization as
algebraic duals from Bayer. My contribution was showing how to
characterize Roger's lattice in terms of powerdomains.)

The treatment of ARG-ST as a head feature using the freeze construct
is not very much like anything I know of in categorial grammar.

In my message I DELIBERATELY cast some vaguely hpsg-ish ideas into a
kind of variant type logic to make the comparison with Bayer more
transparent. (But the pretheoretic analogy between valence features
and categorial slashes has been made explicit since the inception of
HPSG.) To call this inventing categorial grammar is a little bit like
noting the equivalence between boolean rings and boolean algebras, and
then concluding that ring theory is just a reinvention of lattice
theory!

Carl