Fwd: linear and non-linear terms

[Ash Asudeh]

On Sun, 20 Oct 2002, Carl Pollard wrote:

> Hi Ash,
>
> >
> In particular, this reveals that the issue is not vacuous abstraction in
> the *meaning language* or linguistic semantics, just in the proof terms.
> >>
>
> That's not quite right. In a type-theoretic semantics, you have a
> propositional logic whose formulas are the semantic types, and the
> proof terms are PRECISELY the terms of the typed lambda calculus
> (= the meaning language). This is the Curry-Howard perspective
> applied strictly to the semantic domain. So if you had a relevant
> semantic type theory your meaning language would not have vacuous
> abstraction.

Well, I'm coming from the Glue perspective, where we really have:

semantics : proof terms : linear logic

The CH relates the linear logic to the proof terms: the proof terms
therefore have only linear lambdas and no vacuous abstraction. However,
you can have vacuous abstraction or nonlinear lambdas in the meaning
language, by which I mean the linguistic semantics, not the semantics of
the proof terms. I think this same distinction should be possible in
Type-Logical Grammar. Am I confused?

> >
> The reason I got alarmed and came across like a jerk in the message below
> is that I actually need vacuous abstraction in the meaning langauge in the
> theory of resumption that I'm working on for my thesis (at least I'm
> pretty sure I need it, but the thesis is still in progress).
> >>
>
> Can you say briefly why that is?

I'm thinking about resumptive pronouns in the context of
resource-sensitivity. These pronouns are contributing an extraneous
resource. Their distribution I argue is conditioned by
lexically-contributed "manage resources" that basically dispose of a
pronominal resource. These not only occur in "traditional" resumptive
pronoun cases, but also in finite control (e.g. Balkan-style) and copy
raising. When the manager resource disposes of the pronoun's resource, it
also disposes of its meaning: the manager resource vacuously abstracts
over the pronouns meaning, so the end result is that it disappears from
the semantics.

I'll be talking about this at the LSA.

Ash