Prevailing approaches do not have a computational lexicon

[Ash Asudeh]

Dear Mark and list members,

On Sun, 6 Oct 2002, Mark Johnson wrote:

> >... The words are then combined
> >via merge, into phrase markers, where all the relevant features are
> >"checked" (very roughly equivalent to unified -- which is why some of us
> >lurk on these lists). ...
> >
> I haven't kept up with Minimalism since I took my statistical turn, but
> it always seemed to me that MP feature checking doesn't have much to do
> with unification, but instead is really analagous to the kind of
> cancellation you see in categorial grammar or linear logic; i.e., the
> very act of checking a feature consumes or discharges it.

It had struck me, too, that feature checking in Minimalism is really
feature cancellation and that a resource sensitive accounting of features
is what is really desired. One way to do this would be to use linear
logic, as Mark suggested (his paper that he referred to in his message
would be a good starting point for looking at the use of linear logic in
syntax; it's in Dalrymple 1999, MIT Press).

The use of linear logic would also give a handle on the distinction
between features that are "checked" and erased and those that are
"checked" but persist. This issue seems to come up in certain MP analyses,
particularly (I believe) with the "EPP" feature. Suppose there is a
certain feature X that corresponds to a resource x and a "checker" for
feature X/resource x. If the "checker" has a feature/resource like x -o s
('-o' is linear implication), where s is a special resource for
"satisfaction", then x is consumed and can contribute no further to the
derivation. If the "checker" instead has a modificational feature/resource
like x -o x, then it checks x by consuming it, but produces another x to
continue being checked by other consumers in the derivation. A successful
derivation could be defined as one where only a conjunction of s resources
remains.

Ed Stabler and Christian Retoré have done some work on the use of linear
logic with Minimalism, which they presented at ESSLLI '99. I didn't keep
pace with further developments of this post-ESSLLI, though.

Regards,
Ash